「Mathjax2.x コード一覧 Gyre-Termesフォント」の版間の差分

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<style type="text/css">@font-face {font-family: GyreTermesMathJax_Normal;      src: url('https://wiki.yo-net.jp/font/Gyre-Termes/woff/GyreTermesMathJax_Normal-Regular.woff?V=2.7.9') format('woff'),      url('https://wiki.yo-net.jp/font/Gyre-Termes/otf/GyreTermesMathJax_Normal-Regular.otf?V=2.7.9') format('opentype')}</style>
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<script type="text/javascript"                                                        src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.9/jax/output/HTML-CSS/fonts/Gyre-Termes/Marks/Regular/Main.js?V=2.7.9"></script>
<script type="text/x-mathjax-config">
<script type="text/x-mathjax-config">
   MathJax.Ajax.config.path["Contrib"]="https://wiki.yo-net.jp/mathjax/";
   MathJax.Ajax.config.path["Contrib"]="https://wiki.yo-net.jp/mathjax/";
51行目: 75行目:
<code class="tex">\frac{1}{2}
<code class="tex">\frac{1}{2}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
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$$ \frac{1}{2} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{1}{2}" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1000.82em, 2.917em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
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60行目: 84行目:
<code class="tex">\displaystyle \frac{1}{2}
<code class="tex">\displaystyle \frac{1}{2}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \displaystyle \frac{1}{2} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\displaystyle_\frac{1}{2}" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1000.82em, 2.917em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
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69行目: 93行目:
<code class="tex">\dfrac{1}{2}
<code class="tex">\dfrac{1}{2}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dfrac{1}{2} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dfrac{1}{2}" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1000.82em, 2.917em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
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78行目: 102行目:
<code class="tex">\require{physics} \flatfrac{1}{2}
<code class="tex">\require{physics} \flatfrac{1}{2}
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</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \flatfrac{1}{2} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\flatfrac{1}{2}" style="width: 2.866em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.252em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.15em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Main;">(</span></span><span class="texatom"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">/</span></span></span><span class="texatom"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Main;">)</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
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87行目: 111行目:
<code class="tex">\left( -\frac{1}{2} \right)^2
<code class="tex">\left( -\frac{1}{2} \right)^2
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \left( -\frac{1}{2} \right)^2 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\left(_-\frac{1}{2}_\right)^2" style="width: 3.991em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.121em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.412em, 1003.12em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 3.121em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1002.56em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">(</span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -5.059em; left: 2.661em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 3.055em;"></span></span></span></div>
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96行目: 120行目:
<code class="tex">\require{physics} \qty{ -\frac{1}{2} }^2
<code class="tex">\require{physics} \qty{ -\frac{1}{2} }^2
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \qty{ -\frac{1}{2} }^2 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\qty{_-\frac{1}{2}_}^2" style="width: 3.786em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.968em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.412em, 1002.97em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.968em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1002.46em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">{</span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">}</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -5.059em; left: 2.559em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 3.055em;"></span></span></span></div>
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105行目: 129行目:
<code class="tex">\frac{a+b}{c+\frac{d}{e}}
<code class="tex">\frac{a+b}{c+\frac{d}{e}}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{a+b}{c+\frac{d}{e}} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{a+b}{c+\frac{d}{e}}" style="width: 3.377em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.661em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1002.66em, 3.479em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 2.457em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1002.15em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -1.071em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.917em, 1002.36em, 4.502em, -999.997em); top: -3.116em; left: 50%; margin-left: -1.173em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.36em, 4.144em, -999.997em); top: -4.395em; left: 50%; margin-left: -0.202em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1000.31em, 4.144em, -999.997em); top: -3.628em; left: 50%; margin-left: -0.151em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑒</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.51em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.514em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.46em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.457em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.62em; border-left: 0px solid; width: 0px; height: 3.38em;"></span></span></span></div>
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114行目: 138行目:
<code class="tex">\cfrac{a+b}{c+\cfrac{d}{e}}
<code class="tex">\cfrac{a+b}{c+\cfrac{d}{e}}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cfrac{a+b}{c+\cfrac{d}{e}} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cfrac{a+b}{c+\cfrac{d}{e}}" style="width: 3.582em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.156em, 1002.82em, 5.167em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(2.866em, 1002.15em, 4.502em, -999.997em); top: -4.804em; left: 50%; margin-left: -1.071em;"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.15em, 1002.51em, 5.371em, -999.997em); top: -2.298em; left: 50%; margin-left: -1.276em;"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(2.866em, 1000.51em, 4.502em, -999.997em); top: -4.753em; left: 50%; margin-left: -0.253em;"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.866em, 1000.41em, 4.502em, -999.997em); top: -3.116em; left: 50%; margin-left: -0.202em;"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.67em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.667em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.61em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.61em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.763em; border-left: 0px solid; width: 0px; height: 6.042em;"></span></span></span></div>
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126行目: 150行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}}\vbCrLf=_\frac{1}{2}_\left(_1+\sqrt{5}_\right)\vbCrLf\end{eqnarray}" style="width: 15.648em; display: inline-block;"><span style="display: inline-block; position: relative; width: 12.325em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.156em, 1012.22em, 3.531em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 12.018em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.15em, 1011.92em, 5.525em, -999.997em); top: -4.088em; left: 0em;"><span style="display: inline-block; position: relative; width: 12.018em; height: 0px;"><span style="position: absolute; clip: rect(2.61em, 1011.92em, 5.985em, -999.997em); top: -4.548em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 4.246em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.968em, 1004.14em, 5.064em, -999.997em); top: -3.116em; left: 50%; margin-left: -2.094em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 2.252em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.26em, 4.144em, -999.997em); top: -4.395em; left: 50%; margin-left: -0.151em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1002.1em, 4.451em, -999.997em); top: -3.423em; left: 50%; margin-left: -1.071em;"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.479em, 1000.21em, 4.144em, -999.997em); top: -4.343em; left: 50%; margin-left: -0.1em;"><span class="mn" style="font-size: 50%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.479em, 1000.87em, 4.144em, -999.997em); top: -3.679em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mn" style="font-size: 50%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 50%; font-family: GyreTermesMathJax_Main;">+</span><span class="mo" style="font-size: 50%; font-family: GyreTermesMathJax_Main;">⋱</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.02em, 1.23em, -999.997em); top: -1.225em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.025em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.25em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.252em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1004.25em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.246em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size2;">(</span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msqrt" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">5</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -4.548em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.049em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1000.62em, 4.451em, -999.997em); top: -4.037em; left: 0em;"><span style="font-family: GyreTermesMathJax_Size1;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size2;">)</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.093em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.093em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.685em; border-left: 0px solid; width: 0px; height: 4.094em;"></span></span></span></div>
1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}}
= \frac{1}{2} \left( 1+\sqrt{5} \right)
\end{eqnarray} $$
</div>
</div>


138行目: 159行目:
<code class="tex">0.123
<code class="tex">0.123
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ 0.123 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_0.123" style="width: 2.866em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.252em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.2em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0.123</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


147行目: 168行目:
<code class="tex">\frac{1}{11} = 0.\dot{0}\dot{9}
<code class="tex">\frac{1}{11} = 0.\dot{0}\dot{9}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{1}{11} = 0.\dot{0}\dot{9} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{1}{11}_=_0.\dot{0}\dot{9}" style="width: 5.627em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.4em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1004.35em, 5.985em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.87em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">11</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">0.</span><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.21em, 3.582em, -999.997em); top: -4.241em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">˙</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">9</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.21em, 3.582em, -999.997em); top: -4.241em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">˙</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


156行目: 177行目:
<code class="tex">\pi = 3.14 \ldots
<code class="tex">\pi = 3.14 \ldots
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \pi = 3.14 \ldots $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\pi_=_3.14_\ldots" style="width: 6.189em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.86em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1004.76em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜋</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">3.14</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">…</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
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165行目: 186行目:
<code class="tex">\sqrt{2} = 1.4142 \cdots
<code class="tex">\sqrt{2} = 1.4142 \cdots
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sqrt{2} = 1.4142 \cdots $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sqrt{2}_=_1.4142_\cdots" style="width: 7.928em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.24em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.144em, 1006.14em, 5.576em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msqrt"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -4.548em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.049em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1000.62em, 4.451em, -999.997em); top: -4.037em; left: 0em;"><span style="font-family: GyreTermesMathJax_Size1;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">1.4142</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">⋯</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
</div>
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174行目: 195行目:
<code class="tex">\infty
<code class="tex">\infty
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \infty $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\infty" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.82em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∞</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
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183行目: 204行目:
<code class="tex">|x|
<code class="tex">|x|
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ |x| $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_|x|" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
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192行目: 213行目:
<code class="tex">\vert x \vert
<code class="tex">\vert x \vert
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vert x \vert $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vert_x_\vert" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


201行目: 222行目:
<code class="tex">\left| \dfrac{x}{2} \right|
<code class="tex">\left| \dfrac{x}{2} \right|
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \left| \dfrac{x}{2} \right| $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\left|_\dfrac{x}{2}_\right|" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.786em, 1001.18em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">|</span></span><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.202em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">|</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.666em;"></span></span></span></div>
</div>
</div>


210行目: 231行目:
<code class="tex">\require{physics} \qty{\dfrac{x}{2}}
<code class="tex">\require{physics} \qty{\dfrac{x}{2}}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \qty{\dfrac{x}{2}} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\qty{\dfrac{x}{2}}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.888em, 1001.69em, 5.985em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size4;">{</span></span><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.202em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size4;">}</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.406em;"></span></span></span></div>
</div>
</div>


219行目: 240行目:
<code class="tex">\require{physics} \abs{ \dfrac{x}{2} }
<code class="tex">\require{physics} \abs{ \dfrac{x}{2} }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \abs{ \dfrac{x}{2} } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\abs{_\dfrac{x}{2}_}" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.786em, 1001.18em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">|</span></span><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.202em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">|</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.666em;"></span></span></span></div>
</div>
</div>


228行目: 249行目:
<code class="tex">[x]
<code class="tex">[x]
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ [x] $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_[x]" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


237行目: 258行目:
<code class="tex">\lbrack x \rbrack
<code class="tex">\lbrack x \rbrack
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lbrack x \rbrack $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lbrack_x_\rbrack" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


246行目: 267行目:
<code class="tex">\lfloor x \rfloor
<code class="tex">\lfloor x \rfloor
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lfloor x \rfloor $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lfloor_x_\rfloor" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌊</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌋</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


255行目: 276行目:
<code class="tex">\lceil x \rceil
<code class="tex">\lceil x \rceil
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lceil x \rceil $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lceil_x_\rceil" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌉</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


268行目: 289行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf[x]\vbCrLf=_\lfloor_x_\rfloor\vbCrLf=_\max\{_n\in\mathbb{Z}_\mid_n_\leqq_x_\}\vbCrLf\end{eqnarray}" style="width: 17.08em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.45em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1013.35em, 2.508em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 13.143em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.173em, 1013.09em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 13.143em; height: 0px;"><span style="position: absolute; clip: rect(3.121em, 1013.09em, 4.297em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⌊</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌋</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">max</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∈</span><span class="texatom" style="padding-left: 0.309em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℤ</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∣</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
[x]
= \lfloor x \rfloor
= \max\{ n\in\mathbb{Z} \mid n \leqq x \}
\end{eqnarray} $$
</div>
</div>


284行目: 301行目:
<code class="tex">1 + 2
<code class="tex">1 + 2
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ 1 + 2 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_1_+_2" style="width: 2.815em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.201em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.2em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">2</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


293行目: 310行目:
<code class="tex">3 - 1
<code class="tex">3 - 1
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ 3 - 1 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_3_-_1" style="width: 2.815em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.201em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.1em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">1</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


302行目: 319行目:
<code class="tex">2 \times 3
<code class="tex">2 \times 3
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ 2 \times 3 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_2_\times_3" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">×</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">3</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


311行目: 328行目:
<code class="tex">\require{physics} 6 \divisionsymbol 3
<code class="tex">\require{physics} 6 \divisionsymbol 3
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} 6 \divisionsymbol 3 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_6_\divisionsymbol_3" style="width: 3.377em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.661em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.61em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span><span class="texatom"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">&nbsp;</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">÷</span><span class="mtext" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">&nbsp;</span></span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


320行目: 337行目:
<code class="tex">\pm 1
<code class="tex">\pm 1
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \pm 1 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\pm_1" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.08em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">±</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


329行目: 346行目:
<code class="tex">\mp 1
<code class="tex">\mp 1
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mp 1 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mp_1" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.08em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">∓</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


338行目: 355行目:
<code class="tex">a \cdot b = ab
<code class="tex">a \cdot b = ab
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \cdot b = ab $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\cdot_b_=_ab" style="width: 5.167em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.042em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.99em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⋅</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


347行目: 364行目:
<code class="tex">a \divisionsymbol b = \frac{a}{b}
<code class="tex">a \divisionsymbol b = \frac{a}{b}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \divisionsymbol b = \frac{a}{b} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\divisionsymbol_b_=_\frac{a}{b}" style="width: 6.036em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.758em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.888em, 1004.76em, 6.036em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="texatom"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">&nbsp;</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">÷</span><span class="mtext" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">&nbsp;</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.406em;"></span></span></span></div>
</div>
</div>


360行目: 377行目:
\end{align}
\end{align}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{align}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{align}\vbCrLf67_\\\vbCrLf\frac{\times\phantom{0}63}{\phantom{0}201}_\\\vbCrLf\frac{402\phantom{0}}{4221}\vbCrLf\end{align}" style="width: 3.479em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.712em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-1.173em, 1002.71em, 4.911em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.479em, 1002.41em, 9.462em, -999.997em); top: -6.644em; left: 0em;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -6.338em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">67</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1002.41em, 4.86em, -999.997em); top: -4.446em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1002em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -1.02em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">×</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span></span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">63</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.89em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -1.02em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span></span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">201</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.15em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.15em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.508em, 1002.36em, 4.809em, -999.997em); top: -2.043em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -1.02em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">402</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.89em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -1.02em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">4221</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.1em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.099em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.649em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.438em; border-left: 0px solid; width: 0px; height: 7.471em;"></span></span></span></div>
67 \\
\frac{\times\phantom{0}63}{\phantom{0}201} \\
\frac{402\phantom{0}}{4221}
\end{align} $$
</div>
</div>


378行目: 391行目:
\end{align}
\end{align}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{enclose}\begin{align}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{enclose}\begin{align}\vbCrLf\vbCrLf_7.6_\\\vbCrLf_25\enclose{longdiv}{190\phantom{.0}}_\\\vbCrLf_\frac{175\phantom{.0}}{15\phantom{.}0}_\\\vbCrLf_\frac{15\phantom{.}0\phantom{.}}{\phantom{00.}0\phantom{.}}_\\\vbCrLf\vbCrLf\end{align}" style="width: 5.32em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.195em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-2.043em, 1004.2em, 5.729em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 3.888em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(4.297em, 1003.89em, 11.967em, -999.997em); top: -8.332em; left: 0em;"><span style="display: inline-block; position: relative; width: 3.888em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.23em, 4.144em, -999.997em); top: -7.156em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">7.6</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.764em, 1003.89em, 4.4em, -999.997em); top: -5.571em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">25</span><span class="menclose"><span style="display: inline-block; position: relative; width: 2.866em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 2.866em; height: 1.332em; vertical-align: -0.1em; position: absolute; top: -1.071em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -3.986em; left: 0.514em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">190</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">.0</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.525em; left: 0em;"><svg style="width: 2.866em; height: 1.332em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><path d="M 56.107012499999996,1 L 1,1 a4.40055,11.226291999999999 0 0,1 1,22.452583999999998"></path></g></svg><span style="display: inline-block; width: 0px; height: 2.559em;"></span><span style="display: inline-block; width: 0px; height: 3.786em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1002.61em, 4.86em, -999.997em); top: -3.628em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -1.122em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">175</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">.0</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.74em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.867em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">15</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">.</span></span></span></span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.36em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.355em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1002.36em, 4.86em, -999.997em); top: -1.225em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1001.74em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -1.02em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">15</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">.</span></span></span></span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">.</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.74em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -1.02em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">00.</span></span></span></span></span><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">.</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.1em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.099em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 8.337em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -4.477em; border-left: 0px solid; width: 0px; height: 9.614em;"></span></span></span></div>
  7.6 \\
  25\enclose{longdiv}{190\phantom{.0}} \\
  \frac{175\phantom{.0}}{15\phantom{.}0} \\
  \frac{15\phantom{.}0\phantom{.}}{\phantom{00.}0\phantom{.}} \\
\end{align} $$
</div>
</div>


392行目: 400行目:
<code class="tex">a \equiv b \mod n
<code class="tex">a \equiv b \mod n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \equiv b \mod n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\equiv_b_\mod_n" style="width: 8.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.496em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.45em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≡</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span><span class="TeXmathchoice"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 1.127em; display: inline-block; overflow: hidden;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">mod</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.207em; display: inline-block; overflow: hidden;"></span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.207em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑛</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


401行目: 409行目:
<code class="tex">a \equiv b \pmod n
<code class="tex">a \equiv b \pmod n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \equiv b \pmod n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\equiv_b_\pmod_n" style="width: 9.001em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.058em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.96em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≡</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span><span class="TeXmathchoice"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 1.127em; display: inline-block; overflow: hidden;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">mod</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.36em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


410行目: 418行目:
<code class="tex">\gcd(a, b) = \gcd(b, a \bmod b)
<code class="tex">\gcd(a, b) = \gcd(b, a \bmod b)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \gcd(a, b) = \gcd(b, a \bmod b) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\gcd(a,_b)_=_\gcd(b,_a_\bmod_b)" style="width: 14.677em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.558em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1011.46em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">gcd</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">gcd</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em; padding-right: 0.309em;">mod</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


419行目: 427行目:
<code class="tex">x \propto y
<code class="tex">x \propto y
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ x \propto y $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_x_\propto_y" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1002.3em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∝</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


431行目: 439行目:
<code class="tex">a \gt b
<code class="tex">a \gt b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \gt b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\gt_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&gt;</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


440行目: 448行目:
<code class="tex">a \geq b
<code class="tex">a \geq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \geq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\geq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≥</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


449行目: 457行目:
<code class="tex">a \geqq b
<code class="tex">a \geqq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \geqq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\geqq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


458行目: 466行目:
<code class="tex">a \lt b
<code class="tex">a \lt b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \lt b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\lt_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&lt;</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


467行目: 475行目:
<code class="tex">a \leq b
<code class="tex">a \leq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \leq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\leq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≤</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


476行目: 484行目:
<code class="tex">a \leqq b
<code class="tex">a \leqq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \leqq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\leqq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


485行目: 493行目:
<code class="tex">a = b
<code class="tex">a = b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a = b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_=_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


494行目: 502行目:
<code class="tex">a \neq b
<code class="tex">a \neq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \neq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\neq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≠</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


503行目: 511行目:
<code class="tex">a \fallingdotseq b
<code class="tex">a \fallingdotseq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \fallingdotseq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\fallingdotseq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≒</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


512行目: 520行目:
<code class="tex">a \sim b
<code class="tex">a \sim b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \sim b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\sim_b" style="width: 2.866em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.252em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.2em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∼</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


521行目: 529行目:
<code class="tex">a \simeq b
<code class="tex">a \simeq b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \simeq b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\simeq_b" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≃</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


530行目: 538行目:
<code class="tex">a \approx b
<code class="tex">a \approx b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \approx b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\approx_b" style="width: 2.866em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.252em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.2em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


539行目: 547行目:
<code class="tex">a \gg b
<code class="tex">a \gg b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \gg b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\gg_b" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≫</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


548行目: 556行目:
<code class="tex">a \ll b
<code class="tex">a \ll b
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a \ll b $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a_\ll_b" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≪</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


557行目: 565行目:
<code class="tex">\max f(x)
<code class="tex">\max f(x)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \max f(x) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\max_f(x)" style="width: 4.604em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.633em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.53em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">max</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


566行目: 574行目:
<code class="tex">\min f(x)
<code class="tex">\min f(x)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \min f(x) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\min_f(x)" style="width: 4.349em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.428em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.33em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">min</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


582行目: 590行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\max_(_a,_b_)\vbCrLf=\vbCrLf\vbCrLf_\begin{cases}\vbCrLf___a_&_(_a_\geqq_b_)_\\\vbCrLf___b_&_(_a_\lt_b_)\vbCrLf_\end{cases}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 14.114em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.098em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1011.1em, 3.121em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 10.791em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.457em, 1010.79em, 5.013em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.791em; height: 0px;"><span style="position: absolute; clip: rect(2.457em, 1010.79em, 5.013em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">max</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mrow" style="padding-left: 0.309em;"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">{</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 4.707em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.815em, 1000.46em, 4.809em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.548em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.61em, 1002.97em, 4.962em, -999.997em); top: -3.986em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 3.07em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.97em, 4.297em, -999.997em); top: -4.548em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1002.97em, 4.297em, -999.997em); top: -3.321em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&lt;</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑏</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.166em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
\max ( a, b )
=
  \begin{cases}
    a & ( a \geqq b ) \\
    b & ( a \lt b )
  \end{cases}
\end{eqnarray} $$
</div>
</div>


604行目: 605行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfaaa_\\\vbCrLfbbb\vbCrLf\end{eqnarray}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.514em, 1001.79em, 3.173em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.764em, 1001.49em, 4.86em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.144em, -999.997em); top: -4.599em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -3.27em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.231em; border-left: 0px solid; width: 0px; height: 3.12em;"></span></span></span></div>
aaa \\
bbb
\end{eqnarray} $$
</div>
</div>


619行目: 617行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfaaa_\\[5pt]\vbCrLfbbb\vbCrLf\end{eqnarray}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.258em, 1001.79em, 3.428em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.508em, 1001.49em, 5.167em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.144em, -999.997em); top: -4.906em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -2.963em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.555em; border-left: 0px solid; width: 0px; height: 3.834em;"></span></span></span></div>
aaa \\[5pt]
bbb
\end{eqnarray} $$
</div>
</div>


634行目: 629行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfx_+_2x_&=&_3_\\\vbCrLfx_&=&_1\vbCrLf\end{eqnarray}" style="width: 5.934em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.655em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.514em, 1004.6em, 3.173em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 4.349em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1002.56em, 4.86em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.56em, 4.144em, -999.997em); top: -4.599em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">2</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.27em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.866em, 1000.87em, 4.86em, -999.997em); top: -3.986em; left: 2.559em;"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.479em, 1000.87em, 4.144em, -999.997em); top: -4.599em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="mi"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.479em, 1000.87em, 4.144em, -999.997em); top: -3.27em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="mi"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.559em, 1000.41em, 4.86em, -999.997em); top: -3.986em; left: 3.837em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.599em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.27em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.231em; border-left: 0px solid; width: 0px; height: 3.12em;"></span></span></span></div>
x + 2x &=& 3 \\
x &=& 1
\end{eqnarray} $$
</div>
</div>


653行目: 645行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\vbCrLf_\left\{\vbCrLf___\begin{array}{l}\vbCrLf_____x_+_y_=_10_\\\vbCrLf_____2x_+_4y_=_32\vbCrLf___\end{array}\vbCrLf_\right.\vbCrLf\vbCrLf\end{eqnarray}" style="width: 8.337em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.547em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.463em, 1006.55em, 3.224em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 6.24em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.355em, 1006.24em, 5.116em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 6.24em; height: 0px;"><span style="position: absolute; clip: rect(2.355em, 1006.24em, 5.116em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">{</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 5.371em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.457em, 1005.32em, 5.116em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 5.371em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1004.35em, 4.349em, -999.997em); top: -4.65em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑦</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">10</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1005.32em, 4.349em, -999.997em); top: -3.219em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">4</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">32</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
  \left\{
    \begin{array}{l}
      x + y = 10 \\
      2x + 4y = 32
    \end{array}
  \right.
\end{eqnarray} $$
</div>
</div>


676行目: 661行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf|x|\vbCrLf\vbCrLf=\vbCrLf_\begin{cases}\vbCrLf___x_&_(_x_\geqq_0_)_\\\vbCrLf___-x_&_(_x_\lt_0_)\vbCrLf_\end{cases}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 10.842em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.541em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1008.54em, 3.121em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.234em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.457em, 1008.23em, 5.013em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.234em; height: 0px;"><span style="position: absolute; clip: rect(2.457em, 1008.23em, 5.013em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mrow" style="padding-left: 0.309em;"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">{</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 5.269em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.815em, 1001.13em, 4.809em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.548em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1001.13em, 4.144em, -999.997em); top: -3.321em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.61em, 1002.92em, 4.962em, -999.997em); top: -3.986em; left: 2.252em;"><span style="display: inline-block; position: relative; width: 3.019em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.92em, 4.297em, -999.997em); top: -4.548em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≧</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1002.92em, 4.297em, -999.997em); top: -3.321em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&lt;</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.166em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
|x|
=
  \begin{cases}
    x & ( x \geqq 0 ) \\
    -x & ( x \lt 0 )
  \end{cases}
\end{eqnarray} $$
</div>
</div>


695行目: 673行目:
<code class="tex">x \in A
<code class="tex">x \in A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ x \in A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_x_\in_A" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.3em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


704行目: 682行目:
<code class="tex">A \ni x
<code class="tex">A \ni x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \ni x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\ni_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∋</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


713行目: 691行目:
<code class="tex">x \notin A
<code class="tex">x \notin A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ x \notin A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_x_\notin_A" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.3em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∉</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


722行目: 700行目:
<code class="tex">A \subset B
<code class="tex">A \subset B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \subset B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\subset_B" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊂</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


731行目: 709行目:
<code class="tex">A \subseteq B
<code class="tex">A \subseteq B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \subseteq B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\subseteq_B" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊆</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


740行目: 718行目:
<code class="tex">A \subseteqq B
<code class="tex">A \subseteqq B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \subseteqq B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\subseteqq_B" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.195em, 1002.41em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="padding-left: 0.309em;"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">⫅</span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


749行目: 727行目:
<code class="tex">A \supset B
<code class="tex">A \supset B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \supset B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\supset_B" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊃</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


758行目: 736行目:
<code class="tex">A \supseteq B
<code class="tex">A \supseteq B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \supseteq B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\supseteq_B" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊇</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


767行目: 745行目:
<code class="tex">A \supseteqq B
<code class="tex">A \supseteqq B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \supseteqq B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\supseteqq_B" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.195em, 1002.41em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="padding-left: 0.309em;"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">⫆</span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


776行目: 754行目:
<code class="tex">A \not \subset B
<code class="tex">A \not \subset B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \not \subset B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\not_\subset_B" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Operators; padding-left: 0.309em;">⊄</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


785行目: 763行目:
<code class="tex">A \subsetneqq B
<code class="tex">A \subsetneqq B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \subsetneqq B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\subsetneqq_B" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.195em, 1002.41em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="padding-left: 0.309em;"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">⫋</span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


794行目: 772行目:
<code class="tex">A \cap B
<code class="tex">A \cap B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \cap B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\cap_B" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.41em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∩</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


803行目: 781行目:
<code class="tex">A \cup B
<code class="tex">A \cup B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \cup B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\cup_B" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.41em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∪</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


812行目: 790行目:
<code class="tex">\varnothing
<code class="tex">\varnothing
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varnothing $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varnothing" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.246em, 1000.57em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∅</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


821行目: 799行目:
<code class="tex">\emptyset
<code class="tex">\emptyset
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \emptyset $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\emptyset" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.246em, 1000.57em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∅</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


830行目: 808行目:
<code class="tex">A^c
<code class="tex">A^c
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A^c $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A^c" style="width: 1.332em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1001.02em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.616em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


839行目: 817行目:
<code class="tex">\overline{ A }
<code class="tex">\overline{ A }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overline{ A } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overline{_A_}" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.025em, 1000.62em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 4.246em, -999.997em); top: -4.855em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.207em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


848行目: 826行目:
<code class="tex">\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }
<code class="tex">\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overline{ (A\cap B) } = \overline{ A } \cup \overline{ B } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overline{_(A\cap_B)_}_=_\overline{_A_}_\cup_\overline{_B_}" style="width: 8.797em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.905em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.093em, 1006.9em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 3.224em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1003.07em, 4.297em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∩</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1003.22em, 4.246em, -999.997em); top: -4.855em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 3.224em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 3.121em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.207em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.565em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.667em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.718em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.77em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.872em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.923em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.974em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.076em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.127em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.179em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.281em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.332em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.383em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.485em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.536em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.588em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.69em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.741em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.792em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.894em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.945em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.997em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.099em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.15em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.201em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.303em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.355em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.406em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.508em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.559em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.61em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.712em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.764em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.815em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.917em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 2.968em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 3.019em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 4.246em, -999.997em); top: -4.855em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.207em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∪</span><span class="munderover" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 4.246em, -999.997em); top: -4.855em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.207em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.562em;"></span></span></span></div>
</div>
</div>


860行目: 838行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\left(_\bigcup\_{\lambda\in\Lambda}A\_{\lambda}_\right)^c\vbCrLf=\bigcap\_{\lambda\in\Lambda}A\_{\lambda}^c\vbCrLf\end{eqnarray}" style="width: 11.762em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.257em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.309em, 1009.26em, 3.428em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.95em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.201em, 1008.95em, 5.32em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.95em; height: 0px;"><span style="position: absolute; clip: rect(2.15em, 1008.95em, 5.269em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 4.758em; height: 0px;"><span style="position: absolute; clip: rect(2.201em, 1004.2em, 5.269em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mo" style="vertical-align: -0.049em;"><span><span style="font-size: 115.7%; font-family: GyreTermesMathJax_Size6;">(</span></span></span><span class="munderover"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1000.97em, 4.502em, -999.997em); top: -3.986em; left: 0.258em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0.003em;">⋃</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.246em, -999.997em); top: -2.963em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝜆</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∈</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">Λ</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.616em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝜆</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="vertical-align: -0.049em;"><span><span style="font-size: 115.7%; font-family: GyreTermesMathJax_Size6;">)</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -5.366em; left: 4.349em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1000.97em, 4.502em, -999.997em); top: -3.986em; left: 0.258em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0.003em;">⋂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.246em, -999.997em); top: -2.963em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝜆</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∈</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">Λ</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1000.41em, 4.144em, -999.997em); top: -4.343em; left: 0.616em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.57em, 4.144em, -999.997em); top: -3.679em; left: 0.616em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝜆</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.555em; border-left: 0px solid; width: 0px; height: 3.705em;"></span></span></span></div>
\left( \bigcup_{\lambda\in\Lambda}A_{\lambda} \right)^c
=\bigcap_{\lambda\in\Lambda}A_{\lambda}^c
\end{eqnarray} $$
</div>
</div>


872行目: 847行目:
<code class="tex">A \setminus B
<code class="tex">A \setminus B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \setminus B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\setminus_B" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.41em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


883行目: 858行目:
= \{ x \in A \mid x \notin B \}
= \{ x \in A \mid x \notin B \}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \setminus B
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\setminus_B\vbCrLf=_A_\cap_B^c\vbCrLf=_\{_x_\in_A_\mid_x_\notin_B_\}" style="width: 17.898em; display: inline-block;"><span style="display: inline-block; position: relative; width: 14.063em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1013.96em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∩</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.616em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∣</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∉</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
= A \cap B^c
= \{ x \in A \mid x \notin B \} $$
</div>
</div>


894行目: 867行目:
<code class="tex">A \triangle B
<code class="tex">A \triangle B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \triangle B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\triangle_B" style="width: 2.661em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.1em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


904行目: 877行目:
= (A \setminus B) \cup (B \setminus A)
= (A \setminus B) \cup (B \setminus A)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A \triangle B
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A_\triangle_B\vbCrLf=_(A_\setminus_B)_\cup_(B_\setminus_A)" style="width: 13.91em; display: inline-block;"><span style="display: inline-block; position: relative; width: 10.944em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1010.84em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∪</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
= (A \setminus B) \cup (B \setminus A) $$
</div>
</div>


914行目: 886行目:
<code class="tex">\mathbb{ N }
<code class="tex">\mathbb{ N }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ N } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_N_}" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.82em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℕ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


923行目: 895行目:
<code class="tex">\mathbb{ Z }
<code class="tex">\mathbb{ Z }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ Z } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_Z_}" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℤ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


932行目: 904行目:
<code class="tex">\mathbb{ Q }
<code class="tex">\mathbb{ Q }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ Q } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_Q_}" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℚ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


941行目: 913行目:
<code class="tex">\mathbb{ R }
<code class="tex">\mathbb{ R }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ R } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_R_}" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℝ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


950行目: 922行目:
<code class="tex">\mathbb{ C }
<code class="tex">\mathbb{ C }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ C } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_C_}" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℂ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


959行目: 931行目:
<code class="tex">\mathbb{ H }
<code class="tex">\mathbb{ H }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ H } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_H_}" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.82em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℍ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


968行目: 940行目:
<code class="tex">\sup A
<code class="tex">\sup A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sup A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sup_A" style="width: 2.815em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.201em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.15em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">sup</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


977行目: 949行目:
<code class="tex">\inf A
<code class="tex">\inf A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \inf A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\inf_A" style="width: 2.508em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.945em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.89em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">inf</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


986行目: 958行目:
<code class="tex">\aleph
<code class="tex">\aleph
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \aleph $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\aleph" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℵ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


998行目: 970行目:
<code class="tex">P \implies Q
<code class="tex">P \implies Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \implies Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\implies_Q" style="width: 4.758em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.735em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.74em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⟹</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,007行目: 979行目:
<code class="tex">P \Rightarrow Q
<code class="tex">P \Rightarrow Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \Rightarrow Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\Rightarrow_Q" style="width: 3.582em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.82em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⇒</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,016行目: 988行目:
<code class="tex">P \to Q
<code class="tex">P \to Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \to Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\to_Q" style="width: 3.582em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.82em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">→</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,025行目: 997行目:
<code class="tex">P \Leftarrow  Q
<code class="tex">P \Leftarrow  Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \Leftarrow  Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\Leftarrow__Q" style="width: 3.582em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.82em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⇐</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,034行目: 1,006行目:
<code class="tex">P \gets  Q
<code class="tex">P \gets  Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \gets  Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\gets__Q" style="width: 3.582em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.82em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">←</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,043行目: 1,015行目:
<code class="tex">P \iff Q
<code class="tex">P \iff Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \iff Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\iff_Q" style="width: 5.013em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.94em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.94em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⟺</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,052行目: 1,024行目:
<code class="tex">P \Leftrightarrow Q
<code class="tex">P \Leftrightarrow Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \Leftrightarrow Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\Leftrightarrow_Q" style="width: 3.786em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.968em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.97em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⇔</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,061行目: 1,033行目:
<code class="tex">P \leftrightarrow Q
<code class="tex">P \leftrightarrow Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \leftrightarrow Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\leftrightarrow_Q" style="width: 3.786em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.968em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.97em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">↔</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,070行目: 1,042行目:
<code class="tex">P \equiv Q
<code class="tex">P \equiv Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \equiv Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\equiv_Q" style="width: 3.326em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.61em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≡</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,079行目: 1,051行目:
<code class="tex">\therefore
<code class="tex">\therefore
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \therefore $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\therefore" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.41em, 5.218em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">∴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.068em; border-left: 0px solid; width: 0px; height: 0.523em;"></span></span></span></div>
</div>
</div>


1,088行目: 1,060行目:
<code class="tex">\because
<code class="tex">\because
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \because $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\because" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.41em, 5.218em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">∵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.068em; border-left: 0px solid; width: 0px; height: 0.523em;"></span></span></span></div>
</div>
</div>


1,097行目: 1,069行目:
<code class="tex">\forall x
<code class="tex">\forall x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \forall x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\forall_x" style="width: 1.332em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.02em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∀</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,106行目: 1,078行目:
<code class="tex">\exists x
<code class="tex">\exists x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \exists x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\exists_x" style="width: 1.23em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.97em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∃</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,115行目: 1,087行目:
<code class="tex">\nexists
<code class="tex">\nexists
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \nexists $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\nexists" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.41em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,128行目: 1,100行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf&_&_{}^\forall_\varepsilon_\gt_0,_{}^\exists_\delta_\gt_0_\mbox{_s.t._}_\\\vbCrLf&_&_{}^\forall_x_\in_\mathbb{_R_},_0_\lt_|x_-_a|_\lt_\delta\vbCrLf\implies_|f(x)_-_b|_\lt_\varepsilon_\vbCrLf\end{eqnarray}" style="width: 23.42em; display: inline-block;"><span style="display: inline-block; position: relative; width: 18.409em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.463em, 1018.31em, 3.275em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 18.103em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.224em, 1000em, 4.962em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -4.599em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.168em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000em, 4.962em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -4.599em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.168em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1017.75em, 5.167em, -999.997em); top: -3.986em; left: 0.309em;"><span style="display: inline-block; position: relative; width: 17.796em; height: 0px;"><span style="position: absolute; clip: rect(2.968em, 1007.57em, 4.297em, -999.997em); top: -4.599em; left: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∀</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜀</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&gt;</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∃</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛿</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&gt;</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">0</span><span class="mstyle"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">&nbsp;s.t.&nbsp;</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.968em, 1017.75em, 4.349em, -999.997em); top: -3.168em; left: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∀</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∈</span><span class="texatom" style="padding-left: 0.309em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℝ</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&lt;</span><span class="texatom" style="padding-left: 0.309em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑎</span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&lt;</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝛿</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⟹</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="texatom" style="padding-left: 0.309em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">&lt;</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝜀</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.36em; border-left: 0px solid; width: 0px; height: 3.315em;"></span></span></span></div>
& & {}^\forall \varepsilon \gt 0, {}^\exists \delta \gt 0 \mbox{ s.t. } \\
& & {}^\forall x \in \mathbb{ R }, 0 \lt |x - a| \lt \delta
\implies |f(x) - b| \lt \varepsilon
\end{eqnarray} $$
</div>
</div>


1,141行目: 1,109行目:
<code class="tex">P \land Q
<code class="tex">P \land Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \land Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\land_Q" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,150行目: 1,118行目:
<code class="tex">P \lor Q
<code class="tex">P \lor Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \lor Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\lor_Q" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∨</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,159行目: 1,127行目:
<code class="tex">\lnot P
<code class="tex">\lnot P
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lnot P $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lnot_P" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.28em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">¬</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,168行目: 1,136行目:
<code class="tex">\overline{ P }
<code class="tex">\overline{ P }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overline{ P } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overline{_P_}" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.025em, 1000.62em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 4.246em, -999.997em); top: -4.855em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.207em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


1,177行目: 1,145行目:
<code class="tex">!P
<code class="tex">!P
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ !P $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_!P" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.92em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,186行目: 1,154行目:
<code class="tex">P \oplus Q
<code class="tex">P \oplus Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \oplus Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\oplus_Q" style="width: 3.377em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.661em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.66em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⊕</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,195行目: 1,163行目:
<code class="tex">P \veebar Q
<code class="tex">P \veebar Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \veebar Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\veebar_Q" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⊻</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,204行目: 1,172行目:
<code class="tex">P \oplus Q = (P \land \lnot Q) \lor (\lnot P \land Q)
<code class="tex">P \oplus Q = (P \land \lnot Q) \lor (\lnot P \land Q)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \oplus Q = (P \land \lnot Q) \lor (\lnot P \land Q) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\oplus_Q_=_(P_\land_\lnot_Q)_\lor_(\lnot_P_\land_Q)" style="width: 16.62em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.092em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1012.99em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⊕</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑄</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∧</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">¬</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑄</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∨</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">¬</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">∧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑄</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,213行目: 1,181行目:
<code class="tex">\top
<code class="tex">\top
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \top $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\top" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">⊤</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,222行目: 1,190行目:
<code class="tex">\bot
<code class="tex">\bot
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bot $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bot" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">⊥</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,231行目: 1,199行目:
<code class="tex">P \vdash Q
<code class="tex">P \vdash Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \vdash Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\vdash_Q" style="width: 3.326em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.61em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊢</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,240行目: 1,208行目:
<code class="tex">P \models Q
<code class="tex">P \models Q
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P \models Q $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P_\models_Q" style="width: 3.326em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.61em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊨</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,252行目: 1,220行目:
<code class="tex">{}_n \mathrm{ P }_k
<code class="tex">{}_n \mathrm{ P }_k
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ {}_n \mathrm{ P }_k $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{}\_n_\mathrm{_P_}\_k" style="width: 1.792em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1001.38em, 2.406em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">P</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.565em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,261行目: 1,229行目:
<code class="tex">{}_n \mathrm{ C }_k
<code class="tex">{}_n \mathrm{ C }_k
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ {}_n \mathrm{ C }_k $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{}\_n_\mathrm{_C_}\_k" style="width: 1.894em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1001.49em, 2.406em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.667em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,270行目: 1,238行目:
<code class="tex">n!
<code class="tex">n!
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ n! $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_n!" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,279行目: 1,247行目:
<code class="tex">\binom{ n }{ k }
<code class="tex">\binom{ n }{ k }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \binom{ n }{ k } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\binom{_n_}{_k_}" style="width: 2.201em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.741em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.582em, 1001.59em, 6.292em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mrow"><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">(</span></span></span></span></span></span></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">)</span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.185em;"></span></span></span></div>
</div>
</div>


1,288行目: 1,256行目:
<code class="tex">{ n \choose k }
<code class="tex">{ n \choose k }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ { n \choose k } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{_n_\choose_k_}" style="width: 2.201em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.741em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.582em, 1001.59em, 6.292em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mrow"><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">(</span></span></span></span></span></span></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">)</span></span></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.185em;"></span></span></span></div>
</div>
</div>


1,297行目: 1,265行目:
<code class="tex">\dbinom{ n }{ k }
<code class="tex">\dbinom{ n }{ k }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dbinom{ n }{ k } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dbinom{_n_}{_k_}" style="width: 2.201em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.741em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.582em, 1001.59em, 6.292em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="mrow"><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">(</span></span></span></span></span></span></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">)</span></span></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.185em;"></span></span></span></div>
</div>
</div>


1,306行目: 1,274行目:
<code class="tex">{}_n \mathrm{ H }_k
<code class="tex">{}_n \mathrm{ H }_k
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ {}_n \mathrm{ H }_k $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{}\_n_\mathrm{_H_}\_k" style="width: 1.945em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1001.54em, 2.406em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.72em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">H</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.718em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,319行目: 1,287行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf{}\_n_\mathrm{_C_}\_k\vbCrLf\vbCrLf=_\binom{_n_}{_k_}\vbCrLf=_\frac{_n!_}{_k!_(_n_-_k_)!_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 13.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 10.535em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.514em, 1010.53em, 3.224em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 10.229em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.406em, 1010.23em, 5.116em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.229em; height: 0px;"><span style="position: absolute; clip: rect(2.406em, 1010.23em, 5.116em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.667em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mrow" style="padding-left: 0.309em;"><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">(</span></span></span></span></span></span></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="TeXmathchoice"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">)</span></span></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 4.195em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.72em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.406em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1003.99em, 4.297em, -999.997em); top: -3.321em; left: 50%; margin-left: -2.043em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1004.2em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.195em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.185em;"></span></span></span></div>
{}_n \mathrm{ C }_k
</div>
= \binom{ n }{ k }
= \frac{ n! }{ k! ( n - k )! }
\end{eqnarray} $$
</div>




1,336行目: 1,300行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf{}\_n_\mathrm{_P_}\_k\vbCrLf\vbCrLf=_n_\cdot_(_n_-_1_)_\cdots_(_n_-_k_+_1_)\vbCrLf=_\frac{_n!_}{_(_n_-_k_)!_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 22.96em; display: inline-block;"><span style="display: inline-block; position: relative; width: 18.051em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1018.05em, 3.121em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 17.745em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.508em, 1017.75em, 5.013em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.745em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1017.75em, 5.013em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">P</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.565em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⋅</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">⋯</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 3.377em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.72em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.406em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1003.17em, 4.297em, -999.997em); top: -3.321em; left: 50%; margin-left: -1.634em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1003.38em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.377em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.166em; border-left: 0px solid; width: 0px; height: 2.925em;"></span></span></span></div>
{}_n \mathrm{ P }_k
= n \cdot ( n - 1 ) \cdots ( n - k + 1 )
= \frac{ n! }{ ( n - k )! }
\end{eqnarray} $$
</div>
</div>


1,352行目: 1,312行目:
<code class="tex">\sum_{i=1}^{n} a_i
<code class="tex">\sum_{i=1}^{n} a_i
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sum_{i=1}^{n} a_i $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sum\_{i=1}^{n}_a\_i" style="width: 2.764em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.36em, 1002.15em, 3.479em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∑</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.92em, 4.246em, -999.997em); top: -2.861em; left: 0.105em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.162em; left: 0.412em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.62em; border-left: 0px solid; width: 0px; height: 3.705em;"></span></span></span></div>
</div>
</div>


1,361行目: 1,321行目:
<code class="tex">\displaystyle \sum_{i=1}^n a_i
<code class="tex">\displaystyle \sum_{i=1}^n a_i
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \displaystyle \sum_{i=1}^n a_i $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\displaystyle_\sum\_{i=1}^n_a\_i" style="width: 2.764em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.36em, 1002.15em, 3.479em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∑</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.92em, 4.246em, -999.997em); top: -2.861em; left: 0.105em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.162em; left: 0.412em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.62em; border-left: 0px solid; width: 0px; height: 3.705em;"></span></span></span></div>
</div>
</div>


1,374行目: 1,334行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\sum\_{_k_=_1_}^{_n_}_k^2\vbCrLf\vbCrLf=_\overbrace{_1^2_+_2^2_+_\cdots_+_n^2_}^{_n_}\vbCrLf=_\frac{_1_}{_6_}_n_(_n_+_1_)_(_2n_+_1_)\vbCrLf\vbCrLf\end{eqnarray}" style="width: 25.721em; display: inline-block;"><span style="display: inline-block; position: relative; width: 20.25em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.105em, 1020.15em, 3.582em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 19.943em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.15em, 1019.79em, 5.627em, -999.997em); top: -4.139em; left: 0em;"><span style="display: inline-block; position: relative; width: 19.943em; height: 0px;"><span style="position: absolute; clip: rect(2.048em, 1019.79em, 5.525em, -999.997em); top: -4.037em; right: 0em;"><span class="mtd"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∑</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.08em, 4.246em, -999.997em); top: -2.861em; left: 0.003em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.162em; left: 0.412em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 7.212em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1007.21em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 7.212em; height: 0px;"><span style="position: absolute; clip: rect(2.968em, 1007.16em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⋯</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1007.21em, 3.633em, -999.997em); top: -4.497em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 7.212em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 6.343em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 2.712em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.667em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.332em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.048em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 4.297em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 4.962em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 5.627em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.519em; left: 3.428em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 4.144em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.144em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.75em; border-left: 0px solid; width: 0px; height: 4.094em;"></span></span></span></div>
\sum_{ k = 1 }^{ n } k^2
= \overbrace{ 1^2 + 2^2 + \cdots + n^2 }^{ n }
= \frac{ 1 }{ 6 } n ( n + 1 ) ( 2n + 1 )
\end{eqnarray} $$
</div>
</div>


1,387行目: 1,343行目:
<code class="tex">\prod_{ i = 0 }^n x_i
<code class="tex">\prod_{ i = 0 }^n x_i
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \prod_{ i = 0 }^n x_i $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\prod\_{_i_=_0_}^n_x\_i" style="width: 2.764em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.36em, 1002.15em, 3.479em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.02em, 4.246em, -999.997em); top: -2.861em; left: 0.105em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.162em; left: 0.412em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.62em; border-left: 0px solid; width: 0px; height: 3.705em;"></span></span></span></div>
</div>
</div>


1,396行目: 1,352行目:
<code class="tex">\displaystyle \prod_{i=0}^n x_i
<code class="tex">\displaystyle \prod_{i=0}^n x_i
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \displaystyle \prod_{i=0}^n x_i $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\displaystyle_\prod\_{i=0}^n_x\_i" style="width: 2.764em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.36em, 1002.15em, 3.479em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.02em, 4.246em, -999.997em); top: -2.861em; left: 0.105em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.162em; left: 0.412em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.62em; border-left: 0px solid; width: 0px; height: 3.705em;"></span></span></span></div>
</div>
</div>


1,407行目: 1,363行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfn!_=_\prod\_{_k_=_1_}^n_k\vbCrLf\end{eqnarray}" style="width: 5.473em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.297em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.309em, 1004.3em, 3.377em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 3.991em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.201em, 1003.99em, 5.269em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 3.991em; height: 0px;"><span style="position: absolute; clip: rect(2.252em, 1003.99em, 5.371em, -999.997em); top: -4.037em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">!</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.08em, 4.246em, -999.997em); top: -2.861em; left: 0.054em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.162em; left: 0.412em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.49em; border-left: 0px solid; width: 0px; height: 3.705em;"></span></span></span></div>
n! = \prod_{ k = 1 }^n k
\end{eqnarray} $$
</div>
</div>


1,422行目: 1,376行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\zeta_(s)\vbCrLf\vbCrLf=_\prod\_{_p:\mathrm{_prime_}_}\vbCrLf__\frac{_1_}{_1-p^{-s}_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 11.558em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.104em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.36em, 1009.1em, 3.377em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.797em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.252em, 1008.8em, 5.269em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.797em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1008.8em, 5.525em, -999.997em); top: -4.241em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜁</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑠</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 2.201em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.604em, -999.997em); top: -3.986em; left: 0.514em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.2em, 4.4em, -999.997em); top: -2.861em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑝</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">:</span><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">p</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">i</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">m</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">e</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mfrac" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 3.121em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1003.02em, 4.349em, -999.997em); top: -3.321em; left: 50%; margin-left: -1.48em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑝</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1003.12em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.121em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.49em; border-left: 0px solid; width: 0px; height: 3.575em;"></span></span></span></div>
\zeta (s)
= \prod_{ p:\mathrm{ prime } }
  \frac{ 1 }{ 1-p^{-s} }
\end{eqnarray} $$
</div>
</div>


1,438行目: 1,388行目:
<code class="tex">2^3
<code class="tex">2^3
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ 2^3 $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_2^3" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.076em, 1000.92em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,447行目: 1,397行目:
<code class="tex">e^{ i \pi }
<code class="tex">e^{ i \pi }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ e^{ i \pi } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_e^{_i_\pi_}" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.076em, 1001.28em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.463em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝜋</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,456行目: 1,406行目:
<code class="tex">\exp ( x )
<code class="tex">\exp ( x )
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \exp ( x ) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\exp_(_x_)" style="width: 3.479em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.712em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.61em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">exp</span><span class="mo"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,465行目: 1,415行目:
<code class="tex">\sqrt{ 2 }
<code class="tex">\sqrt{ 2 }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sqrt{ 2 } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sqrt{_2_}" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.076em, 1001.13em, 2.508em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msqrt"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -4.548em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.049em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1000.62em, 4.451em, -999.997em); top: -4.037em; left: 0em;"><span style="font-family: GyreTermesMathJax_Size1;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
</div>
</div>


1,474行目: 1,424行目:
<code class="tex">\sqrt{ \mathstrut a } + \sqrt{ \mathstrut b }
<code class="tex">\sqrt{ \mathstrut a } + \sqrt{ \mathstrut b }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sqrt{ \mathstrut a } + \sqrt{ \mathstrut b } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sqrt{_\mathstrut_a_}_+_\sqrt{_\mathstrut_b_}" style="width: 4.349em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.428em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.246em, 1003.43em, 5.627em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msqrt"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.297em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.31em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -4.446em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.049em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1000.62em, 4.451em, -999.997em); top: -3.934em; left: 0em;"><span style="font-family: GyreTermesMathJax_Size1;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msqrt" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.297em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mphantom"><span class="mrow" style="visibility: hidden;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.31em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -4.497em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.049em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1000.62em, 4.451em, -999.997em); top: -3.986em; left: 0em;"><span style="font-family: GyreTermesMathJax_Size1;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.562em;"></span></span></span></div>
</div>
</div>


1,483行目: 1,433行目:
<code class="tex">\sqrt[ n ]{ x }
<code class="tex">\sqrt[ n ]{ x }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sqrt[ n ]{ x } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sqrt[_n_]{_x_}" style="width: 1.383em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.383em, 1001.08em, 2.406em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mroot"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.46em, 3.94em, -999.997em); top: -4.241em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.62em, 4.246em, -999.997em); top: -3.934em; left: 0em;"><span style="font-family: GyreTermesMathJax_Main;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.633em, 1000.26em, 4.144em, -999.997em); top: -4.343em; left: 0.156em;"><span class="mi" style="font-size: 50%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,492行目: 1,442行目:
<code class="tex">\log x
<code class="tex">\log x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \log x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\log_x" style="width: 2.508em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.945em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.95em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">log</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


1,501行目: 1,451行目:
<code class="tex">\log_{ 2 } x
<code class="tex">\log_{ 2 } x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \log_{ 2 } x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\log\_{_2_}_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.576em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.69em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.23em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">log</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.73em; left: 1.281em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


1,510行目: 1,460行目:
<code class="tex">\ln x
<code class="tex">\ln x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ln x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ln_x" style="width: 1.843em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.43em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ln</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,522行目: 1,472行目:
<code class="tex">90^{ \circ }
<code class="tex">90^{ \circ }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ 90^{ \circ } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_90^{_\circ_}" style="width: 1.792em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1001.38em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">90</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 1.025em;"><span class="texatom"><span class="mrow"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∘</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,531行目: 1,481行目:
<code class="tex">\frac{ \pi }{ 2 }
<code class="tex">\frac{ \pi }{ 2 }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ \pi }{ 2 } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_\pi_}{_2_}" style="width: 1.383em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.821em, 1001.08em, 2.917em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.67em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.355em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜋</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.87em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.872em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.406em;"></span></span></span></div>
</div>
</div>


1,540行目: 1,490行目:
<code class="tex">\angle A
<code class="tex">\angle A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \angle A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\angle_A" style="width: 1.69em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.28em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∠</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,549行目: 1,499行目:
<code class="tex">AB /\!/ CD
<code class="tex">AB /\!/ CD
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ AB /\!/ CD $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_AB_/\!/_CD" style="width: 4.246em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.326em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.33em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">/</span></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.202em;"></span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">/</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,558行目: 1,508行目:
<code class="tex">AB \parallel CD
<code class="tex">AB \parallel CD
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ AB \parallel CD $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_AB_\parallel_CD" style="width: 4.553em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.582em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.58em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∥</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,567行目: 1,517行目:
<code class="tex">AB \perp CD
<code class="tex">AB \perp CD
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ AB \perp CD $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_AB_\perp_CD" style="width: 4.962em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.888em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.89em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">⊥</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,576行目: 1,526行目:
<code class="tex">\triangle ABC
<code class="tex">\triangle ABC
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangle ABC $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangle_ABC" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.76em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,585行目: 1,535行目:
<code class="tex">\Box ABCD
<code class="tex">\Box ABCD
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Box ABCD $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Box_ABCD" style="width: 4.195em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.275em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.27em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">□</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,594行目: 1,544行目:
<code class="tex">\stackrel{\huge\frown}{AB}
<code class="tex">\stackrel{\huge\frown}{AB}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \stackrel{\huge\frown}{AB} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\stackrel{\huge\frown}{AB}" style="width: 2.048em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1001.43em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.18em, 4.144em, -999.997em); top: -3.986em; left: 0.207em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 3.888em, -999.997em); top: -4.65em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="mo" style="font-size: 164.7%; font-family: GyreTermesMathJax_Main;">⌢</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.821em;"></span></span></span></div>
</div>
</div>


1,603行目: 1,553行目:
<code class="tex">\overparen{AB}
<code class="tex">\overparen{AB}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overparen{AB} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overparen{AB}" style="width: 1.945em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.974em, 1001.54em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.18em, 4.144em, -999.997em); top: -3.986em; left: 0.156em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.121em, 1001.54em, 3.582em, -999.997em); top: -4.241em; left: 0em;"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size2;">⏜</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></span></div>
</div>
</div>


1,612行目: 1,562行目:
<code class="tex">\triangle ABC \equiv \triangle DEF
<code class="tex">\triangle ABC \equiv \triangle DEF
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangle ABC \equiv \triangle DEF $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangle_ABC_\equiv_\triangle_DEF" style="width: 8.797em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.905em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.9em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≡</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐹<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,621行目: 1,571行目:
<code class="tex">\triangle ABC \cong \triangle DEF
<code class="tex">\triangle ABC \cong \triangle DEF
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangle ABC \cong \triangle DEF $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangle_ABC_\cong_\triangle_DEF" style="width: 8.797em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.905em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.9em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">≅</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐹<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,630行目: 1,580行目:
<code class="tex">\triangle ABC \backsim \triangle DEF
<code class="tex">\triangle ABC \backsim \triangle DEF
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangle ABC \backsim \triangle DEF $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangle_ABC_\backsim_\triangle_DEF" style="width: 8.695em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.854em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.85em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∽</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐹<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,639行目: 1,589行目:
<code class="tex">\triangle ABC \sim \triangle DEF
<code class="tex">\triangle ABC \sim \triangle DEF
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangle ABC \sim \triangle DEF $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangle_ABC_\sim_\triangle_DEF" style="width: 8.695em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.854em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.85em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∼</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">△</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐹<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,651行目: 1,601行目:
<code class="tex">\sin x
<code class="tex">\sin x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sin x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sin_x" style="width: 2.355em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.843em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.84em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">sin</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,660行目: 1,610行目:
<code class="tex">\cos x
<code class="tex">\cos x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cos x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cos_x" style="width: 2.559em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.997em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">cos</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


1,669行目: 1,619行目:
<code class="tex">\tan x
<code class="tex">\tan x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \tan x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\tan_x" style="width: 2.406em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.894em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1001.89em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">tan</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


1,681行目: 1,631行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\sin_45^\circ\vbCrLf\vbCrLf=_\frac{_\sqrt{2}_}{_2_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 7.416em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.831em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1005.83em, 3.121em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 5.525em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.457em, 1005.52em, 5.013em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 5.525em; height: 0px;"><span style="position: absolute; clip: rect(2.252em, 1005.52em, 4.809em, -999.997em); top: -3.781em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">sin</span><span class="mo"></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.92em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">45</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 1.025em;"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∘</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(2.917em, 1001.13em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.56em;"><span class="msqrt"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.616em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -4.599em; left: 0.616em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.1em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Main; top: -3.986em; left: -0.049em;">−<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1000.62em, 4.451em, -999.997em); top: -4.088em; left: 0em;"><span style="font-family: GyreTermesMathJax_Size1;">√</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.23em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.23em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.166em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
\sin 45^\circ
= \frac{ \sqrt{2} }{ 2 }
\end{eqnarray} $$
</div>
</div>


1,696行目: 1,643行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\cos_\frac{_\pi_}{_3_}\vbCrLf\vbCrLf=_\frac{_1_}{_2_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 6.496em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.667em, 1005.12em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 4.809em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1004.81em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 4.809em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1004.81em, 4.86em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">cos</span><span class="mo"></span><span class="mfrac" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.377em, 1000.67em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.355em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜋</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.87em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.872em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
\cos \frac{ \pi }{ 3 }
= \frac{ 1 }{ 2 }
\end{eqnarray} $$
</div>
</div>


1,711行目: 1,655行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\tan_\theta\vbCrLf\vbCrLf=_\frac{_\sin_\theta_}{_\cos_\theta_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 7.723em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.087em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.667em, 1006.09em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 5.78em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1005.78em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 5.78em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1005.78em, 4.86em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">tan</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝜃</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 2.252em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1001.89em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.969em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">sin</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1002.05em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -1.071em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">cos</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1002.25em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.252em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
\tan \theta
= \frac{ \sin \theta }{ \cos \theta }
\end{eqnarray} $$
</div>
</div>


1,723行目: 1,664行目:
<code class="tex">\sec x
<code class="tex">\sec x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sec x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sec_x" style="width: 2.508em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.945em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1001.95em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">sec</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


1,732行目: 1,673行目:
<code class="tex">\csc x
<code class="tex">\csc x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \csc x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\csc_x" style="width: 2.508em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.945em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1001.95em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">csc</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


1,741行目: 1,682行目:
<code class="tex">\cot x
<code class="tex">\cot x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cot x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cot_x" style="width: 2.406em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.894em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1001.89em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">cot</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


1,750行目: 1,691行目:
<code class="tex">\arcsin x
<code class="tex">\arcsin x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \arcsin x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\arcsin_x" style="width: 3.837em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.019em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.02em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">arcsin</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


1,759行目: 1,700行目:
<code class="tex">\arccos x
<code class="tex">\arccos x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \arccos x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\arccos_x" style="width: 4.093em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.224em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1003.22em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">arccos</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


1,768行目: 1,709行目:
<code class="tex">\arctan x
<code class="tex">\arctan x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \arctan x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\arctan_x" style="width: 3.991em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.121em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1003.12em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">arctan</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


1,777行目: 1,718行目:
<code class="tex">\sinh x
<code class="tex">\sinh x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sinh x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sinh_x" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.3em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">sinh</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,786行目: 1,727行目:
<code class="tex">\cosh x
<code class="tex">\cosh x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cosh x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cosh_x" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">cosh</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,795行目: 1,736行目:
<code class="tex">\tanh x
<code class="tex">\tanh x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \tanh x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\tanh_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">tanh</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,804行目: 1,745行目:
<code class="tex">\coth x
<code class="tex">\coth x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \coth x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\coth_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">coth</span><span class="mo"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,816行目: 1,757行目:
<code class="tex">a+bi
<code class="tex">a+bi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a+bi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a+bi" style="width: 3.121em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.457em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.46em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,825行目: 1,766行目:
<code class="tex">\Re x
<code class="tex">\Re x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Re x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Re_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Re</span><span class="mo"></span><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,834行目: 1,775行目:
<code class="tex">\require{physics} \Re x
<code class="tex">\require{physics} \Re x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \Re x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\Re_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Re</span><span class="mo"></span><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,843行目: 1,784行目:
<code class="tex">\Im x
<code class="tex">\Im x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Im x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Im_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Im</span><span class="mo"></span><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,852行目: 1,793行目:
<code class="tex">\require{physics} \Im x
<code class="tex">\require{physics} \Im x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \Im x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\Im_x" style="width: 3.019em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.355em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.25em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Im</span><span class="mo"></span><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


1,861行目: 1,802行目:
<code class="tex">\bar{z}
<code class="tex">\bar{z}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bar{z} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bar{z}" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.332em, 1000.41em, 2.355em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.246em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.31em, 3.582em, -999.997em); top: -3.986em; left: 0.054em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">¯</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


1,870行目: 1,811行目:
<code class="tex">\arg (z)
<code class="tex">\arg (z)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \arg (z) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\arg_(z)" style="width: 3.121em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.457em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">arg</span><span class="mo"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


1,879行目: 1,820行目:
<code class="tex">\omega
<code class="tex">\omega
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \omega $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\omega" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜔</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


1,890行目: 1,831行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfz\bar{z}_=_|z|^2\vbCrLf\end{eqnarray}" style="width: 4.553em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.582em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1003.58em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 3.275em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.019em, 1003.27em, 4.4em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 3.275em; height: 0px;"><span style="position: absolute; clip: rect(2.968em, 1003.27em, 4.297em, -999.997em); top: -3.883em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.246em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.31em, 3.582em, -999.997em); top: -3.986em; left: 0.054em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">¯</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="texatom" style="padding-left: 0.309em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.11em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.207em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
z\bar{z} = |z|^2
\end{eqnarray} $$
</div>
</div>


1,904行目: 1,843行目:
<code class="tex">\lim_{ x \to +0 } \frac{1}{x} = \infty
<code class="tex">\lim_{ x \to +0 } \frac{1}{x} = \infty
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lim_{ x \to +0 } \frac{1}{x} = \infty $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lim\_{_x_\to_+0_}_\frac{1}{x}_=_\infty" style="width: 6.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.013em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1004.91em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.741em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.207em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.74em, 4.246em, -999.997em); top: -3.321em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mfrac" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.202em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∞</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.86em;"></span></span></span></div>
</div>
</div>


1,913行目: 1,852行目:
<code class="tex">\displaystyle \lim_{ n \to \infty } f_n(x) = f(x)
<code class="tex">\displaystyle \lim_{ n \to \infty } f_n(x) = f(x)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \displaystyle \lim_{ n \to \infty } f_n(x) = f(x) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\displaystyle_\lim\_{_n_\to_\infty_}_f\_n(x)_=_f(x)" style="width: 8.592em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.752em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1006.65em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.156em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.321em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.258em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.016em;"></span></span></span></div>
</div>
</div>


1,922行目: 1,861行目:
<code class="tex">\limsup_{ n \to \infty } a_n
<code class="tex">\limsup_{ n \to \infty } a_n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \limsup_{ n \to \infty } a_n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\limsup\_{_n_\to_\infty_}_a\_n" style="width: 5.167em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.042em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1004.04em, 3.275em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 2.917em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.87em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">lim sup</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.116em; left: 0.616em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.36em; border-left: 0px solid; width: 0px; height: 2.276em;"></span></span></span></div>
</div>
</div>


1,931行目: 1,870行目:
<code class="tex">\varlimsup_{ n \to \infty } a_n
<code class="tex">\varlimsup_{ n \to \infty } a_n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varlimsup_{ n \to \infty } a_n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varlimsup\_{_n_\to_\infty_}_a\_n" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.974em, 1002.76em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(2.866em, 1001.38em, 4.144em, -999.997em); top: -3.986em; left: 0.156em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1001.38em, 4.246em, -999.997em); top: -4.906em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.23em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.156em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.565em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.667em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.718em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.77em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.821em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.923em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.974em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.025em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.127em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.179em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.321em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.341em;"></span></span></span></div>
</div>
</div>


1,940行目: 1,879行目:
<code class="tex">\liminf_{ n \to \infty } a_n
<code class="tex">\liminf_{ n \to \infty } a_n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \liminf_{ n \to \infty } a_n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\liminf\_{_n_\to_\infty_}_a\_n" style="width: 4.758em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.735em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1003.74em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.66em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">lim inf</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.321em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.016em;"></span></span></span></div>
</div>
</div>


1,949行目: 1,888行目:
<code class="tex">\varliminf_{ n \to \infty } a_n
<code class="tex">\varliminf_{ n \to \infty } a_n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varliminf_{ n \to \infty } a_n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varliminf\_{_n_\to_\infty_}_a\_n" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1002.76em, 3.275em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.38em, 4.4em, -999.997em); top: -3.986em; left: 0.156em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.888em, 1001.38em, 4.246em, -999.997em); top: -3.832em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 1.179em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.105em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.207em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.412em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.514em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.667em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.77em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.872em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.974em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.076em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.065em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.36em; border-left: 0px solid; width: 0px; height: 2.276em;"></span></span></span></div>
</div>
</div>


1,961行目: 1,900行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\varlimsup\_{_n_\to_\infty_}_a\_n\vbCrLf\vbCrLf=_\lim\_{_n_\to_\infty_}_\sup\_{_k_\geqq_n_}_a\_k\vbCrLf\vbCrLf\end{eqnarray}" style="width: 10.996em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.644em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.667em, 1008.64em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.337em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1008.34em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.337em; height: 0px;"><span style="position: absolute; clip: rect(2.866em, 1008.34em, 5.218em, -999.997em); top: -4.292em; right: 0em;"><span class="mtd"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(2.866em, 1001.38em, 4.144em, -999.997em); top: -3.986em; left: 0.156em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1001.38em, 4.246em, -999.997em); top: -4.906em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.23em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.156em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.565em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.667em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.718em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.77em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.821em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.923em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.974em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.025em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.127em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 1.179em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.321em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.156em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.321em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="munderover" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.38em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">sup</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.13em, 4.349em, -999.997em); top: -3.116em; left: 0.105em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">≧</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
\varlimsup_{ n \to \infty } a_n
= \lim_{ n \to \infty } \sup_{ k \geqq n } a_k
\end{eqnarray} $$
</div>
</div>


1,977行目: 1,913行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\varliminf\_{_n_\to_\infty_}_A\_n\vbCrLf\vbCrLf=_\bigcup\_{_n_=_1_}^{_\infty_}_\bigcap\_{_k_=_n_}^{_\infty_}_A\_k\vbCrLf=_\bigcup\_{_n_\in_\mathbb{_N_}_}_\bigcap\_{_k_\geqq_n_}_A\_k\vbCrLf\vbCrLf\end{eqnarray}" style="width: 17.233em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.552em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.36em, 1013.55em, 3.326em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 13.245em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.252em, 1013.25em, 5.218em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 13.245em; height: 0px;"><span style="position: absolute; clip: rect(2.406em, 1013.25em, 5.32em, -999.997em); top: -4.139em; right: 0em;"><span class="mtd"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.38em, 4.4em, -999.997em); top: -3.986em; left: 0.156em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.888em, 1001.38em, 4.246em, -999.997em); top: -3.832em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.383em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 1.179em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.105em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.207em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.412em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.514em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.667em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.77em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.872em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.974em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.076em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1001.59em, 4.246em, -999.997em); top: -3.065em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo"></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.616em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1000.97em, 4.502em, -999.997em); top: -3.986em; left: 0.054em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0.003em;">⋃</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.08em, 4.246em, -999.997em); top: -2.963em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.62em, 4.093em, -999.997em); top: -5.008em; left: 0.258em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="munderover" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1000.97em, 4.502em, -999.997em); top: -3.986em; left: 0.054em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0.003em;">⋂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.13em, 4.246em, -999.997em); top: -2.963em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.62em, 4.093em, -999.997em); top: -5.008em; left: 0.258em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.616em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1000.97em, 4.502em, -999.997em); top: -3.986em; left: 0.207em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0.003em;">⋃</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1001.43em, 4.246em, -999.997em); top: -2.963em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∈</span><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_DoubleStruck;">ℕ</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="munderover" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1000.97em, 4.502em, -999.997em); top: -3.986em; left: 0.054em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0.003em;">⋂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.13em, 4.349em, -999.997em); top: -2.963em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">≧</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.616em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.425em; border-left: 0px solid; width: 0px; height: 3.445em;"></span></span></span></div>
\varliminf_{ n \to \infty } A_n
= \bigcup_{ n = 1 }^{ \infty } \bigcap_{ k = n }^{ \infty } A_k
= \bigcup_{ n \in \mathbb{ N } } \bigcap_{ k \geqq n } A_k
\end{eqnarray} $$
</div>
</div>


1,990行目: 1,922行目:
<code class="tex">\mathcal{O}
<code class="tex">\mathcal{O}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathcal{O} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathcal{O}" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">O</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


2,002行目: 1,934行目:
<code class="tex">\frac{ dy }{ dx }
<code class="tex">\frac{ dy }{ dx }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ dy }{ dx } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_dy_}{_dx_}" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1001.28em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,011行目: 1,943行目:
<code class="tex">\frac{ \mathrm{ d } y }{ \mathrm{ d } x }
<code class="tex">\frac{ \mathrm{ d } y }{ \mathrm{ d } x }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ \mathrm{ d } y }{ \mathrm{ d } x } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_\mathrm{_d_}_y_}{_\mathrm{_d_}_x_}" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1001.28em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.92em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">d</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">d</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,020行目: 1,952行目:
<code class="tex">\require{physics} \dv{y}{x}
<code class="tex">\require{physics} \dv{y}{x}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \dv{y}{x} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\dv{y}{x}" style="width: 1.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1001.28em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.92em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">d</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">d</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,029行目: 1,961行目:
<code class="tex">\frac{ d^n y }{ dx^n }
<code class="tex">\frac{ d^n y }{ dx^n }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ d^n y }{ dx^n } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_d^n_y_}{_dx^n_}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1001.79em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1001.43em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.565em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.43em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.59em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.588em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,038行目: 1,970行目:
<code class="tex">\require{physics} \dv[n]{f}{x}
<code class="tex">\require{physics} \dv[n]{f}{x}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \dv[n]{f}{x} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\dv[n]{f}{x}" style="width: 3.326em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.633em, 1002.61em, 6.036em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.82em, 4.297em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">d</span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">d</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span></span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,047行目: 1,979行目:
<code class="tex">\left. \frac{dy}{dx} \right|_{x=a}
<code class="tex">\left. \frac{dy}{dx} \right|_{x=a}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \left. \frac{dy}{dx} \right|_{x=a} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\left._\frac{dy}{dx}_\right|\_{x=a}" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1002.76em, 3.019em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px;"><span style="position: absolute; clip: rect(2.457em, 1001.49em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mo"></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">|</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.219em; left: 1.536em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.86em;"></span></span></span></div>
</div>
</div>


2,056行目: 1,988行目:
<code class="tex">\require{physics} \eval{\dv{y}{x}}_{x=a}
<code class="tex">\require{physics} \eval{\dv{y}{x}}_{x=a}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \eval{\dv{y}{x}}_{x=a} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\eval{\dv{y}{x}}\_{x=a}" style="width: 3.479em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.712em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.565em, 1002.71em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.712em; height: 0px;"><span style="position: absolute; clip: rect(2.457em, 1001.43em, 4.86em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.92em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">d</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">d</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.27em; left: 1.536em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">=</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
</div>
</div>


2,065行目: 1,997行目:
<code class="tex">f'
<code class="tex">f'
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ f' $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_f'" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.87em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Variants;">′</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


2,074行目: 2,006行目:
<code class="tex">f^{\prime\prime}
<code class="tex">f^{\prime\prime}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ f^{\prime\prime} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_f^{\prime\prime}" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1001.18em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Variants;">′</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Variants;">′</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


2,083行目: 2,015行目:
<code class="tex">f^{ ( n ) }
<code class="tex">f^{ ( n ) }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ f^{ ( n ) } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_f^{_(_n_)_}" style="width: 1.945em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.076em, 1001.54em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
</div>
</div>


2,092行目: 2,024行目:
<code class="tex">Df
<code class="tex">Df
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ Df $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_Df" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.18em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,101行目: 2,033行目:
<code class="tex">D_x f
<code class="tex">D_x f
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ D_x f $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_D\_x_f" style="width: 2.048em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.59em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.72em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.718em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,110行目: 2,042行目:
<code class="tex">D^n f
<code class="tex">D^n f
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ D^n f $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_D^n_f" style="width: 2.099em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1001.64em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.72em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.718em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


2,119行目: 2,051行目:
<code class="tex">\dot{y} = \frac{dy}{dt}
<code class="tex">\dot{y} = \frac{dy}{dt}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dot{y} = \frac{dy}{dt} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dot{y}_=_\frac{dy}{dt}" style="width: 3.837em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.019em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.633em, 1003.02em, 6.036em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.21em, 3.582em, -999.997em); top: -4.037em; left: 0.054em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">˙</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.82em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.406em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑡<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,128行目: 2,060行目:
<code class="tex">\ddddot{ y } = \frac{ d^4 y }{ dt^4 }
<code class="tex">\ddddot{ y } = \frac{ d^4 y }{ dt^4 }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ddddot{ y } = \frac{ d^4 y }{ dt^4 } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ddddot{_y_}_=_\frac{_d^4_y_}{_dt^4_}" style="width: 4.604em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.633em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.479em, 1003.63em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: -0.151em;"><span style="height: 0em; vertical-align: 0em; width: 0.616em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Marks;">⃜&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.019em, 1001.43em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.565em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">4</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1001.33em, 4.144em, -999.997em); top: -3.27em; left: 50%; margin-left: -0.662em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px;"><span style="position: absolute; clip: rect(3.275em, 1000.31em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑡<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.36em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">4</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.59em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.588em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
</div>
</div>


2,141行目: 2,073行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLff'(x)\vbCrLf\vbCrLf=_\frac{_df_}{_dx_}\vbCrLf=_\lim\_{_\Delta_x_\to_0_}_\frac{_f(x_+_\Delta_x)_-_f(x)_}{_\Delta_x_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 19.841em; display: inline-block;"><span style="display: inline-block; position: relative; width: 15.597em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1015.6em, 3.07em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 15.29em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.508em, 1015.29em, 4.962em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.29em; height: 0px;"><span style="position: absolute; clip: rect(2.457em, 1015.29em, 4.911em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="msup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Variants;">′</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.076em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.08em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.076em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="munderover" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.33em, 4.144em, -999.997em); top: -3.986em; left: 0.258em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">lim</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.79em, 4.246em, -999.997em); top: -3.321em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">Δ</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">→</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mfrac" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 7.007em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1006.75em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -3.423em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">Δ</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.23em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.611em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Δ</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1007.01em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 7.007em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.101em; border-left: 0px solid; width: 0px; height: 2.86em;"></span></span></span></div>
f'(x)
= \frac{ df }{ dx }
= \lim_{ \Delta x \to 0 } \frac{ f(x + \Delta x) - f(x) }{ \Delta x }
\end{eqnarray} $$
</div>
</div>


2,154行目: 2,082行目:
<code class="tex">\frac{ \partial f }{ \partial x }
<code class="tex">\frac{ \partial f }{ \partial x }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ \partial f }{ \partial x } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_\partial_f_}{_\partial_x_}" style="width: 1.69em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1001.33em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.02em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,163行目: 2,091行目:
<code class="tex">\frac{ \partial }{ \partial y } \frac{ \partial }{ \partial x } z
<code class="tex">\frac{ \partial }{ \partial y } \frac{ \partial }{ \partial x } z
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ \partial }{ \partial y } \frac{ \partial }{ \partial x } z $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_\partial_}{_\partial_y_}_\frac{_\partial_}{_\partial_x_}_z" style="width: 3.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.07em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1003.07em, 6.189em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.02em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.166em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
</div>
</div>


2,172行目: 2,100行目:
<code class="tex">\frac{ \partial^n f}{ \partial x^n }
<code class="tex">\frac{ \partial^n f}{ \partial x^n }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \frac{ \partial^n f}{ \partial x^n } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\frac{_\partial^n_f}{_\partial_x^n_}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1001.79em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1001.38em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.565em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.59em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.588em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,181行目: 2,109行目:
<code class="tex">\require{physics} \pdv{f}{x}
<code class="tex">\require{physics} \pdv{f}{x}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \pdv{f}{x} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\pdv{f}{x}" style="width: 1.69em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.616em, 1001.33em, 2.968em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.02em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,190行目: 2,118行目:
<code class="tex">\require{physics} \pdv{f}{x}{y}
<code class="tex">\require{physics} \pdv{f}{x}{y}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \pdv{f}{x}{y} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\pdv{f}{x}{y}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1001.79em, 6.036em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.02em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.13em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.127em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,199行目: 2,127行目:
<code class="tex">\require{physics} \pdv[n]{f}{x}
<code class="tex">\require{physics} \pdv[n]{f}{x}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \pdv[n]{f}{x} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\pdv[n]{f}{x}" style="width: 3.377em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.661em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1002.66em, 6.036em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.87em, 4.297em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.02em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.509em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.18em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.179em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span></span><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.971em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,208行目: 2,136行目:
<code class="tex">f_x
<code class="tex">f_x
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ f_x $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_f\_x" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.67em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.258em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,217行目: 2,145行目:
<code class="tex">f_{ xy }
<code class="tex">f_{ xy }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ f_{ xy } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_f\_{_xy_}" style="width: 1.23em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.97em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.258em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></span></div>
</div>
</div>


2,226行目: 2,154行目:
<code class="tex">\nabla f
<code class="tex">\nabla f
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \nabla f $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\nabla_f" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.18em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∇</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,235行目: 2,163行目:
<code class="tex">\Delta f
<code class="tex">\Delta f
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Delta f $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Delta_f" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.18em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Δ</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,250行目: 2,178行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\Delta_\varphi\vbCrLf\vbCrLf=_\nabla^2_\varphi\vbCrLf=_\frac{_\partial^2_\varphi_}{_\partial_x^2_}\vbCrLf__+_\frac{_\partial^2_\varphi_}{_\partial_y^2_}\vbCrLf__+_\frac{_\partial^2_\varphi_}{_\partial_z^2_}\vbCrLf\vbCrLf\end{eqnarray}" style="width: 18.512em; display: inline-block;"><span style="display: inline-block; position: relative; width: 14.575em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.463em, 1014.58em, 3.224em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 14.268em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.355em, 1014.27em, 5.116em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 14.268em; height: 0px;"><span style="position: absolute; clip: rect(2.303em, 1014.27em, 5.064em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Δ</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜑</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="msubsup" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.67em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∇</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.77em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜑</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.019em, 1001.59em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.816em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.565em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜑</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1001.49em, 4.144em, -999.997em); top: -3.27em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.79em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.792em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.019em, 1001.59em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.816em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.565em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜑</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1001.43em, 4.349em, -999.997em); top: -3.27em; left: 50%; margin-left: -0.713em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.463em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.79em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.792em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.019em, 1001.59em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.816em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.565em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜑</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1001.38em, 4.246em, -999.997em); top: -3.27em; left: 50%; margin-left: -0.662em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∂</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.246em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.292em; left: 0.412em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.79em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.792em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
\Delta \varphi
= \nabla^2 \varphi
= \frac{ \partial^2 \varphi }{ \partial x^2 }
  + \frac{ \partial^2 \varphi }{ \partial y^2 }
  + \frac{ \partial^2 \varphi }{ \partial z^2 }
\end{eqnarray} $$
</div>
</div>


2,271行目: 2,193行目:
\end{array}
\end{array}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{array}{c|ccccc}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{array}{c|ccccc}\vbCrLf\vbCrLf_x_____&_\cdots_&_-1_&_\cdots_&_1_&_\cdots_\\_\vbCrLf_\hline\vbCrLf_f’(x)_&_+_&_0_&_–_&_0_&_+_\\_\vbCrLf_\hline\vbCrLf_f(x)__&_\nearrow_&_e_&_\searrow_&_-e_&_\nearrow\vbCrLf\vbCrLf\end{array}" style="width: 17.54em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.808em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-0.509em, 1013.81em, 4.195em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 13.501em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1002em, 6.394em, -999.997em); top: -4.548em; left: 0.463em;"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1002em, 4.349em, -999.997em); top: -3.934em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.514em;"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Variants;">′</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.54em, 4.349em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.816em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.553em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.77em, 5.934em, -999.997em); top: -4.241em; left: 3.684em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.77em, 3.94em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.304em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">+</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↗</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.246em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1001.08em, 6.292em, -999.997em); top: -4.599em; left: 5.678em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.08em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.303em, 1000.77em, 5.831em, -999.997em); top: -4.19em; left: 7.979em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.77em, 3.94em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">–</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↘</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.195em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1001.08em, 6.292em, -999.997em); top: -4.599em; left: 9.973em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1001.08em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.77em, 5.934em, -999.997em); top: -4.241em; left: 12.223em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.77em, 3.94em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.304em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">+</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↗</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.246em;"></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-left: 1.3px solid; width: 0px; height: 4.4em; position: absolute; top: -2.452em; left: 3.121em; border-top-style: solid; border-right-style: solid; border-bottom-style: solid;"></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 13.501em; height: 0px; position: absolute; top: -1.02em; left: 0em;"></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 13.501em; height: 0px; position: absolute; top: 0.412em; left: 0em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.529em; border-left: 0px solid; width: 0px; height: 5.718em;"></span></span></span></div>
  x    & \cdots & -1 & \cdots & 1 & \cdots \\  
  \hline
  f’(x) & + & 0 & & 0 & + \\  
  \hline
  f(x) & \nearrow & e & \searrow & -e & \nearrow
\end{array} $$
</div>
</div>


2,289行目: 2,205行目:
<code class="tex">\int_0^1 f(x) dx
<code class="tex">\int_0^1 f(x) dx
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \int_0^1 f(x) dx $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\int\_0^1_f(x)_dx" style="width: 5.167em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.042em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.531em, 1004.04em, 6.138em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1000.67em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∫<span style="margin-left: -0.202em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.957em; left: 0.77em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.168em; left: 0.565em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.101em; border-left: 0px solid; width: 0px; height: 3.055em;"></span></span></span></div>
</div>
</div>


2,298行目: 2,214行目:
<code class="tex">\displaystyle \int_{-\infty}^{ \infty } f(x) dx
<code class="tex">\displaystyle \int_{-\infty}^{ \infty } f(x) dx
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \displaystyle \int_{-\infty}^{ \infty } f(x) dx $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\displaystyle_\int\_{-\infty}^{_\infty_}_f(x)_dx" style="width: 5.883em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.604em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.735em, 1004.6em, 6.138em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.741em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1000.67em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∫<span style="margin-left: -0.202em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1000.72em, 4.093em, -999.997em); top: -4.957em; left: 0.77em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.479em, 1001.23em, 4.144em, -999.997em); top: -3.168em; left: 0.565em;"><span class="texatom"><span class="mrow"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">∞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.101em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
</div>
</div>


2,311行目: 2,227行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\int\_0^1_x_dx\vbCrLf=_\left[_\frac{x^2}{2}_\right]\_0^1\vbCrLf=_\frac{1}{2}\vbCrLf\end{eqnarray}" style="width: 11.762em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.257em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.309em, 1009.26em, 3.377em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.95em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.201em, 1008.95em, 5.269em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.95em; height: 0px;"><span style="position: absolute; clip: rect(2.099em, 1008.95em, 5.167em, -999.997em); top: -3.883em; right: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1000.67em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∫<span style="margin-left: -0.202em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.957em; left: 0.77em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.168em; left: 0.565em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="msubsup" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 2.712em; height: 0px;"><span style="position: absolute; clip: rect(2.303em, 1002.15em, 5.116em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">[</span></span><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.019em, 1000.92em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.02em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.025em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">]</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -5.213em; left: 2.252em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -2.963em; left: 2.252em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">0</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.49em; border-left: 0px solid; width: 0px; height: 3.575em;"></span></span></span></div>
\int_0^1 x dx
= \left[ \frac{x^2}{2} \right]_0^1
= \frac{1}{2}
\end{eqnarray} $$
</div>
</div>


2,324行目: 2,236行目:
<code class="tex">\iint_D f(x,y) dxdy
<code class="tex">\iint_D f(x,y) dxdy
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \iint_D f(x,y) dxdy $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\iint\_D_f(x,y)_dxdy" style="width: 8.132em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.394em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.735em, 1006.39em, 6.138em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1001.13em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∬<span style="margin-left: -0.202em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.168em; left: 0.974em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝐷</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑦</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.101em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,333行目: 2,245行目:
<code class="tex">\idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n
<code class="tex">\idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\idotsint\_D_f(x\_1,_x\_2,_\ldots_,_x\_n)_dx\_1_\cdots_dx\_n" style="width: 17.438em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.705em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.735em, 1013.71em, 6.138em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∫<span style="margin-left: -0.202em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">⋯</span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1000.67em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∫<span style="margin-left: -0.202em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.168em; left: 0.565em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝐷</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">…</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">,</span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">⋯</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.101em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


2,342行目: 2,254行目:
<code class="tex">\oint_C f(z) dz
<code class="tex">\oint_C f(z) dz
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \oint_C f(z) dz $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\oint\_C_f(z)_dz" style="width: 5.064em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.991em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.735em, 1003.99em, 6.138em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1000.72em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Size1; vertical-align: 0em;">∮<span style="margin-left: -0.151em;"></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.168em; left: 0.667em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.207em;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.101em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
</div>
</div>


2,354行目: 2,266行目:
<code class="tex">\vec{ a }
<code class="tex">\vec{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vec{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vec{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


2,363行目: 2,275行目:
<code class="tex">\overrightarrow{ AB }
<code class="tex">\overrightarrow{ AB }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overrightarrow{ AB } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overrightarrow{_AB_}" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.77em, 1001.23em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.18em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1001.23em, 4.093em, -999.997em); top: -4.701em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0.872em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.463em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.667em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.627em;"></span></span></span></div>
</div>
</div>


2,372行目: 2,284行目:
<code class="tex">\boldsymbol{ A }
<code class="tex">\boldsymbol{ A }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boldsymbol{ A } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boldsymbol{_A_}" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑨</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


2,381行目: 2,293行目:
<code class="tex">( a_1, a_2, \ldots, a_n )
<code class="tex">( a_1, a_2, \ldots, a_n )
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ ( a_1, a_2, \ldots, a_n ) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_(_a\_1,_a\_2,_\ldots,_a\_n_)" style="width: 7.672em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.036em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1005.93em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">…</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">,</span><span class="msubsup" style="padding-left: 0.207em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,397行目: 2,309行目:
\right)
\right)
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \left(
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\left(\vbCrLf\vbCrLf_\begin{array}{c}\vbCrLf___a\_1_\\\vbCrLf___a\_2_\\\vbCrLf___\vdots_\\\vbCrLf___a\_n\vbCrLf_\end{array}\vbCrLf\vbCrLf\right)" style="width: 3.121em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.457em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.945em, 1002.3em, 7.57em, -999.997em); top: -5.008em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 2.917em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.383em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.787em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.122em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.764em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.458em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.1em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.207em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.224em, 1000.92em, 8.49em, -999.997em); top: -5.929em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.92em, 4.297em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.92em, 4.297em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.92em, 4.297em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.934em;"></span></span></span></span><span class="mo" style="vertical-align: 2.917em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.383em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.787em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.122em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.764em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.458em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.1em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.207em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.013em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.114em; border-left: 0px solid; width: 0px; height: 6.951em;"></span></span></span></div>
  \begin{array}{c}
</div>
    a_1 \\
 
    a_2 \\
    \vdots \\
    a_n
  \end{array}
\right) $$
</div>
 


*ベクトルサンプル
*ベクトルサンプル
2,424行目: 2,329行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\boldsymbol{_1_}\vbCrLf=(_\underbrace{_1,_1,_\ldots,_1_}\_{_n_}_)^{_\mathrm{_T_}_}\vbCrLf=\left(\vbCrLf\vbCrLf__\begin{array}{c}\vbCrLf____1_\\\vbCrLf____1_\\\vbCrLf____\vdots_\\\vbCrLf____1\vbCrLf__\end{array}\vbCrLf\right)\vbCrLf\vbCrLf\end{eqnarray}" style="width: 13.654em; display: inline-block;"><span style="display: inline-block; position: relative; width: 10.74em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-0.969em, 1010.59em, 4.655em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 10.433em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.275em, 1010.28em, 8.899em, -999.997em); top: -6.338em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.433em; height: 0px;"><span style="position: absolute; clip: rect(3.275em, 1010.28em, 8.899em, -999.997em); top: -6.338em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Normal;">𝟏</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">(</span><span class="munderover"><span style="display: inline-block; position: relative; width: 3.991em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1003.99em, 4.758em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 3.991em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1003.84em, 4.297em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">1</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">…</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">,</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">1</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.888em, 1003.99em, 4.502em, -999.997em); top: -3.73em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 3.991em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 3.07em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 1.076em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.565em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.559em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1000.36em, 4.246em, -999.997em); top: -2.707em; left: 1.792em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.26em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.412em;"><span class="texatom"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">T</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mrow" style="padding-left: 0.309em;"><span class="mo" style="vertical-align: 2.917em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.383em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.787em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.122em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.764em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.458em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.1em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.207em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.07em, 1000.41em, 8.439em, -999.997em); top: -6.031em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.036em;"></span></span></span></span><span class="mo" style="vertical-align: 2.917em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.383em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.787em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.122em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.764em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.458em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.1em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.207em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.343em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.343em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.114em; border-left: 0px solid; width: 0px; height: 6.951em;"></span></span></span></div>
\boldsymbol{ 1 }
=( \underbrace{ 1, 1, \ldots, 1 }_{ n } )^{ \mathrm{ T } }
=\left(
  \begin{array}{c}
    1 \\
    1 \\
    \vdots \\
    1
  \end{array}
\right)
\end{eqnarray} $$
</div>
</div>


2,445行目: 2,339行目:
=( 0, \ldots, 0, \stackrel{k}{ 1 }, 0, \ldots, 0 )^{\mathrm{T}}
=( 0, \ldots, 0, \stackrel{k}{ 1 }, 0, \ldots, 0 )^{\mathrm{T}}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boldsymbol{ \rm{ e } }_k
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boldsymbol{_\rm{_e_}_}\_k\vbCrLf=(_0,_\ldots,_0,_\stackrel{k}{_1_},_0,_\ldots,_0_)^{\mathrm{T}}" style="width: 13.859em; display: inline-block;"><span style="display: inline-block; position: relative; width: 10.893em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.531em, 1010.89em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐞</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.463em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">(</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">…</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">,</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="texatom" style="padding-left: 0.207em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.275em, 1000.31em, 4.144em, -999.997em); top: -4.906em; left: 0.105em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">0</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">,</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">…</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">,</span><span class="mn" style="font-family: GyreTermesMathJax_Main; padding-left: 0.207em;">0</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.26em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.412em;"><span class="texatom"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">T</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 2.211em;"></span></span></span></div>
=( 0, \ldots, 0, \stackrel{k}{ 1 }, 0, \ldots, 0 )^{\mathrm{T}} $$
</div>
</div>


2,455行目: 2,348行目:
<code class="tex">\| x \|
<code class="tex">\| x \|
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \| x \| $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\|_x_\|" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.02em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">‖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">‖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,464行目: 2,357行目:
<code class="tex">\require{physics} \norm{ \dfrac{1}{2} }
<code class="tex">\require{physics} \norm{ \dfrac{1}{2} }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{physics} \norm{ \dfrac{1}{2} } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{physics}_\norm{_\dfrac{1}{2}_}" style="width: 2.048em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.588em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1001.49em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">‖</span></span><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">‖</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
</div>
</div>


2,473行目: 2,366行目:
<code class="tex">\vec{ a } \cdot \vec{ b }
<code class="tex">\vec{ a } \cdot \vec{ b }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vec{ a } \cdot \vec{ b } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vec{_a_}_\cdot_\vec{_b_}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.042em, 1001.74em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⋅</span><span class="texatom" style="padding-left: 0.258em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.241em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


2,482行目: 2,375行目:
<code class="tex">\vec{ a } \times \vec{ b }
<code class="tex">\vec{ a } \times \vec{ b }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vec{ a } \times \vec{ b } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vec{_a_}_\times_\vec{_b_}" style="width: 2.661em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.042em, 1002.05em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">×</span><span class="texatom" style="padding-left: 0.258em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.241em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


2,497行目: 2,390行目:
\end{pmatrix}
\end{pmatrix}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{pmatrix}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{pmatrix}\vbCrLfa_&_b_\\\vbCrLfc_&_d\vbCrLf\end{pmatrix}" style="width: 4.758em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.735em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.531em, 1003.58em, 6.292em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">(</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.712em, 1000.46em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1000.51em, 4.911em, -999.997em); top: -3.986em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">)</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
a & b \\
c & d
\end{pmatrix} $$
</div>
</div>


2,512行目: 2,402行目:
\end{bmatrix}
\end{bmatrix}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{bmatrix}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{bmatrix}\vbCrLfa_&_b_\\\vbCrLfc_&_d\vbCrLf\end{bmatrix}" style="width: 4.349em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.428em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.531em, 1003.27em, 6.292em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">[</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.712em, 1000.46em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1000.51em, 4.911em, -999.997em); top: -3.986em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">]</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
a & b \\
c & d
\end{bmatrix} $$
</div>
</div>


2,527行目: 2,414行目:
\end{vmatrix}
\end{vmatrix}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{vmatrix}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{vmatrix}\vbCrLfa_&_b_\\\vbCrLfc_&_d\vbCrLf\end{vmatrix}" style="width: 3.735em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.917em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.531em, 1002.82em, 6.292em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">|</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.712em, 1000.46em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1000.51em, 4.911em, -999.997em); top: -3.986em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">|</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
a & b \\
c & d
\end{vmatrix} $$
</div>
</div>


2,539行目: 2,423行目:
<code class="tex">A^{ \mathrm{ T } }
<code class="tex">A^{ \mathrm{ T } }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A^{ \mathrm{ T } } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A^{_\mathrm{_T_}_}" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.076em, 1001.13em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.616em;"><span class="texatom"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">T</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,548行目: 2,432行目:
<code class="tex">{}^t \! A
<code class="tex">{}^t \! A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ {}^t \! A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{}^t_\!_A" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.195em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.309em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑡<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.202em;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,557行目: 2,441行目:
<code class="tex">\dim
<code class="tex">\dim
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dim $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dim" style="width: 1.945em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.54em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">dim</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


2,566行目: 2,450行目:
<code class="tex">\mathrm{ rank } A
<code class="tex">\mathrm{ rank } A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathrm{ rank } A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathrm{_rank_}_A" style="width: 3.07em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">a</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">n</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


2,575行目: 2,459行目:
<code class="tex">\mathrm{ Tr } A
<code class="tex">\mathrm{ Tr } A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathrm{ Tr } A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathrm{_Tr_}_A" style="width: 1.945em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.49em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">T</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


2,584行目: 2,468行目:
<code class="tex">\mathrm{ det }A
<code class="tex">\mathrm{ det }A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathrm{ det }A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathrm{_det_}A" style="width: 2.355em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.843em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.79em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">d</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">e</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


2,598行目: 2,482行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\mathrm{_det_}A\vbCrLf\vbCrLf=_|_A_|\vbCrLf=_\begin{vmatrix}_a_&_b_\\_c_&_d_\end{vmatrix}\vbCrLf=_ad_-_bc\vbCrLf\vbCrLf\end{eqnarray}" style="width: 16.62em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.092em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.463em, 1013.09em, 3.224em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 12.785em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.355em, 1012.73em, 5.116em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 12.785em; height: 0px;"><span style="position: absolute; clip: rect(2.355em, 1012.73em, 5.116em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">d</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">e</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="texatom" style="padding-left: 0.309em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mrow" style="padding-left: 0.309em;"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">|</span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.712em, 1000.46em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.457em, 1000.51em, 4.911em, -999.997em); top: -3.986em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">|</span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
\mathrm{ det }A
= | A |
= \begin{vmatrix} a & b \\ c & d \end{vmatrix}
= ad - bc
\end{eqnarray} $$
</div>
</div>


2,616行目: 2,495行目:
\end{pmatrix}
\end{pmatrix}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{pmatrix}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{pmatrix}\vbCrLf\vbCrLf_a_&_b_&_c_\\\vbCrLf_d_&_e_&_f_\\\vbCrLf_g_&_h_&_I\vbCrLf\vbCrLf\end{pmatrix}" style="width: 6.701em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.269em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.945em, 1005.12em, 6.138em, -999.997em); top: -4.292em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 2.201em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -0.049em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.145em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.838em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.531em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.173em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 3.735em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1000.51em, 6.394em, -999.997em); top: -4.548em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.349em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑔</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.553em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.46em, 6.292em, -999.997em); top: -4.599em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">ℎ</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.41em, 5.985em, -999.997em); top: -4.343em; left: 3.275em;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.349em;"></span></span></span></span><span class="mo" style="vertical-align: 2.201em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -0.049em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.145em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.838em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.531em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.173em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.297em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.205em; border-left: 0px solid; width: 0px; height: 5.133em;"></span></span></span></div>
  a & b & c \\
  d & e & f \\
  g & h & I
\end{pmatrix} $$
</div>
</div>


2,637行目: 2,512行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\left(\vbCrLf\vbCrLf_\begin{array}{ccc}\vbCrLf___a_&_b_&_c_\\\vbCrLf___d_&_e_&_f_\\\vbCrLf___g_&_h_&_i\vbCrLf_\end{array}\vbCrLf\vbCrLf\right)\vbCrLf\end{eqnarray}" style="width: 7.161em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.627em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-0.253em, 1005.47em, 3.94em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 5.32em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1005.17em, 6.752em, -999.997em); top: -4.906em; left: 0em;"><span style="display: inline-block; position: relative; width: 5.32em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1005.17em, 6.752em, -999.997em); top: -4.906em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 2.201em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -0.049em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.145em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.838em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.531em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.173em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 3.735em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1000.51em, 6.394em, -999.997em); top: -4.548em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.349em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑔</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.553em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.46em, 6.292em, -999.997em); top: -4.599em; left: 1.639em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">ℎ</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.41em, 6.036em, -999.997em); top: -4.343em; left: 3.275em;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.26em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑖</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.349em;"></span></span></span></span><span class="mo" style="vertical-align: 2.201em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -0.049em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.145em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.838em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.531em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.173em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.911em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.911em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.205em; border-left: 0px solid; width: 0px; height: 5.133em;"></span></span></span></div>
\left(
  \begin{array}{ccc}
    a & b & c \\
    d & e & f \\
    g & h & i
  \end{array}
\right)
\end{eqnarray} $$
</div>
</div>


2,662行目: 2,529行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\left(\vbCrLf\vbCrLf_\begin{array}{rrr}\vbCrLf___111_&_111_&_111_\\\vbCrLf___22_&_0.2_&_-2_\\\vbCrLf___3_&_3_&_3\vbCrLf_\end{array}\vbCrLf\vbCrLf\right)\vbCrLf\end{eqnarray}" style="width: 10.996em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.644em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-0.253em, 1008.49em, 3.94em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.337em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1008.18em, 6.752em, -999.997em); top: -4.906em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.337em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1008.18em, 6.752em, -999.997em); top: -4.906em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 2.201em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -0.1em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.145em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.838em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.531em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.225em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 6.752em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.355em, 1001.38em, 6.292em, -999.997em); top: -4.599em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.38em, 4.144em, -999.997em); top: -5.366em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">111</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.97em, 4.144em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">22</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -2.503em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1001.38em, 6.292em, -999.997em); top: -4.599em; left: 2.61em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.38em, 4.144em, -999.997em); top: -5.366em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">111</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.23em, 4.144em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0.2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -2.503em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1001.38em, 6.292em, -999.997em); top: -4.599em; left: 5.269em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.38em, 4.144em, -999.997em); top: -5.366em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">111</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.13em, 4.144em, -999.997em); top: -3.934em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -2.503em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span></span></span><span class="mo" style="vertical-align: 2.201em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -0.1em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.145em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.838em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.531em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.225em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.911em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.911em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.205em; border-left: 0px solid; width: 0px; height: 5.068em;"></span></span></span></div>
\left(
  \begin{array}{rrr}
    111 & 111 & 111 \\
    22 & 0.2 & -2 \\
    3 & 3 & 3
  \end{array}
\right)
\end{eqnarray} $$
</div>
</div>


2,688行目: 2,547行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfA_=_\left(\vbCrLf\vbCrLf_\begin{array}{cccc}\vbCrLf___a\_{_11_}_&_a\_{_12_}_&_\ldots_&_a\_{_1n_}_\\\vbCrLf___a\_{_21_}_&_a\_{_22_}_&_\ldots_&_a\_{_2n_}_\\\vbCrLf___\vdots_&_\vdots_&_\ddots_&_\vdots_\\\vbCrLf___a\_{_m1_}_&_a\_{_m2_}_&_\ldots_&_a\_{_mn_}\vbCrLf_\end{array}\vbCrLf\vbCrLf\right)\vbCrLf\end{eqnarray}" style="width: 15.648em; display: inline-block;"><span style="display: inline-block; position: relative; width: 12.325em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-0.969em, 1012.17em, 4.655em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 12.018em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.275em, 1011.92em, 8.899em, -999.997em); top: -6.338em; left: 0em;"><span style="display: inline-block; position: relative; width: 12.018em; height: 0px;"><span style="position: absolute; clip: rect(3.275em, 1011.92em, 8.899em, -999.997em); top: -6.338em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mrow" style="padding-left: 0.309em;"><span class="mo" style="vertical-align: 2.917em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.383em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.787em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.122em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.764em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.458em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.1em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.207em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 8.541em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.224em, 1001.43em, 8.49em, -999.997em); top: -5.929em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.28em, 4.297em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">11</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.28em, 4.297em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">21</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.43em, 4.297em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑚</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.934em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1001.43em, 8.49em, -999.997em); top: -5.929em; left: 2.559em;"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.28em, 4.297em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">12</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.28em, 4.297em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">22</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.43em, 4.297em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑚</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.934em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1000.77em, 7.877em, -999.997em); top: -5.468em; left: 5.116em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.473em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1001.43em, 8.49em, -999.997em); top: -5.929em; left: 7.11em;"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.28em, 4.297em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.28em, 4.297em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.281em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.43em, 4.297em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.434em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑚</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.934em;"></span></span></span></span><span class="mo" style="vertical-align: 2.917em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.383em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.787em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.122em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.764em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.458em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.1em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.207em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.343em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.343em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.114em; border-left: 0px solid; width: 0px; height: 6.951em;"></span></span></span></div>
A = \left(
  \begin{array}{cccc}
    a_{ 11 } & a_{ 12 } & \ldots & a_{ 1n } \\
    a_{ 21 } & a_{ 22 } & \ldots & a_{ 2n } \\
    \vdots & \vdots & \ddots & \vdots \\
    a_{ m1 } & a_{ m2 } & \ldots & a_{ mn }
  \end{array}
\right)
\end{eqnarray} $$
</div>
</div>


2,716行目: 2,566行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\left(\vbCrLf\vbCrLf_\begin{array}{cc|cc}\vbCrLf___a_&_b_&_0_&_0_\\\vbCrLf___c_&_d_&_0_&_0_\\\vbCrLf___\hline\vbCrLf___x_&_y_&_1_&_0_\\\vbCrLf___z_&_w_&_0_&_1_\\\vbCrLf_\end{array}\vbCrLf\vbCrLf\right)\vbCrLf\end{eqnarray}" style="width: 10.586em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.337em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-1.225em, 1008.18em, 4.911em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 8.03em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.531em, 1007.88em, 9.666em, -999.997em); top: -6.849em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.03em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1007.88em, 9.666em, -999.997em); top: -6.849em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 3.173em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.843em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.736em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.378em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.02em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.713em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.355em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.003em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.36em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.718em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 6.445em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 8.337em, -999.997em); top: -5.877em; left: 0.463em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.246em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.883em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1000.67em, 8.439em, -999.997em); top: -6.031em; left: 2.099em;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.51em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑑<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.349em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.67em, 4.144em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑤</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.036em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1000.46em, 8.439em, -999.997em); top: -6.031em; left: 3.888em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.036em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1000.46em, 8.439em, -999.997em); top: -6.031em; left: 5.473em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -6.133em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -1.736em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.036em;"></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-left: 1.3px solid; width: 0px; height: 5.831em; position: absolute; top: -3.168em; left: 3.326em; border-top-style: solid; border-right-style: solid; border-bottom-style: solid;"></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 6.445em; height: 0px; position: absolute; top: -0.304em; left: 0em;"></span></span></span><span class="mo" style="vertical-align: 3.173em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 1.843em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.736em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.378em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.02em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.713em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.355em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.003em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.36em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.718em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.854em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.854em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.438em; border-left: 0px solid; width: 0px; height: 7.536em;"></span></span></span></div>
\left(
  \begin{array}{cc|cc}
    a & b & 0 & 0 \\
    c & d & 0 & 0 \\
    \hline
    x & y & 1 & 0 \\
    z & w & 0 & 1 \\
  \end{array}
\right)
\end{eqnarray} $$
</div>
</div>


2,743行目: 2,583行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\begin{pmatrix}\vbCrLf\vbCrLf_\lambda_&_1_&___&__&_0_\\\vbCrLf___&_\lambda_&_1_&___&___\\\vbCrLf___&___&_\ddots_&_\ddots_&___\\\vbCrLf___&___&___&_\lambda_&_1__\\\vbCrLf_0_&___&___&___&_\lambda\vbCrLf\vbCrLf\end{pmatrix}\vbCrLf\end{eqnarray}" style="width: 12.478em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.82em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-1.685em, 1009.67em, 5.422em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 9.513em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(4.042em, 1009.36em, 11.149em, -999.997em); top: -7.82em; left: 0em;"><span style="display: inline-block; position: relative; width: 9.513em; height: 0px;"><span style="position: absolute; clip: rect(4.042em, 1009.36em, 11.149em, -999.997em); top: -7.82em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 3.633em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎛<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 2.815em; left: 0em;">⎝<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.736em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.071em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.713em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.406em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.049em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.309em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.616em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.974em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 1.332em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 1.69em; left: 0em;">⎜<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 7.928em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.837em, 1000.62em, 10.586em, -999.997em); top: -7.462em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -6.849em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜆</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -5.366em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -1.02em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.468em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 10.586em, -999.997em); top: -7.462em; left: 1.792em;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -6.849em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -5.366em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜆</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -1.02em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.468em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 9.922em, -999.997em); top: -6.798em; left: 3.582em;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -6.849em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -5.366em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -1.02em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.803em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 9.922em, -999.997em); top: -6.798em; left: 5.422em;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -6.849em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -5.366em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜆</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -1.02em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.803em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000.62em, 10.638em, -999.997em); top: -7.514em; left: 7.212em;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -6.849em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -5.366em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -1.02em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜆</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.519em;"></span></span></span></span><span class="mo" style="vertical-align: 3.633em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: -2.758em; left: 0em;">⎞<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Symbols; top: 2.815em; left: 0em;">⎠<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.452em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -2.094em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.736em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.429em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -1.071em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.713em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.406em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: -0.049em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.309em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.616em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 0.974em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 1.332em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Symbols; position: absolute; top: 1.69em; left: 0em;">⎟<span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 7.825em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.825em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -4.088em; border-left: 0px solid; width: 0px; height: 8.769em;"></span></span></span></div>
\begin{pmatrix}
  \lambda & 1 &   & & 0 \\
    & \lambda & 1 &   &   \\
    &   & \ddots & \ddots &   \\
    &   &   & \lambda & \\
  0 &   &   &   & \lambda
\end{pmatrix}
\end{eqnarray} $$
</div>
</div>


2,771行目: 2,603行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf&_&_(-1)^{_i+j_}_\times_\\[5pt]\vbCrLf&_&_\quad\vbCrLf\begin{vmatrix}\vbCrLf\vbCrLf_a\_{1,1}_&_\ldots_&_a\_{1,j-1}_&_a\_{1,j+1}_&_\ldots_&_a\_{1,n}_\\\vbCrLf_\vdots_&_\ddots_&_\vdots_&_\vdots_&_\ddots_&_\vdots_\\\vbCrLf_a\_{i-1,1}_&_\ldots_&_a\_{i-1,_j-1}_&_a\_{i-1,_j+1}_&_\ldots_&_a\_{i-1,_n}_\\\vbCrLf_a\_{i+1,1}_&_\ldots_&_a\_{i+1,_j-1}_&_a\_{i+1,_j+1}_&_\ldots_&_a\_{i+1,_n}_\\\vbCrLf_\vdots_&_\ddots_&_\vdots_&_\vdots_&_\ddots_&_\vdots_\\\vbCrLf_a\_{n,1}_&_\ldots_&_a\_{n,_j-1}_&_a\_{n,_j+1}_&_\ldots_&_a\_{n,_n}\vbCrLf\vbCrLf\end{vmatrix}\vbCrLf\end{eqnarray}" style="width: 25.107em; display: inline-block;"><span style="display: inline-block; position: relative; width: 19.739em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-3.628em, 1019.64em, 7.314em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 19.432em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(1.792em, 1000em, 7.774em, -999.997em); top: -6.644em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -8.69em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.014em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.649em;"></span></span><span style="position: absolute; clip: rect(1.792em, 1000em, 7.774em, -999.997em); top: -6.644em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -8.69em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.014em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.649em;"></span></span><span style="position: absolute; clip: rect(5.883em, 1019.02em, 16.824em, -999.997em); top: -11.604em; left: 0.309em;"><span style="display: inline-block; position: relative; width: 19.125em; height: 0px;"><span style="position: absolute; clip: rect(2.968em, 1003.38em, 4.297em, -999.997em); top: -8.69em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.26em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.412em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">×</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(4.911em, 1019.02em, 13.859em, -999.997em); top: -8.638em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 1.127em; display: inline-block; overflow: hidden;"></span><span class="mrow"><span class="mo" style="vertical-align: 4.553em;"><span style="display: inline-block; position: relative; width: 0.207em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.168em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: 4.655em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.452em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -1.787em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -1.071em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -0.355em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 0.36em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 1.076em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 1.792em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 2.508em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 3.224em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 3.94em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mtable"><span style="display: inline-block; position: relative; width: 17.233em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(4.911em, 1002.15em, 13.45em, -999.997em); top: -9.252em; left: 0em;"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.4em, -999.997em); top: -7.769em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -6.184em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.4em, -999.997em); top: -4.753em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.4em, -999.997em); top: -3.219em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -1.685em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.4em, -999.997em); top: -0.202em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 9.257em;"></span></span><span style="position: absolute; clip: rect(4.604em, 1000.77em, 12.581em, -999.997em); top: -8.638em; left: 3.275em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -7.769em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -6.184em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -4.753em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -1.685em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -0.202em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 8.644em;"></span></span><span style="position: absolute; clip: rect(4.911em, 1002.82em, 13.501em, -999.997em); top: -9.252em; left: 5.269em;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.451em, -999.997em); top: -7.769em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -6.184em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.82em, 4.451em, -999.997em); top: -4.753em; left: 50%; margin-left: -1.378em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.82em, 4.451em, -999.997em); top: -3.219em; left: 50%; margin-left: -1.378em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -1.685em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.451em, -999.997em); top: -0.202em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 9.257em;"></span></span><span style="position: absolute; clip: rect(4.911em, 1002.82em, 13.501em, -999.997em); top: -9.252em; left: 9.155em;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.451em, -999.997em); top: -7.769em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -6.184em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.82em, 4.451em, -999.997em); top: -4.753em; left: 50%; margin-left: -1.378em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.82em, 4.451em, -999.997em); top: -3.219em; left: 50%; margin-left: -1.378em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -1.685em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.451em, -999.997em); top: -0.202em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑗<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 9.257em;"></span></span><span style="position: absolute; clip: rect(4.604em, 1000.77em, 12.581em, -999.997em); top: -8.638em; left: 13.092em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -7.769em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -6.184em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -4.753em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.62em, 4.144em, -999.997em); top: -1.685em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000.77em, 4.144em, -999.997em); top: -0.202em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 8.644em;"></span></span><span style="position: absolute; clip: rect(4.911em, 1002.15em, 13.45em, -999.997em); top: -9.252em; left: 15.086em;"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.4em, -999.997em); top: -7.769em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -6.184em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.4em, -999.997em); top: -4.753em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1002.15em, 4.4em, -999.997em); top: -3.219em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 2.15em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑖</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.21em, 4.246em, -999.997em); top: -1.685em; left: 50%; margin-left: -0.151em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.4em, -999.997em); top: -0.202em; left: 50%; margin-left: -0.713em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">,</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 9.257em;"></span></span></span></span><span class="mo" style="vertical-align: 4.553em;"><span style="display: inline-block; position: relative; width: 0.207em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.168em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: 4.655em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.452em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -1.787em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -1.071em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -0.355em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 0.36em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 1.076em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 1.792em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 2.508em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 3.224em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: 3.94em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 9.615em;"></span></span></span><span style="display: inline-block; width: 0px; height: 11.609em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -6.49em; border-left: 0px solid; width: 0px; height: 13.575em;"></span></span></span></div>
& & (-1)^{ i+j } \times \\[5pt]
& & \quad
\begin{vmatrix}
  a_{1,1} & \ldots & a_{1,j-1} & a_{1,j+1} & \ldots & a_{1,n} \\
  \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\
  a_{i-1,1} & \ldots & a_{i-1, j-1} & a_{i-1, j+1} & \ldots & a_{i-1, n} \\
  a_{i+1,1} & \ldots & a_{i+1, j-1} & a_{i+1, j+1} & \ldots & a_{i+1, n} \\
  \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\
  a_{n,1} & \ldots & a_{n, j-1} & a_{n, j+1} & \ldots & a_{n, n}
\end{vmatrix}
\end{eqnarray} $$
</div>
</div>


2,797行目: 2,618行目:
\end{array}
\end{array}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{array}{ccc}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{array}{ccc}\vbCrLf\vbCrLf_xxx_&_yyy_&_zzz_\\\vbCrLf_1___&_2___&_3\vbCrLf\vbCrLf\end{array}" style="width: 8.132em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.394em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.463em, 1006.39em, 3.224em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 6.087em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.712em, 1001.33em, 4.911em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.33em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.712em, 1001.33em, 4.911em, -999.997em); top: -3.986em; left: 2.457em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.33em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.712em, 1001.18em, 4.911em, -999.997em); top: -3.986em; left: 4.911em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1001.18em, 4.246em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.295em; border-left: 0px solid; width: 0px; height: 3.25em;"></span></span></span></div>
  xxx & yyy & zzz \\
  1  & & 3
\end{array} $$
</div>
</div>


2,812行目: 2,630行目:
\end{array}
\end{array}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{array}{|c|c|c|}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{array}{|c|c|c|}\vbCrLf\vbCrLf_xxx_&_yyy_&_zzz_\\\vbCrLf_1___&_2___&_3_\\\vbCrLf\vbCrLf\end{array}" style="width: 9.104em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.161em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.156em, 1007.16em, 3.582em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 7.161em; height: 0px;"><span  style="border-width: 1.7px 0.105em; border-style: none solid; border-color: initial; border-image: initial; display: inline-block; overflow: hidden; width: 7.007em; height: 3.121em; vertical-align: -0.1em; position: absolute; top: -1.787em; left: 0em;"></span><span style="position: absolute; clip: rect(2.099em, 1006.55em, 5.371em, -999.997em); top: -3.986em; left: 0.105em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 7.007em; height: 0px;"><span style="position: absolute; clip: rect(2.712em, 1001.33em, 4.911em, -999.997em); top: -3.986em; left: 0.463em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.33em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.712em, 1001.33em, 4.911em, -999.997em); top: -3.986em; left: 2.917em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.33em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.712em, 1001.18em, 4.911em, -999.997em); top: -3.986em; left: 5.371em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1001.18em, 4.246em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-left: 1.3px solid; width: 0px; height: 2.968em; position: absolute; top: -1.736em; left: 2.355em; border-top-style: solid; border-right-style: solid; border-bottom-style: solid;"></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-left: 1.3px solid; width: 0px; height: 2.968em; position: absolute; top: -1.736em; left: 4.809em; border-top-style: solid; border-right-style: solid; border-bottom-style: solid;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.75em; border-left: 0px solid; width: 0px; height: 4.094em;"></span></span></span></div>
  xxx & yyy & zzz \\
  1  & & 3 \\
\end{array} $$
</div>
</div>


2,830行目: 2,645行目:
\end{array}
\end{array}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{array}{ccc}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{array}{ccc}\vbCrLf\vbCrLf_\hline\vbCrLf_xxx_&_yyy_&_zzz_\\\vbCrLf_\hline\vbCrLf_1___&_2___&_3_\\\vbCrLf_\hline\vbCrLf\vbCrLf\end{array}" style="width: 9.104em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.161em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.156em, 1007.16em, 3.582em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 7.161em; height: 0px;"><span  style="border-width: 0.105em 1.7px; border-style: solid none; border-color: initial; border-image: initial; display: inline-block; overflow: hidden; width: 7.161em; height: 2.968em; vertical-align: -0.1em; position: absolute; top: -1.787em; left: 0em;"></span><span style="position: absolute; clip: rect(2.099em, 1007.01em, 5.371em, -999.997em); top: -3.986em; left: 0.105em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 7.007em; height: 0px;"><span style="position: absolute; clip: rect(2.712em, 1001.33em, 4.911em, -999.997em); top: -3.986em; left: 0.463em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.33em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.712em, 1001.33em, 4.911em, -999.997em); top: -3.986em; left: 2.917em;"><span style="display: inline-block; position: relative; width: 1.332em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.33em, 4.349em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.662em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.712em, 1001.18em, 4.911em, -999.997em); top: -3.986em; left: 5.371em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1001.18em, 4.246em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑧</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.219em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 7.007em; height: 0px; position: absolute; top: -0.304em; left: 0em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.75em; border-left: 0px solid; width: 0px; height: 4.094em;"></span></span></span></div>
  \hline
  xxx & yyy & zzz \\
  \hline
  1  & & 3 \\
  \hline
\end{array} $$
</div>
</div>


2,851行目: 2,660行目:
\end{array}
\end{array}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{array}{c|ccccc}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{array}{c|ccccc}\vbCrLf\vbCrLf_x_____&_\cdots_&_-1_&_\cdots_&_1_&_\cdots_\\_\vbCrLf_\hline\vbCrLf_f’(x)_&_+_&_0_&_–_&_0_&_+_\\_\vbCrLf_\hline\vbCrLf_f(x)__&_\nearrow_&_e_&_\searrow_&_-e_&_\nearrow\vbCrLf\vbCrLf\end{array}" style="width: 17.54em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.808em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-0.509em, 1013.81em, 4.195em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 13.501em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.559em, 1002em, 6.394em, -999.997em); top: -4.548em; left: 0.463em;"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1002em, 4.349em, -999.997em); top: -3.934em; left: 50%; margin-left: -1.071em;"><span class="mtd"><span class="mrow"><span class="msup"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.343em; left: 0.514em;"><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Variants;">′</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.54em, 4.349em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.816em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.156em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.553em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.77em, 5.934em, -999.997em); top: -4.241em; left: 3.684em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.77em, 3.94em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.304em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">+</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↗</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.246em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1001.08em, 6.292em, -999.997em); top: -4.599em; left: 5.678em;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.08em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.202em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.303em, 1000.77em, 5.831em, -999.997em); top: -4.19em; left: 7.979em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.77em, 3.94em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.51em, 3.94em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">–</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↘</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.195em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1001.08em, 6.292em, -999.997em); top: -4.599em; left: 9.973em;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">0</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1001.08em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.56em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">−</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑒</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.604em;"></span></span><span style="position: absolute; clip: rect(2.355em, 1000.77em, 5.934em, -999.997em); top: -4.241em; left: 12.223em;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.77em, 3.94em, -999.997em); top: -5.417em; left: 50%; margin-left: -0.406em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -3.934em; left: 50%; margin-left: -0.304em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">+</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.326em, 1000.57em, 4.144em, -999.997em); top: -2.503em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↗</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.246em;"></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-left: 1.3px solid; width: 0px; height: 4.4em; position: absolute; top: -2.452em; left: 3.121em; border-top-style: solid; border-right-style: solid; border-bottom-style: solid;"></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 13.501em; height: 0px; position: absolute; top: -1.02em; left: 0em;"></span><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 13.501em; height: 0px; position: absolute; top: 0.412em; left: 0em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.529em; border-left: 0px solid; width: 0px; height: 5.718em;"></span></span></span></div>
  x    & \cdots & -1 & \cdots & 1 & \cdots \\  
  \hline
  f’(x) & + & 0 & & 0 & + \\  
  \hline
  f(x) & \nearrow & e & \searrow & -e & \nearrow
\end{array} $$
</div>
</div>


2,874行目: 2,677行目:
\end{CD}
\end{CD}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \require{AMScd}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\require{AMScd}\vbCrLf\begin{CD}\vbCrLfA_@\&gt;{f}\&gt;\&gt;_B\\\vbCrLf@V{gg}VV_{\large\circlearrowleft}_@VV{hh}V\\\vbCrLfC_@\&gt;\&gt;{k}\&gt;_D\vbCrLf\end{CD}" style="width: 9.053em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.11em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-1.429em, 1007.11em, 5.116em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 6.803em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.224em, 1000.67em, 9.001em, -999.997em); top: -6.44em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px;"><span style="position: absolute; clip: rect(2.866em, 1000.62em, 4.349em, -999.997em); top: -6.082em; left: 50%; margin-left: -0.304em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.61em, 1000.46em, 4.86em, -999.997em); top: -4.088em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.531em, 1000.67em, 4.297em, -999.997em); top: -3.986em; left: -0.713em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑔</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑔</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span></span><span class="mo" style="vertical-align: 1.23em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.628em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -1.992em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.423em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.168em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.963em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.758em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.554em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.349em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.866em, 1000.67em, 4.349em, -999.997em); top: -1.838em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.445em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1003.74em, 10.28em, -999.997em); top: -7.258em; left: 1.23em;"><span style="display: inline-block; position: relative; width: 3.684em; height: 0px;"><span style="position: absolute; clip: rect(2.559em, 1003.74em, 4.093em, -999.997em); top: -6.082em; left: 50%; margin-left: -1.838em;"><span class="mtd" style=""><span class="mrow"><span class="munderover" style=""><span style="display: inline-block; position: relative; width: 3.735em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1003.74em, 4.093em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 3.735em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 3.326em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.514em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.718em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.923em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.127em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.332em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.536em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.741em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.945em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.15em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.355em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.559em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.712em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.917em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 3.121em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.62em, 4.297em, -999.997em); top: -4.701em; left: 1.434em;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.31em, 4.297em, -999.997em); top: -4.088em; left: 0.309em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑓<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.121em, 1000.87em, 4.144em, -999.997em); top: -4.088em; left: 50%; margin-left: -0.509em;"><span class="mtd"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="mo" style="font-size: 135%; font-family: GyreTermesMathJax_Main;">↺</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1003.74em, 4.86em, -999.997em); top: -1.838em; left: 50%; margin-left: -1.838em;"><span class="mtd" style=""><span class="mrow"><span class="munderover" style=""><span style="display: inline-block; position: relative; width: 3.735em; height: 0px;"><span style="position: absolute; clip: rect(3.428em, 1003.74em, 4.093em, -999.997em); top: -3.986em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 3.735em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 3.326em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.514em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.718em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.923em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.127em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.332em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.536em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.741em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 1.945em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.15em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.355em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.559em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.712em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.917em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 3.121em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.67em, 4.246em, -999.997em); top: -3.372em; left: 1.434em;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.31em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑘<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1003.43em, 4.144em, -999.997em); top: -4.65em; left: 0.003em;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 3.684em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1003.12em, 4.144em, -999.997em); top: -4.088em; left: 0.309em;"><span class="mrow"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 3.121em; display: inline-block; overflow: hidden;"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.263em;"></span></span><span style="position: absolute; clip: rect(3.019em, 1001.23em, 8.234em, -999.997em); top: -5.929em; left: 5.525em;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -6.082em; left: 50%; margin-left: -0.304em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.61em, 1001.23em, 4.86em, -999.997em); top: -4.088em; left: 50%; margin-left: -0.253em;"><span class="mtd"><span class="mrow"><span class="mrow"><span class="mo" style="vertical-align: 1.23em;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.628em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -1.992em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.423em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.168em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.963em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.758em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.554em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -2.349em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.72em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">ℎ</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">ℎ</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.72em, 4.144em, -999.997em); top: -1.838em; left: 50%; margin-left: -0.355em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.934em;"></span></span><span style="position: absolute; clip: rect(3.735em, 1000em, 4.042em, -999.997em); top: -3.986em; left: 6.803em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -4.088em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.698em; border-left: 0px solid; width: 0px; height: 8.12em;"></span></span></span></div>
\begin{CD}
A @>{f}>> B\\
@V{gg}VV {\large\circlearrowleft} @VV{hh}V\\
C @>>{k}> D
\end{CD} $$
</div>
</div>


2,891行目: 2,689行目:
<code class="tex">| x |
<code class="tex">| x |
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ | x | $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_|_x_|" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,900行目: 2,698行目:
<code class="tex">\vert x \vert
<code class="tex">\vert x \vert
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vert x \vert $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vert_x_\vert" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">|</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,909行目: 2,707行目:
<code class="tex">\{ x \mid x \in A \}
<code class="tex">\{ x \mid x \in A \}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \{ x \mid x \in A \} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\{_x_\mid_x_\in_A_\}" style="width: 5.627em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.4em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1004.3em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∣</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐴</span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,918行目: 2,716行目:
<code class="tex">\Vert x \Vert
<code class="tex">\Vert x \Vert
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Vert x \Vert $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Vert_x_\Vert" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.02em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">‖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">‖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,927行目: 2,725行目:
<code class="tex">AB \parallel CD
<code class="tex">AB \parallel CD
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ AB \parallel CD $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_AB_\parallel_CD" style="width: 4.553em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.582em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.58em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">∥</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.309em;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,936行目: 2,734行目:
<code class="tex">\overline{ A }
<code class="tex">\overline{ A }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overline{ A } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overline{_A_}" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.025em, 1000.62em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.786em, 1000.62em, 4.246em, -999.997em); top: -4.855em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; top: -3.986em; left: 0em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.514em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.054em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.207em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.258em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.309em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.36em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.463em;"><span style="font-size: 70.7%; font-family: GyreTermesMathJax_Size6;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


2,945行目: 2,743行目:
<code class="tex">\bar{ A }
<code class="tex">\bar{ A }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bar{ A } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bar{_A_}" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.076em, 1000.57em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.31em, 3.582em, -999.997em); top: -4.241em; left: 0.156em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">¯</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


2,954行目: 2,752行目:
<code class="tex">\underline{ A }
<code class="tex">\underline{ A }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \underline{ A } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\underline{_A_}" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.62em, 2.508em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.57em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.888em, 1000.62em, 4.246em, -999.997em); top: -3.832em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0.463em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.105em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.207em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.36em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


2,963行目: 2,761行目:
<code class="tex">/
<code class="tex">/
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ / $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_/" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.36em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">/</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


2,972行目: 2,770行目:
<code class="tex">\backslash
<code class="tex">\backslash
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \backslash $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\backslash" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.57em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


2,981行目: 2,779行目:
<code class="tex">\diagdown
<code class="tex">\diagdown
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \diagdown $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\diagdown" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.46em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: italic; font-weight: normal;">╲</span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


2,990行目: 2,788行目:
<code class="tex">\diagup
<code class="tex">\diagup
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \diagup $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\diagup" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.46em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: italic; font-weight: normal;">╱</span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


2,999行目: 2,797行目:
<code class="tex">\cancel{a}
<code class="tex">\cancel{a}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cancel{a} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cancel{a}" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1001.13em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.076em; vertical-align: -0.1em; position: absolute; top: -0.764em; left: 0em;"></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -1.992em; left: 0em;"><svg style="width: 1.127em; height: 1.076em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="19.291522250000003" x2="20.230306249999995" y2="1.6502062499999999"></line></g></svg><span style="display: inline-block; width: 0px; height: 2.303em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
</div>
</div>


3,008行目: 2,806行目:
<code class="tex">\bcancel{a}
<code class="tex">\bcancel{a}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bcancel{a} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bcancel{a}" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1001.13em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.076em; vertical-align: -0.1em; position: absolute; top: -0.764em; left: 0em;"></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -1.992em; left: 0em;"><svg style="width: 1.127em; height: 1.076em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="1.6502062499999999" x2="20.230306249999995" y2="19.291522250000003"></line></g></svg><span style="display: inline-block; width: 0px; height: 2.303em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
</div>
</div>


3,017行目: 2,815行目:
<code class="tex">\xcancel{a}
<code class="tex">\xcancel{a}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \xcancel{a} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\xcancel{a}" style="width: 1.434em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1001.13em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.076em; vertical-align: -0.1em; position: absolute; top: -0.764em; left: 0em;"></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -1.992em; left: 0em;"><svg style="width: 1.127em; height: 1.076em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="19.291522250000003" x2="20.230306249999995" y2="1.6502062499999999"></line><line x1="1" y1="1.6502062499999999" x2="20.230306249999995" y2="19.291522250000003"></line></g></svg><span style="display: inline-block; width: 0px; height: 2.303em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.497em;"></span></span></span></div>
</div>
</div>


3,026行目: 2,824行目:
<code class="tex">\cancelto{A}{a}
<code class="tex">\cancelto{A}{a}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cancelto{A}{a} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cancelto{A}{a}" style="width: 2.099em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.872em, 1001.64em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msup"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px;"><span style="position: absolute; clip: rect(3.07em, 1001.13em, 4.451em, -999.997em); top: -3.986em; left: 0em;"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.076em; vertical-align: -0.1em; position: absolute; top: -0.764em; left: 0em;"></span><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -1.992em; left: 0em;"><svg style="width: 1.127em; height: 1.076em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="19.291522250000003" x2="15.366234006457614" y2="6.2701842654395605"></line><polygon points="21.055409374999996,0.8251031249999999 9.816541053973983,5.352833115032296 15.366234006457614,6.2701842654395605 16.039490928762053,11.85474782193788 21.055409374999996,0.8251031249999999" fill="currentColor" stroke="none"></polygon></g></svg><span style="display: inline-block; width: 0px; height: 2.303em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.446em; left: 1.127em;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.088em; left: 0em;"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.886em;"></span></span></span></div>
</div>
</div>


3,037行目: 2,835行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\frac{\cancel{2}}{\cancel{6}}=\frac{1}{3}\vbCrLf\end{eqnarray}" style="width: 5.013em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.94em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.156em, 1003.94em, 3.531em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 3.633em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.099em, 1003.63em, 5.473em, -999.997em); top: -4.037em; left: 0em;"><span style="display: inline-block; position: relative; width: 3.633em; height: 0px;"><span style="position: absolute; clip: rect(2.15em, 1003.63em, 5.473em, -999.997em); top: -4.037em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(2.866em, 1001.13em, 4.451em, -999.997em); top: -4.753em; left: 50%; margin-left: -0.56em;"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.281em; vertical-align: -0.1em; position: absolute; top: -0.969em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -2.196em; left: 0em;"><svg style="width: 1.127em; height: 1.281em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="23.67251425" x2="20.230306249999995" y2="1.6502062499999999"></line></g></svg><span style="display: inline-block; width: 0px; height: 2.508em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.866em, 1001.13em, 4.451em, -999.997em); top: -3.014em; left: 50%; margin-left: -0.56em;"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.332em; vertical-align: -0.1em; position: absolute; top: -0.969em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -2.247em; left: 0em;"><svg style="width: 1.127em; height: 1.332em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="24.102790249999998" x2="20.230306249999995" y2="1.6502062499999999"></line></g></svg><span style="display: inline-block; width: 0px; height: 2.559em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.23em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.23em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="mfrac" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.042em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.042em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.685em; border-left: 0px solid; width: 0px; height: 4.029em;"></span></span></span></div>
\frac{\cancel{2}}{\cancel{6}}=\frac{1}{3}
\end{eqnarray} $$
</div>
</div>


3,050行目: 2,846行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\frac{1}{\cancel{3}}_\times_\frac{\cancelto{2}{6}}{5}\vbCrLf\end{eqnarray}" style="width: 6.036em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.758em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.003em, 1004.76em, 3.684em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 4.451em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.303em, 1004.45em, 5.985em, -999.997em); top: -4.395em; left: 0em;"><span style="display: inline-block; position: relative; width: 4.451em; height: 0px;"><span style="position: absolute; clip: rect(2.15em, 1004.45em, 5.831em, -999.997em); top: -4.241em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.866em, 1001.13em, 4.451em, -999.997em); top: -3.014em; left: 50%; margin-left: -0.56em;"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.332em; vertical-align: -0.1em; position: absolute; top: -0.969em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -2.247em; left: 0em;"><svg style="width: 1.127em; height: 1.332em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="23.94632625" x2="20.230306249999995" y2="1.6502062499999999"></line></g></svg><span style="display: inline-block; width: 0px; height: 2.559em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.23em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.23em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">×</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.69em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(2.508em, 1001.54em, 4.451em, -999.997em); top: -4.753em; left: 50%; margin-left: -0.764em;"><span class="msup"><span style="display: inline-block; position: relative; width: 1.536em; height: 0px;"><span style="position: absolute; clip: rect(2.866em, 1001.13em, 4.451em, -999.997em); top: -3.986em; left: 0em;"><span class="menclose"><span style="display: inline-block; position: relative; width: 1.127em; height: 0px;"><span  style="border: 1.7px none; display: inline-block; overflow: hidden; width: 1.127em; height: 1.332em; vertical-align: -0.1em; position: absolute; top: -0.969em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -2.247em; left: 0em;"><svg style="width: 1.127em; height: 1.332em;"><g fill="none" stroke="currentColor" stroke-width="1.6502062499999999"><line x1="1" y1="24.102790249999998" x2="15.956468103337548" y2="6.826471544630418"></line><polygon points="21.055409374999996,0.8251031249999999 10.3418541756934,6.4848058549506264 15.956468103337548,6.826471544630418 17.20056094098531,12.312167308279141 21.055409374999996,0.8251031249999999" fill="currentColor" stroke="none"></polygon></g></svg><span style="display: inline-block; width: 0px; height: 2.559em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.701em; left: 1.127em;"><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.36em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.36em, 4.144em, -999.997em); top: -4.088em; left: 0em;"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">5</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1001.69em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.69em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.4em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.4em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.88em; border-left: 0px solid; width: 0px; height: 4.419em;"></span></span></span></div>
\frac{1}{\cancel{3}} \times \frac{\cancelto{2}{6}}{5}
\end{eqnarray} $$
</div>
</div>


3,061行目: 2,855行目:
<code class="tex">\llcorner
<code class="tex">\llcorner
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \llcorner $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\llcorner" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.911em, 1000.31em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Symbols;">⌞</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 0.458em;"></span></span></span></div>
</div>
</div>


3,070行目: 2,864行目:
<code class="tex">\lrcorner
<code class="tex">\lrcorner
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lrcorner $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lrcorner" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.911em, 1000.31em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Symbols;">⌟</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 0.458em;"></span></span></span></div>
</div>
</div>


3,079行目: 2,873行目:
<code class="tex">\ulcorner
<code class="tex">\ulcorner
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ulcorner $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ulcorner" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.31em, 4.911em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Symbols;">⌜</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.458em; border-left: 0px solid; width: 0px; height: 0.458em;"></span></span></span></div>
</div>
</div>


3,088行目: 2,882行目:
<code class="tex">\urcorner
<code class="tex">\urcorner
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \urcorner $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\urcorner" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.31em, 4.911em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Symbols;">⌝</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.458em; border-left: 0px solid; width: 0px; height: 0.458em;"></span></span></span></div>
</div>
</div>


3,100行目: 2,894行目:
<code class="tex">\leftarrow
<code class="tex">\leftarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \leftarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\leftarrow" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">←</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,109行目: 2,903行目:
<code class="tex">\longleftarrow
<code class="tex">\longleftarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \longleftarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\longleftarrow" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1001.08em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,118行目: 2,912行目:
<code class="tex">\rightarrow
<code class="tex">\rightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \rightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\rightarrow" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">→</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,127行目: 2,921行目:
<code class="tex">\longrightarrow
<code class="tex">\longrightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \longrightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\longrightarrow" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1001.08em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟶</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,136行目: 2,930行目:
<code class="tex">\uparrow
<code class="tex">\uparrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \uparrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\uparrow" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.41em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↑</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,145行目: 2,939行目:
<code class="tex">\downarrow
<code class="tex">\downarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \downarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\downarrow" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.41em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↓</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,154行目: 2,948行目:
<code class="tex">\leftrightarrow
<code class="tex">\leftrightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \leftrightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\leftrightarrow" style="width: 1.332em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.92em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↔</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,163行目: 2,957行目:
<code class="tex">\longleftrightarrow
<code class="tex">\longleftrightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \longleftrightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\longleftrightarrow" style="width: 1.792em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1001.28em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,172行目: 2,966行目:
<code class="tex">\updownarrow
<code class="tex">\updownarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \updownarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\updownarrow" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.41em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↕</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


3,181行目: 2,975行目:
<code class="tex">\Leftarrow
<code class="tex">\Leftarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Leftarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Leftarrow" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⇐</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


3,190行目: 2,984行目:
<code class="tex">\Longleftarrow
<code class="tex">\Longleftarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Longleftarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Longleftarrow" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1001.08em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟸</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


3,199行目: 2,993行目:
<code class="tex">\Rightarrow
<code class="tex">\Rightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Rightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Rightarrow" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⇒</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


3,208行目: 3,002行目:
<code class="tex">\Longrightarrow
<code class="tex">\Longrightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Longrightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Longrightarrow" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1001.08em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟹</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


3,217行目: 3,011行目:
<code class="tex">\Uparrow
<code class="tex">\Uparrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Uparrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Uparrow" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.51em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⇑</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,226行目: 3,020行目:
<code class="tex">\Downarrow
<code class="tex">\Downarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Downarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Downarrow" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.51em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⇓</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,235行目: 3,029行目:
<code class="tex">\Leftrightarrow
<code class="tex">\Leftrightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Leftrightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Leftrightarrow" style="width: 1.332em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.025em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.92em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⇔</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


3,244行目: 3,038行目:
<code class="tex">\Longleftrightarrow
<code class="tex">\Longleftrightarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Longleftrightarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Longleftrightarrow" style="width: 1.792em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.383em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1001.28em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟺</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


3,253行目: 3,047行目:
<code class="tex">\Updownarrow
<code class="tex">\Updownarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Updownarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Updownarrow" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.51em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⇕</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


3,262行目: 3,056行目:
<code class="tex">\nearrow
<code class="tex">\nearrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \nearrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\nearrow" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↗</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,271行目: 3,065行目:
<code class="tex">\searrow
<code class="tex">\searrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \searrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\searrow" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↘</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,280行目: 3,074行目:
<code class="tex">\nwarrow
<code class="tex">\nwarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \nwarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\nwarrow" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,289行目: 3,083行目:
<code class="tex">\swarrow
<code class="tex">\swarrow
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \swarrow $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\swarrow" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↙</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,298行目: 3,092行目:
<code class="tex">\mapsto
<code class="tex">\mapsto
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mapsto $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mapsto" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↦</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,307行目: 3,101行目:
<code class="tex">\longmapsto
<code class="tex">\longmapsto
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \longmapsto $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\longmapsto" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1001.08em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟼</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.588em;"></span></span></span></div>
</div>
</div>


3,316行目: 3,110行目:
<code class="tex">\vec{ a }
<code class="tex">\vec{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vec{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vec{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


3,325行目: 3,119行目:
<code class="tex">\overrightarrow{ AB }
<code class="tex">\overrightarrow{ AB }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overrightarrow{ AB } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overrightarrow{_AB_}" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.77em, 1001.23em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.18em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1001.23em, 4.093em, -999.997em); top: -4.701em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0.872em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.463em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.667em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.627em;"></span></span></span></div>
</div>
</div>


3,334行目: 3,128行目:
<code class="tex">\overleftarrow{ AB }
<code class="tex">\overleftarrow{ AB }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overleftarrow{ AB } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overleftarrow{_AB_}" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.77em, 1001.23em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.18em, 4.144em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1001.23em, 4.093em, -999.997em); top: -4.701em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0.872em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.309em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.463em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.667em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.627em;"></span></span></span></div>
</div>
</div>


3,343行目: 3,137行目:
<code class="tex">\circlearrowright
<code class="tex">\circlearrowright
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \circlearrowright $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\circlearrowright" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↻</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.847em;"></span></span></span></div>
</div>
</div>


3,352行目: 3,146行目:
<code class="tex">\circlearrowleft
<code class="tex">\circlearrowleft
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \circlearrowleft $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\circlearrowleft" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">↺</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.847em;"></span></span></span></div>
</div>
</div>


3,364行目: 3,158行目:
<code class="tex">( x )
<code class="tex">( x )
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ ( x ) $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_(_x_)" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">(</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,373行目: 3,167行目:
<code class="tex">[ x ]
<code class="tex">[ x ]
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ [ x ] $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_[_x_]" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,382行目: 3,176行目:
<code class="tex">\lbrack x \rbrack
<code class="tex">\lbrack x \rbrack
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lbrack x \rbrack $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lbrack_x_\rbrack" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">[</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">]</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,391行目: 3,185行目:
<code class="tex">\lceil x \rfloor
<code class="tex">\lceil x \rfloor
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lceil x \rfloor $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lceil_x_\rfloor" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌋</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,400行目: 3,194行目:
<code class="tex">\lfloor x \rceil
<code class="tex">\lfloor x \rceil
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lfloor x \rceil $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lfloor_x_\rceil" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌊</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⌉</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,409行目: 3,203行目:
<code class="tex">\{ x \}
<code class="tex">\{ x \}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \{ x \} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\{_x_\}" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,418行目: 3,212行目:
<code class="tex">\lbrace x \rbrace
<code class="tex">\lbrace x \rbrace
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lbrace x \rbrace $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lbrace_x_\rbrace" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.13em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">{</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,427行目: 3,221行目:
<code class="tex">\langle x \rangle
<code class="tex">\langle x \rangle
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \langle x \rangle $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\langle_x_\rangle" style="width: 1.536em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.179em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.08em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟨</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⟩</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,436行目: 3,230行目:
<code class="tex">\left[ \dfrac{ 1 }{ 2 } \right]
<code class="tex">\left[ \dfrac{ 1 }{ 2 } \right]
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \left[ \dfrac{ 1 }{ 2 } \right] $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\left[_\dfrac{_1_}{_2_}_\right]" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.684em, 1001.64em, 6.087em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mrow"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">[</span></span><span class="mstyle"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size5;">]</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.036em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
</div>
</div>


3,445行目: 3,239行目:
<code class="tex">\overbrace{ x + y + z }
<code class="tex">\overbrace{ x + y + z }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overbrace{ x + y + z } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overbrace{_x_+_y_+_z_}" style="width: 4.707em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.684em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.025em, 1003.68em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 3.684em; height: 0px;"><span style="position: absolute; clip: rect(3.326em, 1003.63em, 4.349em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑦</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑧</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1003.68em, 3.633em, -999.997em); top: -4.088em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 3.684em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 2.764em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0.923em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.463em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.303em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.562em;"></span></span></span></div>
</div>
</div>


3,454行目: 3,248行目:
<code class="tex">\overbrace{ a_1 + \cdots + a_n }^{ n }
<code class="tex">\overbrace{ a_1 + \cdots + a_n }^{ n }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \overbrace{ a_1 + \cdots + a_n }^{ n } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\overbrace{_a\_1_+_\cdots_+_a\_n_}^{_n_}" style="width: 6.496em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.412em, 1005.12em, 2.406em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px;"><span style="position: absolute; clip: rect(2.917em, 1005.12em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px;"><span style="position: absolute; clip: rect(3.326em, 1005.06em, 4.297em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⋯</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.07em, 1005.12em, 3.633em, -999.997em); top: -4.088em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 5.116em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 4.246em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 1.639em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.821em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 3.377em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.428em, 1000.36em, 4.144em, -999.997em); top: -5.11em; left: 2.355em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 2.276em;"></span></span></span></div>
</div>
</div>


3,463行目: 3,257行目:
<code class="tex">\underbrace{ x + y + z }
<code class="tex">\underbrace{ x + y + z }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \underbrace{ x + y + z } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\underbrace{_x_+_y_+_z_}" style="width: 4.707em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.684em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.434em, 1003.68em, 2.917em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 3.684em; height: 0px;"><span style="position: absolute; clip: rect(3.326em, 1003.63em, 4.349em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑦</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑧</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.888em, 1003.68em, 4.502em, -999.997em); top: -3.628em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 3.684em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 2.764em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0.923em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.463em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 2.303em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 1.627em;"></span></span></span></div>
</div>
</div>


3,472行目: 3,266行目:
<code class="tex">\underbrace{ a_1 + \cdots + a_n }_{ n }
<code class="tex">\underbrace{ a_1 + \cdots + a_n }_{ n }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \underbrace{ a_1 + \cdots + a_n }_{ n } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\underbrace{_a\_1_+_\cdots_+_a\_n_}\_{_n_}" style="width: 6.496em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.434em, 1005.12em, 3.684em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px;"><span style="position: absolute; clip: rect(3.326em, 1005.12em, 4.758em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 5.116em; height: 0px;"><span style="position: absolute; clip: rect(3.326em, 1005.06em, 4.297em, -999.997em); top: -3.986em; left: 0.003em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">⋯</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.888em, 1005.12em, 4.502em, -999.997em); top: -3.679em; left: 0em;"><span class="mo" style=""><span style="display: inline-block; position: relative; width: 5.116em; height: 0px;"><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 4.246em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; font-family: GyreTermesMathJax_Size6; top: -3.986em; left: 1.639em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 0.821em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="font-family: GyreTermesMathJax_Size6; position: absolute; top: -3.986em; left: 3.377em;"><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1000.36em, 4.246em, -999.997em); top: -2.707em; left: 2.355em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.88em; border-left: 0px solid; width: 0px; height: 2.536em;"></span></span></span></div>
</div>
</div>


3,484行目: 3,278行目:
<code class="tex">\cdot
<code class="tex">\cdot
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cdot $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cdot" style="width: 0.36em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.258em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.707em, 1000.16em, 5.116em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋅</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.198em; border-left: 0px solid; width: 0px; height: 0.263em;"></span></span></span></div>
</div>
</div>


3,493行目: 3,287行目:
<code class="tex">\cdots
<code class="tex">\cdots
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \cdots $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\cdots" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.707em, 1000.77em, 5.116em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋯</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.198em; border-left: 0px solid; width: 0px; height: 0.263em;"></span></span></span></div>
</div>
</div>


3,502行目: 3,296行目:
<code class="tex">\ldots
<code class="tex">\ldots
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ldots $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ldots" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.911em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">…</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.263em;"></span></span></span></div>
</div>
</div>


3,511行目: 3,305行目:
<code class="tex">\vdots
<code class="tex">\vdots
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vdots $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vdots" style="width: 0.36em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.258em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.16em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋮</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


3,520行目: 3,314行目:
<code class="tex">\ddots
<code class="tex">\ddots
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ddots $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ddots" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋱</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,529行目: 3,323行目:
<code class="tex">\dot{ a }
<code class="tex">\dot{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dot{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dot{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.21em, 3.582em, -999.997em); top: -4.037em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">˙</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,538行目: 3,332行目:
<code class="tex">\ddot{ a }
<code class="tex">\ddot{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ddot{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ddot{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.31em, 3.582em, -999.997em); top: -4.037em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">¨</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,550行目: 3,344行目:
<code class="tex">\circ
<code class="tex">\circ
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \circ $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\circ" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.36em, 5.218em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">∘</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.068em; border-left: 0px solid; width: 0px; height: 0.523em;"></span></span></span></div>
</div>
</div>


3,559行目: 3,353行目:
<code class="tex">\bullet
<code class="tex">\bullet
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bullet $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bullet" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.36em, 5.218em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">∙</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.068em; border-left: 0px solid; width: 0px; height: 0.523em;"></span></span></span></div>
</div>
</div>


3,568行目: 3,362行目:
<code class="tex">\bigcirc
<code class="tex">\bigcirc
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bigcirc $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bigcirc" style="width: 1.23em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.87em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">◯</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,577行目: 3,371行目:
<code class="tex">\oplus
<code class="tex">\oplus
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \oplus $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\oplus" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.72em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊕</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,586行目: 3,380行目:
<code class="tex">\ominus
<code class="tex">\ominus
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ominus $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ominus" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.72em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,595行目: 3,389行目:
<code class="tex">\otimes
<code class="tex">\otimes
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \otimes $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\otimes" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.72em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊗</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,604行目: 3,398行目:
<code class="tex">\odot
<code class="tex">\odot
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \odot $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\odot" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.72em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊙</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,616行目: 3,410行目:
<code class="tex">\triangle
<code class="tex">\triangle
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangle $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangle" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">△</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,625行目: 3,419行目:
<code class="tex">\triangledown
<code class="tex">\triangledown
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangledown $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangledown" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">▽</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,634行目: 3,428行目:
<code class="tex">\bigtriangleup
<code class="tex">\bigtriangleup
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bigtriangleup $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bigtriangleup" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">△</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,643行目: 3,437行目:
<code class="tex">\bigtriangledown
<code class="tex">\bigtriangledown
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bigtriangledown $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bigtriangledown" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.77em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">▽</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,652行目: 3,446行目:
<code class="tex">\triangleleft
<code class="tex">\triangleleft
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangleleft $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangleleft" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.46em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mo"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">◃</span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


3,661行目: 3,455行目:
<code class="tex">\lhd
<code class="tex">\lhd
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lhd $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lhd" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.62em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊲</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.847em;"></span></span></span></div>
</div>
</div>


3,670行目: 3,464行目:
<code class="tex">\triangleright
<code class="tex">\triangleright
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \triangleright $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\triangleright" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.46em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mo"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">▹</span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


3,679行目: 3,473行目:
<code class="tex">\rhd
<code class="tex">\rhd
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \rhd $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\rhd" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.62em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊳</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.847em;"></span></span></span></div>
</div>
</div>


3,688行目: 3,482行目:
<code class="tex">\unlhd
<code class="tex">\unlhd
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \unlhd $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\unlhd" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.62em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,697行目: 3,491行目:
<code class="tex">\unrhd
<code class="tex">\unrhd
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \unrhd $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\unrhd" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.62em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,706行目: 3,500行目:
<code class="tex">\blacktriangle
<code class="tex">\blacktriangle
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \blacktriangle $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\blacktriangle" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">▲</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,718行目: 3,512行目:
<code class="tex">\square
<code class="tex">\square
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \square $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\square" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">□</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,727行目: 3,521行目:
<code class="tex">\Box
<code class="tex">\Box
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Box $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Box" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">□</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,736行目: 3,530行目:
<code class="tex">\boxplus
<code class="tex">\boxplus
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boxplus $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boxplus" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊞</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,745行目: 3,539行目:
<code class="tex">\boxminus
<code class="tex">\boxminus
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boxminus $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boxminus" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊟</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,754行目: 3,548行目:
<code class="tex">\boxtimes
<code class="tex">\boxtimes
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boxtimes $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boxtimes" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊠</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,763行目: 3,557行目:
<code class="tex">\boxdot
<code class="tex">\boxdot
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boxdot $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boxdot" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⊡</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,772行目: 3,566行目:
<code class="tex">\blacksquare
<code class="tex">\blacksquare
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \blacksquare $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\blacksquare" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.502em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">■</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.782em;"></span></span></span></div>
</div>
</div>


3,781行目: 3,575行目:
<code class="tex">\diamond
<code class="tex">\diamond
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \diamond $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\diamond" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
</div>


3,790行目: 3,584行目:
<code class="tex">\Diamond
<code class="tex">\Diamond
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Diamond $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Diamond" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.46em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">◊</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,799行目: 3,593行目:
<code class="tex">\lozenge
<code class="tex">\lozenge
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lozenge $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lozenge" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1000.46em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">◊</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


3,808行目: 3,602行目:
<code class="tex">\blacklozenge
<code class="tex">\blacklozenge
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \blacklozenge $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\blacklozenge" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1000.41em, 2.508em, -999.997em); top: -2.145em; left: 0em;"><span class="mrow"><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: italic; font-weight: normal;">⧫</span></span></span><span style="display: inline-block; width: 0px; height: 2.15em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


3,817行目: 3,611行目:
<code class="tex">\boxed{ abc }
<code class="tex">\boxed{ abc }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \boxed{ abc } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\boxed{_abc_}" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.974em, 1002.05em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px;"><span  style="border: 0.105em solid; display: inline-block; overflow: hidden; width: 1.894em; height: 1.127em; vertical-align: -0.1em; position: absolute; top: -0.969em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1001.43em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.821em;"></span></span></span></div>
</div>
</div>


3,826行目: 3,620行目:
<code class="tex">\fbox{ abc }
<code class="tex">\fbox{ abc }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \fbox{ abc } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\fbox{_abc_}" style="width: 3.224em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.974em, 1002.51em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="menclose"><span style="display: inline-block; position: relative; width: 2.508em; height: 0px;"><span  style="border: 0.105em solid; display: inline-block; overflow: hidden; width: 2.355em; height: 1.127em; vertical-align: -0.1em; position: absolute; top: -0.969em; left: 0em;"></span><span style="position: absolute; clip: rect(3.173em, 1001.64em, 4.144em, -999.997em); top: -3.986em; left: 0.309em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">&nbsp;abc&nbsp;</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.821em;"></span></span></span></div>
</div>
</div>


3,835行目: 3,629行目:
<code class="tex">\bbox[yellow, 5pt, border: 2px dotted red]{abc}
<code class="tex">\bbox[yellow, 5pt, border: 2px dotted red]{abc}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bbox[yellow, 5pt, border: 2px dotted red]{abc} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bbox[yellow,_5pt,_border:_2px_dotted_red]{abc}" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.69em, 1002em, 3.991em, -999.997em); top: -3.168em; left: 0em;"><span class="mrow"><span  style="display: inline-block; background-color: yellow; width: 2.661em; height: 1.945em; vertical-align: -0.713em; margin-left: -0.049em; margin-right: -2.707em; border-width: 2px; border-style: dotted; border-color: red;"></span><span class="mstyle" style="padding-right: 0.105em;"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.43em, 4.144em, -999.997em); top: -3.986em; left: 0.565em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.173em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


3,847行目: 3,641行目:
<code class="tex">\ast
<code class="tex">\ast
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ast $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ast" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.41em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">∗</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
</div>


3,856行目: 3,650行目:
<code class="tex">\star
<code class="tex">\star
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \star $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\star" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.41em, 5.218em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋆</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.068em; border-left: 0px solid; width: 0px; height: 0.523em;"></span></span></span></div>
</div>
</div>


3,865行目: 3,659行目:
<code class="tex">\ltimes
<code class="tex">\ltimes
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ltimes $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ltimes" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋉</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
</div>


3,874行目: 3,668行目:
<code class="tex">\rtimes
<code class="tex">\rtimes
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \rtimes $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\rtimes" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋊</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
</div>


3,883行目: 3,677行目:
<code class="tex">\Join
<code class="tex">\Join
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Join $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Join" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.269em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">⋈</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.003em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
</div>


3,895行目: 3,689行目:
<code class="tex">\$
<code class="tex">\$
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \$ $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\$" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.46em, 5.422em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">$</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.192em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,904行目: 3,698行目:
<code class="tex">\And
<code class="tex">\And
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \And $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\And" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">&amp;</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,913行目: 3,707行目:
<code class="tex">\yen
<code class="tex">\yen
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \yen $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\yen" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">¥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,922行目: 3,716行目:
<code class="tex">\checkmark
<code class="tex">\checkmark
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \checkmark $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\checkmark" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">✓</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,931行目: 3,725行目:
<code class="tex">\diamondsuit
<code class="tex">\diamondsuit
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \diamondsuit $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\diamondsuit" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♢</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,940行目: 3,734行目:
<code class="tex">\heartsuit
<code class="tex">\heartsuit
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \heartsuit $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\heartsuit" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♡</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,949行目: 3,743行目:
<code class="tex">\clubsuit
<code class="tex">\clubsuit
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \clubsuit $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\clubsuit" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♣</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,958行目: 3,752行目:
<code class="tex">\spadesuit
<code class="tex">\spadesuit
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \spadesuit $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\spadesuit" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♠</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,967行目: 3,761行目:
<code class="tex">\flat
<code class="tex">\flat
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \flat $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\flat" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.31em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♭</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


3,976行目: 3,770行目:
<code class="tex">\natural
<code class="tex">\natural
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \natural $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\natural" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.31em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♮</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


3,985行目: 3,779行目:
<code class="tex">\sharp
<code class="tex">\sharp
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sharp $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sharp" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.41em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">♯</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


3,994行目: 3,788行目:
<code class="tex">\dagger
<code class="tex">\dagger
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dagger $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dagger" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.46em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">†</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


4,003行目: 3,797行目:
<code class="tex">\ddagger
<code class="tex">\ddagger
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ddagger $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ddagger" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.46em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mo" style="font-family: GyreTermesMathJax_Main;">‡</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


4,015行目: 3,809行目:
<code class="tex">aaa \ bbb
<code class="tex">aaa \ bbb
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ aaa \ bbb $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_aaa_\_bbb" style="width: 4.195em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.275em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1003.22em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mtext" style="font-family: GyreTermesMathJax_Main;">&nbsp;</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,024行目: 3,818行目:
<code class="tex">aaa \quad bbb
<code class="tex">aaa \quad bbb
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ aaa \quad bbb $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_aaa_\quad_bbb" style="width: 5.269em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.144em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1004.09em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 1.127em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,033行目: 3,827行目:
<code class="tex">aaa \qquad bbb
<code class="tex">aaa \qquad bbb
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ aaa \qquad bbb $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_aaa_\qquad_bbb" style="width: 6.701em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.269em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1005.22em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 2.252em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,042行目: 3,836行目:
<code class="tex">aaa \hspace{ 10pt } bbb
<code class="tex">aaa \hspace{ 10pt } bbb
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ aaa \hspace{ 10pt } bbb $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_aaa_\hspace{_10pt_}_bbb" style="width: 5.269em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.144em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1004.09em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mspace" style="height: 0em; vertical-align: 0em; width: 1.127em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,051行目: 3,845行目:
<code class="tex">aaa \! bbb
<code class="tex">aaa \! bbb
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ aaa \! bbb $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_aaa_\!_bbb" style="width: 3.582em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.815em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.76em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.202em;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,062行目: 3,856行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}  
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}_\vbCrLfaaa_\\_bbb\vbCrLf\end{eqnarray}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.514em, 1001.79em, 3.173em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.764em, 1001.49em, 4.86em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.144em, -999.997em); top: -4.599em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -3.27em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.231em; border-left: 0px solid; width: 0px; height: 3.12em;"></span></span></span></div>
aaa \\ bbb
\end{eqnarray} $$
</div>
</div>


4,075行目: 3,867行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}  
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}_\vbCrLfaaa_\\[5pt]_bbb\vbCrLf\end{eqnarray}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.258em, 1001.79em, 3.428em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(2.508em, 1001.49em, 5.167em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.485em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1001.49em, 4.144em, -999.997em); top: -4.906em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 4.144em, -999.997em); top: -2.963em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.555em; border-left: 0px solid; width: 0px; height: 3.834em;"></span></span></span></div>
aaa \\[5pt] bbb
\end{eqnarray} $$
</div>
</div>


4,090行目: 3,880行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf&_&_\frac{1}{2}_+\frac{1}{3}_+\frac{1}{6}_\\[_5pt_]\vbCrLf&=&_\frac{3}{6}_+\frac{2}{6}_+\frac{1}{6}_\\\vbCrLf&=&_1\vbCrLf\end{eqnarray}" style="width: 8.337em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.547em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(-1.48em, 1006.55em, 5.167em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 6.24em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.582em, 1000em, 8.644em, -999.997em); top: -5.775em; left: 0em;"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -6.031em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.116em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -1.276em; right: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.78em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1000.87em, 8.644em, -999.997em); top: -5.775em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.974em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -6.031em; left: 50%; margin-left: 0em;"><span class="mtd"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.479em, 1000.87em, 4.144em, -999.997em); top: -3.116em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="mi"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.479em, 1000.87em, 4.144em, -999.997em); top: -1.276em; left: 50%; margin-left: -0.458em;"><span class="mtd"><span class="mrow"><span class="mi"></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.78em;"></span></span><span style="position: absolute; clip: rect(3.582em, 1004.91em, 10.024em, -999.997em); top: -7.156em; left: 1.281em;"><span style="display: inline-block; position: relative; width: 4.911em; height: 0px;"><span style="position: absolute; clip: rect(2.508em, 1004.91em, 4.86em, -999.997em); top: -6.031em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(2.508em, 1004.91em, 4.86em, -999.997em); top: -3.116em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mfrac"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="mfrac" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; margin-right: 0.105em; margin-left: 0.105em;"><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -4.65em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.46em, 4.144em, -999.997em); top: -3.321em; left: 50%; margin-left: -0.253em;"><span class="mn" style="font-family: GyreTermesMathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(0.872em, 1000.62em, 1.23em, -999.997em); top: -1.276em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.616em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.076em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.41em, 4.144em, -999.997em); top: -1.276em; left: 0em;"><span class="mtd"><span class="mrow"><span class="mn" style="font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.161em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -3.763em; border-left: 0px solid; width: 0px; height: 8.185em;"></span></span></span></div>
& & \frac{1}{2} +\frac{1}{3} +\frac{1}{6} \\[ 5pt ]
&=& \frac{3}{6} +\frac{2}{6} +\frac{1}{6} \\
&=& 1
\end{eqnarray} $$
</div>
</div>


4,106行目: 3,892行目:
<code class="tex">\tiny{ abc ABC }
<code class="tex">\tiny{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \tiny{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\tiny{_abc_ABC_}" style="width: 2.406em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.894em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(2.815em, 1001.89em, 3.531em, -999.997em); top: -3.372em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 56.3%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 56.3%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 56.3%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 56.3%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 56.3%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 56.3%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.377em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.653em;"></span></span></span></div>
</div>
</div>


4,115行目: 3,901行目:
<code class="tex">\scriptsize{ abc ABC }
<code class="tex">\scriptsize{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \scriptsize{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\scriptsize{_abc_ABC_}" style="width: 3.326em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.61em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(3.531em, 1002.61em, 4.4em, -999.997em); top: -4.241em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 78.8%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 78.8%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 78.8%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 78.8%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 78.8%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 78.8%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.246em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.847em;"></span></span></span></div>
</div>
</div>


4,124行目: 3,910行目:
<code class="tex">\small{ abc ABC }
<code class="tex">\small{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \small{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\small{_abc_ABC_}" style="width: 4.042em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.173em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.195em, 1003.17em, 5.167em, -999.997em); top: -5.008em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 95.6%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 95.6%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 95.6%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 95.6%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 95.6%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 95.6%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.013em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,133行目: 3,919行目:
<code class="tex">\normalsize{ abc ABC }
<code class="tex">\normalsize{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \normalsize{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\normalsize{_abc_ABC_}" style="width: 4.758em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.735em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.758em, 1003.74em, 5.831em, -999.997em); top: -5.673em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 112.5%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 112.5%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 112.5%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 112.5%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 112.5%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 112.5%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.678em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


4,142行目: 3,928行目:
<code class="tex">\large{ abc ABC }
<code class="tex">\large{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \large{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\large{_abc_ABC_}" style="width: 5.729em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.502em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(5.525em, 1004.5em, 6.752em, -999.997em); top: -6.593em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 135%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 135%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 135%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 135%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 135%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 135%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.598em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></span></div>
</div>
</div>


4,151行目: 3,937行目:
<code class="tex">\Large{ abc ABC }
<code class="tex">\Large{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Large{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Large{_abc_ABC_}" style="width: 6.905em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.422em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(6.445em, 1005.42em, 7.928em, -999.997em); top: -7.718em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 162%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 162%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 162%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 162%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 162%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 162%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 7.723em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.562em;"></span></span></span></div>
</div>
</div>


4,160行目: 3,946行目:
<code class="tex">\LARGE{ abc ABC }
<code class="tex">\LARGE{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \LARGE{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\LARGE{_abc_ABC_}" style="width: 8.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.496em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(7.621em, 1006.5em, 9.308em, -999.997em); top: -9.099em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 194.6%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 194.6%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 194.6%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 194.6%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 194.6%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 194.6%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 9.104em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.886em;"></span></span></span></div>
</div>
</div>


4,169行目: 3,955行目:
<code class="tex">\huge{ abc ABC }
<code class="tex">\huge{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \huge{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\huge{_abc_ABC_}" style="width: 9.871em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.774em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(8.95em, 1007.77em, 10.893em, -999.997em); top: -10.684em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 232.9%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 232.9%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 232.9%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 232.9%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 232.9%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 232.9%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 10.689em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 2.211em;"></span></span></span></div>
</div>
</div>


4,178行目: 3,964行目:
<code class="tex">\Huge{ abc ABC }
<code class="tex">\Huge{ abc ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Huge{ abc ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Huge{_abc_ABC_}" style="width: 11.916em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.359em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(10.586em, 1009.36em, 12.836em, -999.997em); top: -12.627em; left: 0em;"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 280.1%; font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-size: 280.1%; font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-size: 280.1%; font-family: GyreTermesMathJax_Normal;">𝑐</span><span class="mi" style="font-size: 280.1%; font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-size: 280.1%; font-family: GyreTermesMathJax_Normal;">𝐵</span><span class="mi" style="font-size: 280.1%; font-family: GyreTermesMathJax_Normal;">𝐶<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 12.632em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 2.601em;"></span></span></span></div>
</div>
</div>


4,190行目: 3,976行目:
<code class="tex">\mathrm{ ABC }
<code class="tex">\mathrm{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathrm{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathrm{_ABC_}" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">A</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">B</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,199行目: 3,985行目:
<code class="tex">\mathtt{ ABC }
<code class="tex">\mathtt{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathtt{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathtt{_ABC_}" style="width: 2.303em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.792em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.451em, 1001.74em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙰</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙱</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙲</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


4,208行目: 3,994行目:
<code class="tex">\mathsf{ ABC }
<code class="tex">\mathsf{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathsf{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathsf{_ABC_}" style="width: 2.406em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.894em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.84em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖠</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖡</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖢</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,217行目: 4,003行目:
<code class="tex">\mathcal{ ABC }
<code class="tex">\mathcal{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathcal{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathcal{_ABC_}" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">A</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">B</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,226行目: 4,012行目:
<code class="tex">\mathbf{ ABC }
<code class="tex">\mathbf{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbf{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbf{_ABC_}" style="width: 2.661em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1002.05em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐀</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐁</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐂</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,235行目: 4,021行目:
<code class="tex">\mathit{ ABC }
<code class="tex">\mathit{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathit{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathit{_ABC_}" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">A</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">B</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,244行目: 4,030行目:
<code class="tex">\mathbb{ ABC }
<code class="tex">\mathbb{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_ABC_}" style="width: 3.275em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1002.46em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔸</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔹</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℂ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,253行目: 4,039行目:
<code class="tex">\mathscr{ ABC }
<code class="tex">\mathscr{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathscr{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathscr{_ABC_}" style="width: 3.735em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.917em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.82em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒜</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℬ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒞</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,262行目: 4,048行目:
<code class="tex">\mathfrak{ ABC }
<code class="tex">\mathfrak{ ABC }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathfrak{ ABC } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathfrak{_ABC_}" style="width: 2.917em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.303em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002.2em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔄</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔅</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">ℭ</span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,272行目: 4,058行目:
abcdefghijklmnopqrstuvwxyz }
abcdefghijklmnopqrstuvwxyz }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathrm{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathrm{_ABCDEFGHIJKLMNOPQRSTUVWXYZ_\\\vbCrLfabcdefghijklmnopqrstuvwxyz_}" style="width: 22.04em; display: inline-block;"><span style="display: inline-block; position: relative; width: 17.336em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1017.34em, 3.837em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 17.336em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1017.34em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">A</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">B</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">D</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">E</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">F</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">G</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">H</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">I</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">J</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">K<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">L</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">M</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">N</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">O</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">P</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Q</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">R</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">S</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">T</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">U</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">V</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">W</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">X</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Y</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Z</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1011.97em, 4.349em, -999.997em); top: -2.656em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">a</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">b</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">c</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">d</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">e</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">g</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">h</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">i</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">j</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">l</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">m</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">n</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">o</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">p</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">q</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">s</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">u</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">v</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">w</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">x</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">y</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">z</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.075em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
abcdefghijklmnopqrstuvwxyz } $$
</div>
</div>


4,283行目: 4,068行目:
abcdefghijklmnopqrstuvwxyz }
abcdefghijklmnopqrstuvwxyz }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathtt{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathtt{_ABCDEFGHIJKLMNOPQRSTUVWXYZ_\\\vbCrLfabcdefghijklmnopqrstuvwxyz_}" style="width: 19.841em; display: inline-block;"><span style="display: inline-block; position: relative; width: 15.597em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.383em, 1015.5em, 3.633em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 15.597em; height: 0px;"><span style="position: absolute; clip: rect(3.275em, 1015.5em, 4.246em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙰</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙱</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙲</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙳</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙴</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙵</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙶</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙷</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙸</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙹</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙺</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙻</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙼</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙽</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙾</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝙿</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚀</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚁</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚂</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚃</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚄</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚅</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚆</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚇</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚈</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚉</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1015.5em, 4.349em, -999.997em); top: -2.758em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚊</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚋</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚌</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚍</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚎</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚏</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚐</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚑</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚒</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚓</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚔</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚕</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚖</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚗</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚘</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚙</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚚</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚛</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚜</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚝</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚞</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚟</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚠</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚡</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚢</span><span class="mi" style="font-family: GyreTermesMathJax_Monospace;">𝚣</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.815em; border-left: 0px solid; width: 0px; height: 2.666em;"></span></span></span></div>
abcdefghijklmnopqrstuvwxyz } $$
</div>
</div>


4,294行目: 4,078行目:
abcdefghijklmnopqrstuvwxyz }
abcdefghijklmnopqrstuvwxyz }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathsf{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathsf{_ABCDEFGHIJKLMNOPQRSTUVWXYZ_\\\vbCrLfabcdefghijklmnopqrstuvwxyz_}" style="width: 20.864em; display: inline-block;"><span style="display: inline-block; position: relative; width: 16.415em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1016.36em, 3.684em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 16.415em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1016.36em, 4.195em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖠</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖡</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖢</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖣</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖤</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖥</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖦</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖧</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖨</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖩</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖪</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖫</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖬</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖭</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖮</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖯</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖰</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖱</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖲</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖳</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖴</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖵</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖶</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖷</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖸</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖹</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1011.81em, 4.349em, -999.997em); top: -2.758em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖺</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖻</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖼</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖽</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖾</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝖿</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗀</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗁</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗂</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗃</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗄<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗅</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗆</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗇</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗈</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗉</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗊</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗋</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗌</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗍</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗎</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗏</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗐</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗑</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗒</span><span class="mi" style="font-family: GyreTermesMathJax_SansSerif;">𝗓</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.88em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
abcdefghijklmnopqrstuvwxyz } $$
</div>
</div>


4,305行目: 4,088行目:
NOPQRSTUVWXYZ }
NOPQRSTUVWXYZ }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathcal{ ABCDEFGHIJKLM \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathcal{_ABCDEFGHIJKLM_\\\vbCrLfNOPQRSTUVWXYZ_}" style="width: 11.456em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.001em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1009em, 3.633em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 9.001em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1008.29em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">A</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">B</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">D</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">E</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">F</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">G</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">H</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">I</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">J</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">K<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">L</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">M</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1009em, 4.297em, -999.997em); top: -2.81em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">N</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">O</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">P</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Q</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">R</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">S</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">T</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">U</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">V</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">W</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">X</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Y</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Z</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.815em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
NOPQRSTUVWXYZ } $$
</div>
</div>


4,316行目: 4,098行目:
abcdefghijklmnopqrstuvwxyz }
abcdefghijklmnopqrstuvwxyz }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbf{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbf{_ABCDEFGHIJKLMNOPQRSTUVWXYZ_\\\vbCrLfabcdefghijklmnopqrstuvwxyz_}" style="width: 23.318em; display: inline-block;"><span style="display: inline-block; position: relative; width: 18.358em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1018.31em, 3.786em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 18.358em; height: 0px;"><span style="position: absolute; clip: rect(3.121em, 1018.31em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐀</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐁</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐂</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐃</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐄</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐅</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐆</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐇</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐈</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐉</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐊</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐋</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐌</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐍</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐐</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐑</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐒</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐓</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐔</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐕</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐖</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐗</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐘</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐙</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.121em, 1012.73em, 4.349em, -999.997em); top: -2.656em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐚</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐛</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐜</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐝</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐞</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐟<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐠</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐡</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐢</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐣</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐤</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐥</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐦</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐧</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐨</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐩</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐪</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐫</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐬</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐭</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐮</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐯</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐰</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐱</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐲</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐳</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.01em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
abcdefghijklmnopqrstuvwxyz } $$
</div>
</div>


4,327行目: 4,108行目:
abcdefghijklmnopqrstuvwxyz }
abcdefghijklmnopqrstuvwxyz }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathit{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathit{_ABCDEFGHIJKLMNOPQRSTUVWXYZ_\\\vbCrLfabcdefghijklmnopqrstuvwxyz_}" style="width: 22.04em; display: inline-block;"><span style="display: inline-block; position: relative; width: 17.336em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1017.34em, 3.837em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 17.336em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1017.34em, 4.297em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Main;">A</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">B</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">C</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">D</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">E</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">F</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">G</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">H</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">I</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">J</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">K</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">L</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">M</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">N</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">O</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">P</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Q</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">R</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">S</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">T</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">U</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">V</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">W</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">X</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Y</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">Z</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1011.92em, 4.349em, -999.997em); top: -2.656em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Main;">a</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">b</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">c</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">d</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">e</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">f</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">g</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">h</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">i</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">j</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">k</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">l</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">m</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">n</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">o</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">p</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">q</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">r</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">s</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">t</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">u</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">v</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">w</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">x</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">y</span><span class="mi" style="font-family: GyreTermesMathJax_Main;">z</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.075em; border-left: 0px solid; width: 0px; height: 2.99em;"></span></span></span></div>
abcdefghijklmnopqrstuvwxyz } $$
</div>
</div>


4,338行目: 4,118行目:
NOPQRSTUVWXYZ }
NOPQRSTUVWXYZ }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathbb{ ABCDEFGHIJKLM \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathbb{_ABCDEFGHIJKLM_\\\vbCrLfNOPQRSTUVWXYZ_}" style="width: 14.421em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.353em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1011.25em, 3.633em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 11.353em; height: 0px;"><span style="position: absolute; clip: rect(3.121em, 1010.59em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔸</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔹</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℂ</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔻</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔼</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔽</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝔾</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℍ</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕀</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕁</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕂</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕃</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕄</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.121em, 1011.3em, 4.297em, -999.997em); top: -2.758em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℕ</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕆</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℙ</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℚ</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℝ</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕊</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕋</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕌</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕍</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕎</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕏</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕐</span><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">ℤ</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.815em; border-left: 0px solid; width: 0px; height: 2.795em;"></span></span></span></div>
NOPQRSTUVWXYZ } $$
</div>
</div>


4,349行目: 4,128行目:
NOPQRSTUVWXYZ }
NOPQRSTUVWXYZ }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathscr{ ABCDEFGHIJKLM \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathscr{_ABCDEFGHIJKLM_\\\vbCrLfNOPQRSTUVWXYZ_}" style="width: 16.62em; display: inline-block;"><span style="display: inline-block; position: relative; width: 13.092em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1012.99em, 3.94em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 13.092em; height: 0px;"><span style="position: absolute; clip: rect(3.121em, 1012.43em, 4.4em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒜</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℬ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒞</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒟</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℰ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℱ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒢</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℋ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℐ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒥</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒦</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℒ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℳ</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.121em, 1012.99em, 4.4em, -999.997em); top: -2.554em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒩</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒪</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒫</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒬</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">ℛ</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒮</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒯</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒰</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒱</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒲</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒳</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒴</span><span class="mi" style="font-family: GyreTermesMathJax_Script;">𝒵</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.205em; border-left: 0px solid; width: 0px; height: 3.185em;"></span></span></span></div>
NOPQRSTUVWXYZ } $$
</div>
</div>


4,360行目: 4,138行目:
abcdefghijklmnopqrstuvwxyz }
abcdefghijklmnopqrstuvwxyz }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mathfrak{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mathfrak{_ABCDEFGHIJKLMNOPQRSTUVWXYZ_\\\vbCrLfabcdefghijklmnopqrstuvwxyz_}" style="width: 24.698em; display: inline-block;"><span style="display: inline-block; position: relative; width: 19.432em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1019.33em, 3.786em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span style="display: inline-block; position: relative; width: 19.432em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1019.38em, 4.349em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔄</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔅</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">ℭ</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔇</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔈</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔉</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔊</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">ℌ</span><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">ℑ</span></span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔍</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔎</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔏</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔐</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔑</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔒</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔓</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔔</span><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">ℜ</span></span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔖</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔗</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔘</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔙</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔚</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔛</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔜</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">ℨ</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1011.87em, 4.297em, -999.997em); top: -2.656em; left: 0em;"><span class="mspace" style="height: 0em; vertical-align: 0em; width: 0em; display: inline-block; overflow: hidden;"></span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔞</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔟</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔠</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔡</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔢</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔣</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔤</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔥</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔦</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔧</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔨</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔩</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔪</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔫</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔬</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔭</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔮</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔯</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔰</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔱</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔲</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔳</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔴</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔵</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔶</span><span class="mi" style="font-family: GyreTermesMathJax_Fraktur;">𝔷</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.01em; border-left: 0px solid; width: 0px; height: 3.055em;"></span></span></span></div>
abcdefghijklmnopqrstuvwxyz } $$
</div>
</div>


4,373行目: 4,150行目:
<code class="tex">a^{ xy }
<code class="tex">a^{ xy }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a^{ xy } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a^{_xy_}" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1001.23em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,382行目: 4,159行目:
<code class="tex">{}^{ xy } a
<code class="tex">{}^{ xy } a
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ {}^{ xy } a $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{}^{_xy_}_a" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1001.23em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.395em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,391行目: 4,168行目:
<code class="tex">a_{ xy }
<code class="tex">a_{ xy }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ a_{ xy } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_a\_{_xy_}" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.485em, 1001.23em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,400行目: 4,177行目:
<code class="tex">{}_{ xy } a
<code class="tex">{}_{ xy } a
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ {}_{ xy } a $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_{}\_{_xy_}_a" style="width: 1.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.23em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1001.23em, 5.627em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px;"><span style="position: absolute; clip: rect(3.837em, 1000em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="texatom"><span class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑥<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑦</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,411行目: 4,188行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLfa\_n^2_+_a\_{_n_+_1_}^2_=_a\_{_2n_+_1_}\vbCrLf\end{eqnarray}" style="width: 9.564em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.519em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1007.52em, 2.559em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 7.212em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.019em, 1007.21em, 4.451em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 7.212em; height: 0px;"><span style="position: absolute; clip: rect(3.019em, 1007.21em, 4.451em, -999.997em); top: -3.986em; right: 0em;"><span class="mtd"><span class="mrow"><span class="msubsup"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.343em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.531em, 1000.41em, 4.144em, -999.997em); top: -3.832em; left: 0.514em;"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">+</span><span class="msubsup" style="padding-left: 0.258em;"><span style="display: inline-block; position: relative; width: 1.741em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.343em; left: 0.514em;"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.377em, 1001.23em, 4.144em, -999.997em); top: -3.679em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.309em;">=</span><span class="msubsup" style="padding-left: 0.309em;"><span style="display: inline-block; position: relative; width: 2.099em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.832em; left: 0.514em;"><span class="texatom"><span class="mrow"><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">2</span><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝑛</span><span class="mo" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">+</span><span class="mn" style="font-size: 70.7%; font-family: GyreTermesMathJax_Main;">1</span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.451em; border-left: 0px solid; width: 0px; height: 1.562em;"></span></span></span></div>
a_n^2 + a_{ n + 1 }^2 = a_{ 2n + 1 }
\end{eqnarray} $$
</div>
</div>


4,425行目: 4,200行目:
<code class="tex">\hat{ a }
<code class="tex">\hat{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \hat{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\hat{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="height: 0em; vertical-align: 0em; width: 0.412em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">̂&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,434行目: 4,209行目:
<code class="tex">\grave{ a }
<code class="tex">\grave{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \grave{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\grave{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.156em;"><span style="height: 0em; vertical-align: 0em; width: 0.412em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">̀&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


4,443行目: 4,218行目:
<code class="tex">\acute{ a }
<code class="tex">\acute{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \acute{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\acute{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.156em;"><span style="height: 0em; vertical-align: 0em; width: 0.309em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">́&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


4,452行目: 4,227行目:
<code class="tex">\dot{ a }
<code class="tex">\dot{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \dot{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\dot{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.21em, 3.582em, -999.997em); top: -4.037em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">˙</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,461行目: 4,236行目:
<code class="tex">\ddot{ a }
<code class="tex">\ddot{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ddot{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ddot{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.31em, 3.582em, -999.997em); top: -4.037em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">¨</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,470行目: 4,245行目:
<code class="tex">\bar{ a }
<code class="tex">\bar{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bar{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bar{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.332em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.224em, 1000.31em, 3.582em, -999.997em); top: -3.986em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">¯</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


4,479行目: 4,254行目:
<code class="tex">\vec{ a }
<code class="tex">\vec{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vec{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vec{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -4.037em; left: 0.054em;"><span style="height: 0em; vertical-align: 0em; width: 0.463em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">⃗&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


4,488行目: 4,263行目:
<code class="tex">\check{ a }
<code class="tex">\check{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \check{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\check{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.31em, 3.633em, -999.997em); top: -4.037em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">ˇ</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


4,497行目: 4,272行目:
<code class="tex">\tilde{ a }
<code class="tex">\tilde{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \tilde{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\tilde{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; top: -3.986em; left: 0.105em;"><span style="height: 0em; vertical-align: 0em; width: 0.412em; display: inline-block; overflow: hidden;"></span><span class="mo" style="font-family: GyreTermesMathJax_Main;">̃&nbsp;<span style="height: 0em; vertical-align: 0em; margin-left: -0.253em;"></span></span><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,506行目: 4,281行目:
<code class="tex">\breve{ a }
<code class="tex">\breve{ a }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \breve{ a } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\breve{_a_}" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.23em, 1000.51em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.46em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1000.31em, 3.633em, -999.997em); top: -4.037em; left: 0.105em;"><span class="mo" style="font-family: GyreTermesMathJax_Main;">˘</span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,515行目: 4,290行目:
<code class="tex">\widehat{ AAA }
<code class="tex">\widehat{ AAA }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \widehat{ AAA } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\widehat{_AAA_}" style="width: 2.355em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.843em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.974em, 1001.79em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.843em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.79em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.121em, 1001.49em, 3.633em, -999.997em); top: -4.241em; left: 0.156em;"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">̂</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></span></div>
</div>
</div>


4,524行目: 4,299行目:
<code class="tex">\widetilde{ AAA }
<code class="tex">\widetilde{ AAA }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \widetilde{ AAA } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\widetilde{_AAA_}" style="width: 2.355em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.843em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(0.974em, 1001.79em, 2.252em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="munderover"><span style="display: inline-block; position: relative; width: 1.843em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.79em, 4.144em, -999.997em); top: -3.986em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span><span style="position: absolute; clip: rect(3.173em, 1001.49em, 3.633em, -999.997em); top: -4.241em; left: 0.156em;"><span class="mo" style=""><span style="font-family: GyreTermesMathJax_Size6;">̃</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></span></div>
</div>
</div>


4,536行目: 4,311行目:
<code class="tex">\forall
<code class="tex">\forall
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \forall $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\forall" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∀</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,545行目: 4,320行目:
<code class="tex">\exists
<code class="tex">\exists
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \exists $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\exists" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.41em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">∃</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,554行目: 4,329行目:
<code class="tex">\Finv
<code class="tex">\Finv
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Finv $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Finv" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.46em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: italic; font-weight: normal;">Ⅎ</span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


4,563行目: 4,338行目:
<code class="tex">\hbar
<code class="tex">\hbar
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \hbar $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\hbar" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℏ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,572行目: 4,347行目:
<code class="tex">\imath
<code class="tex">\imath
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \imath $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\imath" style="width: 0.36em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.258em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.26em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ı</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,581行目: 4,356行目:
<code class="tex">\jmath
<code class="tex">\jmath
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \jmath $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\jmath" style="width: 0.36em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.258em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.16em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ȷ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,590行目: 4,365行目:
<code class="tex">\Bbbk
<code class="tex">\Bbbk
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Bbbk $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Bbbk" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_DoubleStruck;">𝕜</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,599行目: 4,374行目:
<code class="tex">\ell
<code class="tex">\ell
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \ell $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\ell" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.36em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℓ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,608行目: 4,383行目:
<code class="tex">\circledR
<code class="tex">\circledR
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \circledR $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\circledR" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">®</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


4,617行目: 4,392行目:
<code class="tex">\circledS
<code class="tex">\circledS
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \circledS $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\circledS" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.127em, 1000.77em, 2.457em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mi"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">Ⓢ</span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
</div>
</div>


4,629行目: 4,404行目:
<code class="tex">\alpha
<code class="tex">\alpha
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \alpha $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\alpha" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛼</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,638行目: 4,413行目:
<code class="tex">\beta
<code class="tex">\beta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \beta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\beta" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛽</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.237em;"></span></span></span></div>
</div>
</div>


4,647行目: 4,422行目:
<code class="tex">\gamma
<code class="tex">\gamma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \gamma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\gamma" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛾</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,656行目: 4,431行目:
<code class="tex">\delta
<code class="tex">\delta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \delta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\delta" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛿</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,665行目: 4,440行目:
<code class="tex">\epsilon
<code class="tex">\epsilon
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \epsilon $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\epsilon" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.41em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜖</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,674行目: 4,449行目:
<code class="tex">\varepsilon
<code class="tex">\varepsilon
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varepsilon $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varepsilon" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜀</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,683行目: 4,458行目:
<code class="tex">\zeta
<code class="tex">\zeta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \zeta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\zeta" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.51em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜁</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


4,692行目: 4,467行目:
<code class="tex">\eta
<code class="tex">\eta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \eta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\eta" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜂</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,701行目: 4,476行目:
<code class="tex">\theta
<code class="tex">\theta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \theta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\theta" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.46em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,710行目: 4,485行目:
<code class="tex">\vartheta
<code class="tex">\vartheta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \vartheta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\vartheta" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜗</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,719行目: 4,494行目:
<code class="tex">\iota
<code class="tex">\iota
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \iota $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\iota" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.31em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜄</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,728行目: 4,503行目:
<code class="tex">\kappa
<code class="tex">\kappa
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \kappa $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\kappa" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜅</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,737行目: 4,512行目:
<code class="tex">\lambda
<code class="tex">\lambda
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \lambda $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\lambda" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜆</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,746行目: 4,521行目:
<code class="tex">\mu
<code class="tex">\mu
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \mu $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\mu" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.604em, 1000.57em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜇</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.912em;"></span></span></span></div>
</div>
</div>


4,755行目: 4,530行目:
<code class="tex">\nu
<code class="tex">\nu
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \nu $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\nu" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜈</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,764行目: 4,539行目:
<code class="tex">\xi
<code class="tex">\xi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \xi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\xi" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.51em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜉</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


4,773行目: 4,548行目:
<code class="tex">o
<code class="tex">o
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ o $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_o" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑜</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,782行目: 4,557行目:
<code class="tex">\pi
<code class="tex">\pi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \pi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\pi" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜋</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,791行目: 4,566行目:
<code class="tex">\varpi
<code class="tex">\varpi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varpi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varpi" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.82em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜛</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,800行目: 4,575行目:
<code class="tex">\rho
<code class="tex">\rho
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \rho $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\rho" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜌</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,809行目: 4,584行目:
<code class="tex">\varrho
<code class="tex">\varrho
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varrho $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varrho" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜚</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,818行目: 4,593行目:
<code class="tex">\sigma
<code class="tex">\sigma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \sigma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\sigma" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜎</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,827行目: 4,602行目:
<code class="tex">\varsigma
<code class="tex">\varsigma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varsigma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varsigma" style="width: 0.718em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.46em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜍</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,836行目: 4,611行目:
<code class="tex">\tau
<code class="tex">\tau
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \tau $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\tau" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜏</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,845行目: 4,620行目:
<code class="tex">\upsilon
<code class="tex">\upsilon
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \upsilon $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\upsilon" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.51em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜐</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,854行目: 4,629行目:
<code class="tex">\phi
<code class="tex">\phi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \phi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\phi" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.4em, 1000.62em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜙</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


4,863行目: 4,638行目:
<code class="tex">\varphi
<code class="tex">\varphi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varphi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varphi" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.57em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜑</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,872行目: 4,647行目:
<code class="tex">\chi
<code class="tex">\chi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \chi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\chi" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.72em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜒</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,881行目: 4,656行目:
<code class="tex">\psi
<code class="tex">\psi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \psi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\psi" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.67em, 5.525em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜓</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.321em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,890行目: 4,665行目:
<code class="tex">\omega
<code class="tex">\omega
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \omega $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\omega" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.553em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝜔</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></span></div>
</div>
</div>


4,899行目: 4,674行目:
<code class="tex">A
<code class="tex">A
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ A $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_A" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,908行目: 4,683行目:
<code class="tex">B
<code class="tex">B
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ B $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_B" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐵</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,917行目: 4,692行目:
<code class="tex">\Gamma
<code class="tex">\Gamma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Gamma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Gamma" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Γ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,926行目: 4,701行目:
<code class="tex">\varGamma
<code class="tex">\varGamma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varGamma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varGamma" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛤</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,935行目: 4,710行目:
<code class="tex">\Delta
<code class="tex">\Delta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Delta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Delta" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Δ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,944行目: 4,719行目:
<code class="tex">\varDelta
<code class="tex">\varDelta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varDelta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varDelta" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛥</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,953行目: 4,728行目:
<code class="tex">E
<code class="tex">E
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ E $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_E" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,962行目: 4,737行目:
<code class="tex">Z
<code class="tex">Z
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ Z $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_Z" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑍<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,971行目: 4,746行目:
<code class="tex">H
<code class="tex">H
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ H $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_H" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐻<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,980行目: 4,755行目:
<code class="tex">\Theta
<code class="tex">\Theta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Theta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Theta" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Θ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,989行目: 4,764行目:
<code class="tex">\varTheta
<code class="tex">\varTheta
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varTheta $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varTheta" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛩</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


4,998行目: 4,773行目:
<code class="tex">I
<code class="tex">I
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ I $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_I" style="width: 0.514em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.41em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,007行目: 4,782行目:
<code class="tex">K
<code class="tex">K
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ K $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_K" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐾<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,016行目: 4,791行目:
<code class="tex">\Lambda
<code class="tex">\Lambda
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Lambda $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Lambda" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Λ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,025行目: 4,800行目:
<code class="tex">\varLambda
<code class="tex">\varLambda
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varLambda $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varLambda" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛬</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,034行目: 4,809行目:
<code class="tex">M
<code class="tex">M
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ M $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_M" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.87em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑀<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,043行目: 4,818行目:
<code class="tex">N
<code class="tex">N
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ N $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_N" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑁<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,052行目: 4,827行目:
<code class="tex">\Xi
<code class="tex">\Xi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Xi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Xi" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Ξ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,061行目: 4,836行目:
<code class="tex">\varXi
<code class="tex">\varXi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varXi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varXi" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛯</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,070行目: 4,845行目:
<code class="tex">O
<code class="tex">O
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ O $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_O" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑂</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,079行目: 4,854行目:
<code class="tex">\Pi
<code class="tex">\Pi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Pi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Pi" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Π</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,088行目: 4,863行目:
<code class="tex">\varPi
<code class="tex">\varPi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varPi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varPi" style="width: 1.179em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.923em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.82em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛱</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,097行目: 4,872行目:
<code class="tex">P
<code class="tex">P
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ P $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_P" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑃</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,106行目: 4,881行目:
<code class="tex">\Sigma
<code class="tex">\Sigma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Sigma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Sigma" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Σ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,115行目: 4,890行目:
<code class="tex">\varSigma
<code class="tex">\varSigma
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varSigma $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varSigma" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛴</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,124行目: 4,899行目:
<code class="tex">T
<code class="tex">T
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ T $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_T" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑇<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,133行目: 4,908行目:
<code class="tex">\Upsilon
<code class="tex">\Upsilon
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Upsilon $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Upsilon" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Υ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,142行目: 4,917行目:
<code class="tex">\varUpsilon
<code class="tex">\varUpsilon
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varUpsilon $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varUpsilon" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛶</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,151行目: 4,926行目:
<code class="tex">\Phi
<code class="tex">\Phi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Phi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Phi" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Φ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,160行目: 4,935行目:
<code class="tex">\varPhi
<code class="tex">\varPhi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varPhi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varPhi" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.62em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛷</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,169行目: 4,944行目:
<code class="tex">X
<code class="tex">X
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ X $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_X" style="width: 0.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.667em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,178行目: 4,953行目:
<code class="tex">\Psi
<code class="tex">\Psi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Psi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Psi" style="width: 1.076em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.821em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Ψ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,187行目: 4,962行目:
<code class="tex">\varPsi
<code class="tex">\varPsi
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varPsi $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varPsi" style="width: 0.974em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.77em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.67em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛹</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,196行目: 4,971行目:
<code class="tex">\Omega
<code class="tex">\Omega
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \Omega $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\Omega" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">Ω</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,205行目: 4,980行目:
<code class="tex">\varOmega
<code class="tex">\varOmega
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \varOmega $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\varOmega" style="width: 1.127em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.872em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.77em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝛺</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,217行目: 4,992行目:
<code class="tex">\color{red}{a \times b}
<code class="tex">\color{red}{a \times b}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \color{red}{a \times b} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\color{red}{a_\times_b}" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mstyle" style="color: red;"><span class="mrow" style="color: red;"><span class="texatom" style="color: red;"><span class="mrow" style="color: red;"><span class="mi" style="font-family: GyreTermesMathJax_Normal; color: red;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em; color: red;">×</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em; color: red;">𝑏</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


5,226行目: 5,001行目:
<code class="tex">\color{ #ff0000 }{a \times b}
<code class="tex">\color{ #ff0000 }{a \times b}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \color{ #ff0000 }{a \times b} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\color{_#ff0000_}{a_\times_b}" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1002em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mstyle" style="color: rgb(255, 0, 0);"><span class="mrow" style="color: rgb(255, 0, 0);"><span class="texatom" style="color: rgb(255, 0, 0);"><span class="mrow" style="color: rgb(255, 0, 0);"><span class="mi" style="font-family: GyreTermesMathJax_Normal; color: rgb(255, 0, 0);">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em; color: rgb(255, 0, 0);">×</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em; color: rgb(255, 0, 0);">𝑏</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


5,235行目: 5,010行目:
<code class="tex">\colorbox{red}{ Important! }
<code class="tex">\colorbox{red}{ Important! }
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \colorbox{red}{ Important! } $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\colorbox{red}{_Important!_}" style="width: 6.701em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.269em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.434em, 1004.76em, 3.121em, -999.997em); top: -2.503em; left: 0em;"><span class="mrow"><span  style="display: inline-block; background-color: red; width: 5.371em; height: 1.485em; vertical-align: -0.509em; margin-left: -0.049em; margin-right: -5.315em;"></span><span class="mpadded"><span style="display: inline-block; position: relative; width: 5.269em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1004.55em, 4.349em, -999.997em); top: -3.986em; left: 0.258em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">&nbsp;Important!&nbsp;</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.508em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.646em; border-left: 0px solid; width: 0px; height: 1.886em;"></span></span></span></div>
</div>
</div>


5,244行目: 5,019行目:
<code class="tex">\colorbox{red}{$a \times b$}
<code class="tex">\colorbox{red}{$a \times b$}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \colorbox{red}{$a \times b$} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\colorbox{red}{$a_\times_b$}" style="width: 3.275em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.281em, 1002.25em, 2.764em, -999.997em); top: -2.349em; left: 0em;"><span class="mrow"><span  style="display: inline-block; background-color: red; width: 2.661em; height: 1.332em; vertical-align: -0.304em; margin-left: -0.049em; margin-right: -2.605em;"></span><span class="mpadded"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.05em, 4.144em, -999.997em); top: -3.986em; left: 0.258em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">×</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.355em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.692em;"></span></span></span></div>
</div>
</div>


5,253行目: 5,028行目:
<code class="tex">\fcolorbox{black}{ #00ff00 }{$a \times b$}
<code class="tex">\fcolorbox{black}{ #00ff00 }{$a \times b$}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \fcolorbox{black}{ #00ff00 }{$a \times b$} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\fcolorbox{black}{_#00ff00_}{$a_\times_b$}" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.383em, 1002.25em, 3.07em, -999.997em); top: -2.554em; left: 0em;"><span class="mrow"><span  style="display: inline-block; background-color: rgb(0, 255, 0); width: 2.661em; height: 1.332em; vertical-align: -0.406em; margin-left: -0.049em; margin-right: -2.707em; border-width: 2px; border-style: solid; border-color: black;"></span><span class="mpadded" style="padding-right: 0.105em;"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1002.05em, 4.144em, -999.997em); top: -3.986em; left: 0.258em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mo" style="font-family: GyreTermesMathJax_Main; padding-left: 0.258em;">×</span><span class="mi" style="font-family: GyreTermesMathJax_Normal; padding-left: 0.258em;">𝑏</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.559em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.516em; border-left: 0px solid; width: 0px; height: 1.951em;"></span></span></span></div>
</div>
</div>


5,262行目: 5,037行目:
<code class="tex">\bbox[yellow, 5pt, border: 2px dotted red]{abc}
<code class="tex">\bbox[yellow, 5pt, border: 2px dotted red]{abc}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \bbox[yellow, 5pt, border: 2px dotted red]{abc} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\bbox[yellow,_5pt,_border:_2px_dotted_red]{abc}" style="width: 3.531em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.764em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.69em, 1002em, 3.991em, -999.997em); top: -3.168em; left: 0em;"><span class="mrow"><span  style="display: inline-block; background-color: yellow; width: 2.661em; height: 1.945em; vertical-align: -0.713em; margin-left: -0.049em; margin-right: -2.707em; border-width: 2px; border-style: dotted; border-color: red;"></span><span class="mstyle" style="padding-right: 0.105em;"><span class="mrow"><span class="mpadded"><span style="display: inline-block; position: relative; width: 2.559em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1001.43em, 4.144em, -999.997em); top: -3.986em; left: 0.565em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑎</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑏</span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑐</span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.173em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.906em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></span></div>
</div>
</div>


5,271行目: 5,046行目:
<code class="tex">\unicode{x0041}
<code class="tex">\unicode{x0041}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \unicode{x0041} $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\unicode{x0041}" style="width: 0.923em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.718em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.72em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mtext" style="font-family: GyreTermesMathJax_Main;">A</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 0.977em;"></span></span></span></div>
</div>
</div>


5,282行目: 5,057行目:
\end{eqnarray}
\end{eqnarray}
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \begin{eqnarray}
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\begin{eqnarray}\vbCrLf\unicode{x5F45}\text{は、弓へんに剪。}\vbCrLf\end{eqnarray}" style="width: 9.41em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.416em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(1.179em, 1007.42em, 2.508em, -999.997em); top: -2.094em; left: 0em;"><span class="mrow"><span class="mtable"><span style="display: inline-block; position: relative; width: 7.11em; height: 0px; margin-right: 0.156em; margin-left: 0.156em;"><span style="position: absolute; clip: rect(3.07em, 1007.11em, 4.4em, -999.997em); top: -3.986em; left: 0em;"><span style="display: inline-block; position: relative; width: 7.11em; height: 0px;"><span style="position: absolute; clip: rect(1.127em, 1007.11em, 2.457em, -999.997em); top: -2.043em; right: 0em;"><span class="mtd"><span class="mrow"><span class="mtext"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;; font-size: 79%; font-style: normal; font-weight: normal;">彅</span></span><span class="mtext"><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">は</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">、</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">弓</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">へ</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">ん</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">に</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">剪</span><span style="font-family: STIXGeneral, &quot;Arial Unicode MS&quot;, serif; font-size: 79%; font-style: normal; font-weight: normal;">。</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.099em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.432em;"></span></span></span></div>
\unicode{x5F45}\text{は、弓へんに剪。}
\end{eqnarray} $$
</div>
</div>


5,296行目: 5,069行目:
<code class="tex">\S
<code class="tex">\S
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \S $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\S" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1000.46em, 5.473em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">§</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.256em; border-left: 0px solid; width: 0px; height: 1.172em;"></span></span></span></div>
</div>
</div>


5,305行目: 5,078行目:
<code class="tex">\aleph
<code class="tex">\aleph
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \aleph $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\aleph" style="width: 0.821em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.57em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℵ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


5,314行目: 5,087行目:
<code class="tex">\beth
<code class="tex">\beth
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \beth $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\beth" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.46em, 5.371em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℶ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.127em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


5,323行目: 5,096行目:
<code class="tex">\gimel
<code class="tex">\gimel
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \gimel $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\gimel" style="width: 0.616em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.463em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.41em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℷ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.107em;"></span></span></span></div>
</div>
</div>


5,332行目: 5,105行目:
<code class="tex">\daleth
<code class="tex">\daleth
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \daleth $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\daleth" style="width: 0.667em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.514em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1000.46em, 5.32em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Main;">ℸ</span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.062em; border-left: 0px solid; width: 0px; height: 1.042em;"></span></span></span></div>
</div>
</div>


5,344行目: 5,117行目:
<code class="tex">\TeX
<code class="tex">\TeX
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \TeX $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\TeX" style="width: 2.099em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.639em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.349em, 1001.64em, 5.576em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑇<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.151em;"></span><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.73em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.151em;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.302em;"></span></span></span></div>
</div>
</div>


5,353行目: 5,126行目:
<code class="tex">\LaTeX
<code class="tex">\LaTeX
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
</code></pre></div><script></freescript><div style="background-color:#eeeeee; border:2px solid;">
$$ \LaTeX $$
<span class="MathJax_Preview" style="color: inherit;"></span><div class="MathJax_Display" style="text-align: center;"><span class="MathJax" tabindex="0" role="presentation" style="text-align: center; position: relative;"><span class="none-math" id="Display:_\LaTeX" style="width: 2.61em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.048em; height: 0px; font-size: 127%;"><span style="position: absolute; clip: rect(4.297em, 1002.05em, 5.576em, -999.997em); top: -5.162em; left: 0em;"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐿<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.355em;"></span><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.412em; height: 0px;"><span style="position: absolute; clip: rect(3.377em, 1000.41em, 4.144em, -999.997em); top: -4.241em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-size: 70.7%; font-family: GyreTermesMathJax_Normal;">𝐴</span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.202em;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑇<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.105em;"></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.151em;"></span><span class="mpadded"><span style="display: inline-block; position: relative; width: 0.616em; height: 0px;"><span style="position: absolute; clip: rect(3.173em, 1000.62em, 4.144em, -999.997em); top: -3.73em; left: 0em;"><span class="mrow"><span class="texatom"><span class="mrow"><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝐸<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.991em;"></span></span></span></span><span class="mspace" style="height: 0em; vertical-align: 0em; margin-left: -0.151em;"></span><span class="mi" style="font-family: GyreTermesMathJax_Normal;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.054em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.167em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.386em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></span></div>
</div>
</div>



2025年1月26日 (日) 00:59時点における最新版

Mathjax 2.7に戻る。

概要

 Gyre-Termesフォントでの一覧。

 

  • 分数

\frac{1}{2}
12


  • 分数(大)

\displaystyle \frac{1}{2}
12


  • 分数(大)2

\dfrac{1}{2}
12


  • 分数(1行)

\require{physics} \flatfrac{1}{2}
(1/2)


  • 分数と括弧

\left( -\frac{1}{2} \right)^2
(12)2


  • 分数と括弧2

\require{physics} \qty{ -\frac{1}{2} }^2
{12}2


  • 連分数

\frac{a+b}{c+\frac{d}{e}}
𝑎+𝑏𝑐+𝑑𝑒


  • 連分数2

\cfrac{a+b}{c+\cfrac{d}{e}}
𝑎+𝑏𝑐+𝑑𝑒


  • 無限連分数

\begin{eqnarray}
1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}}
= \frac{1}{2} \left( 1+\sqrt{5} \right)
\end{eqnarray}
1+11+11+11+=12(1+5)


  • 小数

0.123
0.123


  • 循環小数

\frac{1}{11} = 0.\dot{0}\dot{9}
111=0.0˙9˙


  • 無限小数1

\pi = 3.14 \ldots
𝜋=3.14


  • 無限小数2

\sqrt{2} = 1.4142 \cdots
2=1.4142


  • 無限大

\infty


  • 絶対値

|x|
|𝑥|


  • 絶対値2

\vert x \vert
|𝑥|


  • 分数と絶対値

\left| \dfrac{x}{2} \right|
|𝑥2|


  • 分数と絶対値2

\require{physics} \qty{\dfrac{x}{2}}
{𝑥2}


  • 分数と絶対値3

\require{physics} \abs{ \dfrac{x}{2} }
|𝑥2|


  • ガウス記号

[x]
[𝑥]


  • ガウス記号2

\lbrack x \rbrack
[𝑥]


  • 床関数

\lfloor x \rfloor
𝑥


  • 天井関数

\lceil x \rceil
𝑥


  • ガウス記号サンプル

\begin{eqnarray}
[x]
= \lfloor x \rfloor
= \max\{ n\in\mathbb{Z} \mid n \leqq x \}
\end{eqnarray}
[𝑥]=𝑥=max{𝑛𝑛𝑥}

 

四則演算

  • 足す

1 + 2
1+2


  • 引く

3 - 1
31


  • 掛ける

2 \times 3
2×3


  • 割る

\require{physics} 6 \divisionsymbol 3
6 ÷ 3


  • プラスマイナス

\pm 1
±1


  • マイナスプラス

\mp 1
1


  • 掛ける(簡略)

a \cdot b = ab
𝑎𝑏=𝑎𝑏


  • 割る(分数)

a \divisionsymbol b = \frac{a}{b}
𝑎 ÷ 𝑏=𝑎𝑏


  • 掛け算の筆算

\begin{align}
67 \\
\frac{\times\phantom{0}63}{\phantom{0}201} \\
\frac{402\phantom{0}}{4221}
\end{align}
67×632014024221


  • 割り算の筆算

\require{enclose}\begin{align}
  7.6 \\
  25\enclose{longdiv}{190\phantom{.0}} \\
  \frac{175\phantom{.0}}{15\phantom{.}0} \\
  \frac{15\phantom{.}0\phantom{.}}{\phantom{00.}0\phantom{.}} \\
\end{align}
7.6251901751501500


  • 合同式

a \equiv b \mod n
𝑎𝑏mod𝑛


  • 合同式(括弧付)

a \equiv b \pmod n
𝑎𝑏(mod𝑛)


  • 合同式(二項演算子)

\gcd(a, b) = \gcd(b, a \bmod b)
gcd(𝑎,𝑏)=gcd(𝑏,𝑎mod𝑏)


  • 比例

x \propto y
𝑥𝑦

 

大小

  • 大なり

a \gt b
𝑎>𝑏


  • 大なりイコール

a \geq b
𝑎𝑏


  • 大なりイコール2

a \geqq b
𝑎𝑏


  • 小なり

a \lt b
𝑎<𝑏


  • 小なりイコール

a \leq b
𝑎𝑏


  • 小なりイコール2

a \leqq b
𝑎𝑏


  • 等しい

a = b
𝑎=𝑏


  • 等しくない

a \neq b
𝑎𝑏


  • ほぼ等しい

a \fallingdotseq b
𝑎𝑏


  • ほぼ等しい2

a \sim b
𝑎𝑏


  • ほぼ等しい3

a \simeq b
𝑎𝑏


  • ほぼ等しい4

a \approx b
𝑎𝑏


  • 十分大きい

a \gg b
𝑎𝑏


  • 十分小さい

a \ll b
𝑎𝑏


  • 最大

\max f(x)
max𝑓(𝑥)


  • 最小

\min f(x)
min𝑓(𝑥)


  • 最大サンプル

\begin{eqnarray}
\max ( a, b )
=
  \begin{cases}
    a & ( a \geqq b ) \\
    b & ( a \lt b )
  \end{cases}
\end{eqnarray}
max(𝑎,𝑏)={𝑎𝑏(𝑎𝑏)(𝑎<𝑏)

 

複数行数式

  • 改行

\begin{eqnarray}
aaa \\
bbb
\end{eqnarray}
𝑎𝑎𝑎𝑏𝑏𝑏


  • 改行(サイズ指定)

\begin{eqnarray}
aaa \\[5pt]
bbb
\end{eqnarray}
𝑎𝑎𝑎𝑏𝑏𝑏


  • 位置合わせ

\begin{eqnarray}
x + 2x &=& 3 \\
x &=& 1
\end{eqnarray}
𝑥+2𝑥𝑥==31


  • 連立方程式

\begin{eqnarray}
  \left\{
    \begin{array}{l}
      x + y = 10 \\
      2x + 4y = 32
    \end{array}
  \right.
\end{eqnarray}
{𝑥+𝑦=102𝑥+4𝑦=32


  • 場合分け

\begin{eqnarray}
|x|
 =
  \begin{cases}
    x & ( x \geqq 0 ) \\
    -x & ( x \lt 0 )
  \end{cases}
\end{eqnarray}
|𝑥|={𝑥𝑥(𝑥0)(𝑥<0)

 

集合

  • 帰属関係

x \in A
𝑥𝐴


  • 帰属関係2

A \ni x
𝐴𝑥


  • 帰属していない

x \notin A
𝑥𝐴


  • 部分集合

A \subset B
𝐴𝐵


  • 部分集合2

A \subseteq B
𝐴𝐵


  • 部分集合3

A \subseteqq B
𝐴𝐵


  • 上位集合

A \supset B
𝐴𝐵


  • 上位集合2

A \supseteq B
𝐴𝐵


  • 上位集合3

A \supseteqq B
𝐴𝐵


  • 部分集合でない

A \not \subset B
𝐴𝐵


  • 真の部分集合

A \subsetneqq B
𝐴𝐵


  • 集合の交わり

A \cap B
𝐴𝐵


  • 集合の結び

A \cup B
𝐴𝐵


  • 空集合

\varnothing


  • 空集合2

\emptyset


  • 補集合

A^c
𝐴𝑐


  • 補集合2

\overline{ A }
𝐴


  • 補集合サンプル

\overline{ (A\cap B) } = \overline{ A } \cup \overline{ B }
(𝐴𝐵)=𝐴𝐵


  • 補集合サンプル2

\begin{eqnarray}
\left( \bigcup_{\lambda\in\Lambda}A_{\lambda} \right)^c
=\bigcap_{\lambda\in\Lambda}A_{\lambda}^c
\end{eqnarray}
(𝜆Λ𝐴𝜆)𝑐=𝜆Λ𝐴𝑐𝜆


  • 差集合

A \setminus B
𝐴𝐵


  • 差集合サンプル

A \setminus B
= A \cap B^c
= \{ x \in A \mid x \notin B \}
𝐴𝐵=𝐴𝐵𝑐={𝑥𝐴𝑥𝐵}


  • 対称差

A \triangle B
𝐴𝐵


  • 対称差サンプル

A \triangle B
= (A \setminus B) \cup (B \setminus A)
𝐴𝐵=(𝐴𝐵)(𝐵𝐴)


  • 自然数全体の集合

\mathbb{ N }


  • 整数全体の集合

\mathbb{ Z }


  • 有理数全体の集合

\mathbb{ Q }


  • 実数全体の集合

\mathbb{ R }


  • 複素数全体の集合

\mathbb{ C }


  • 四元数全体の集合

\mathbb{ H }


  • 上限

\sup A
sup𝐴


  • 下限

\inf A
inf𝐴


  • アレフ数

\aleph

 

論理

  • 含意

P \implies Q
𝑃𝑄


  • 含意2

P \Rightarrow Q
𝑃𝑄


  • 含意3

P \to Q
𝑃𝑄


  • 含意(逆向き)

P \Leftarrow  Q
𝑃𝑄


  • 含意(逆向き)2

P \gets  Q
𝑃𝑄


  • 同値

P \iff Q
𝑃𝑄


  • 同値2

P \Leftrightarrow Q
𝑃𝑄


  • 同値3

P \leftrightarrow Q
𝑃𝑄


  • 同値4

P \equiv Q
𝑃𝑄


  • よって

\therefore


  • なぜならば

\because


  • すべての

\forall x
𝑥


  • 在る

\exists x
𝑥


  • 存在しない

\nexists


  • 量化記号サンプル

\begin{eqnarray}
& & {}^\forall \varepsilon \gt 0, {}^\exists \delta \gt 0 \mbox{ s.t. } \\
& & {}^\forall x \in \mathbb{ R }, 0 \lt |x - a| \lt \delta
\implies |f(x) - b| \lt \varepsilon 
\end{eqnarray}
𝜀>0,𝛿>0 s.t. 𝑥,0<|𝑥𝑎|<𝛿|𝑓(𝑥)𝑏|<𝜀


  • 論理積

P \land Q
𝑃𝑄


  • 論理和

P \lor Q
𝑃𝑄


  • 否定

\lnot P
¬𝑃


  • 否定2

\overline{ P }
𝑃


  • 否定3

!P
!𝑃


  • 排他的論理和

P \oplus Q
𝑃𝑄


  • 排他的論理和2

P \veebar Q
𝑃𝑄


  • 排他的論理和サンプル

P \oplus Q = (P \land \lnot Q) \lor (\lnot P \land Q)
𝑃𝑄=(𝑃¬𝑄)(¬𝑃𝑄)


  • トートロジー

\top


  • 矛盾

\bot


  • 証明可能

P \vdash Q
𝑃𝑄


  • 論理的帰結

P \models Q
𝑃𝑄

 

順列と組合せ

  • 順列

{}_n \mathrm{ P }_k
𝑛P𝑘


  • 組合せ

{}_n \mathrm{ C }_k
𝑛C𝑘


  • 階乗

n!
𝑛!


  • 二項係数

\binom{ n }{ k }
(𝑛𝑘)


  • 二項係数2

{ n \choose k }
(𝑛𝑘)


  • 二項係数3

\dbinom{ n }{ k }
(𝑛𝑘)


  • 重複組合せ

{}_n \mathrm{ H }_k
𝑛H𝑘


  • 組合せサンプル

\begin{eqnarray}
{}_n \mathrm{ C }_k
 = \binom{ n }{ k }
 = \frac{ n! }{ k! ( n - k )! }
\end{eqnarray}
𝑛C𝑘=(𝑛𝑘)=𝑛!𝑘!(𝑛𝑘)!


  • 順列サンプル

\begin{eqnarray}
{}_n \mathrm{ P }_k
 = n \cdot ( n - 1 ) \cdots ( n - k + 1 )
 = \frac{ n! }{ ( n - k )! }
\end{eqnarray}
𝑛P𝑘=𝑛(𝑛1)(𝑛𝑘+1)=𝑛!(𝑛𝑘)!

 

総和・総乗

  • 総和

\sum_{i=1}^{n} a_i
𝑖=1𝑛𝑎𝑖


  • 総和(大)

\displaystyle \sum_{i=1}^n a_i
𝑖=1𝑛𝑎𝑖


  • 総和サンプル

\begin{eqnarray}
\sum_{ k = 1 }^{ n } k^2
 = \overbrace{ 1^2 + 2^2 + \cdots + n^2 }^{ n }
 = \frac{ 1 }{ 6 } n ( n + 1 ) ( 2n + 1 )
\end{eqnarray}
𝑘=1𝑛𝑘2=12+22++𝑛2𝑛=16𝑛(𝑛+1)(2𝑛+1)


  • 総乗

\prod_{ i = 0 }^n x_i
𝑖=0𝑛𝑥𝑖


  • 総乗(大)

\displaystyle \prod_{i=0}^n x_i
𝑖=0𝑛𝑥𝑖


  • 総乗サンプル

\begin{eqnarray}
n! = \prod_{ k = 1 }^n k
\end{eqnarray}
𝑛!=𝑘=1𝑛𝑘


  • 総乗サンプル2

\begin{eqnarray}
\zeta (s)
 = \prod_{ p:\mathrm{ prime } }
   \frac{ 1 }{ 1-p^{-s} }
\end{eqnarray}
𝜁(𝑠)=𝑝:prime11𝑝𝑠

 

指数・対数

  • べき乗

2^3
23


  • べき乗2

e^{ i \pi }
𝑒𝑖𝜋


  • 指数関数

\exp ( x )
exp(𝑥)


  • 平方根

\sqrt{ 2 }
2


  • 平方根(高さを揃える)

\sqrt{ \mathstrut a } + \sqrt{ \mathstrut b }
𝑎+𝑏


  • べき根

\sqrt[ n ]{ x }
𝑥𝑛


  • 対数

\log x
log𝑥


  • 対数(底)

\log_{ 2 } x
log2𝑥


  • 自然対数

\ln x
ln𝑥

 

図形

  • 角度(度数)

90^{ \circ }
90


  • 角度(ラジアン)

\frac{ \pi }{ 2 }
𝜋2


  • 角記号

\angle A
𝐴


  • 平行(日本スタイル)

AB /\!/ CD
𝐴𝐵//𝐶𝐷


  • 平行(海外スタイル)

AB \parallel CD
𝐴𝐵𝐶𝐷


  • 垂直

AB \perp CD
𝐴𝐵𝐶𝐷


  • 三角形

\triangle ABC
𝐴𝐵𝐶


  • 四角形

\Box ABCD
𝐴𝐵𝐶𝐷


\stackrel{\huge\frown}{AB}
𝐴𝐵


\overparen{AB}
𝐴𝐵


  • 合同(日本スタイル)

\triangle ABC \equiv \triangle DEF
𝐴𝐵𝐶𝐷𝐸𝐹


  • 合同(海外スタイル)

\triangle ABC \cong \triangle DEF
𝐴𝐵𝐶𝐷𝐸𝐹


  • 相似(日本スタイル)

\triangle ABC \backsim \triangle DEF
𝐴𝐵𝐶𝐷𝐸𝐹


  • 相似(海外スタイル)

\triangle ABC \sim \triangle DEF
𝐴𝐵𝐶𝐷𝐸𝐹

 

三角関数

  • サイン

\sin x
sin𝑥


  • コサイン

\cos x
cos𝑥


  • タンジェント

\tan x
tan𝑥


  • サインサンプル

\begin{eqnarray}
\sin 45^\circ
 = \frac{ \sqrt{2} }{ 2 }
\end{eqnarray}
sin45=22


  • コサインサンプル

\begin{eqnarray}
\cos \frac{ \pi }{ 3 }
 = \frac{ 1 }{ 2 }
\end{eqnarray}
cos𝜋3=12


  • タンジェントサンプル

\begin{eqnarray}
\tan \theta
 = \frac{ \sin \theta }{ \cos \theta }
\end{eqnarray}
tan𝜃=sin𝜃cos𝜃


  • セカント

\sec x
sec𝑥


  • コセカント

\csc x
csc𝑥


  • コタンジェント

\cot x
cot𝑥


  • アークサイン

\arcsin x
arcsin𝑥


  • アークコサイン

\arccos x
arccos𝑥


  • アークタンジェント

\arctan x
arctan𝑥


  • ハイパボリックサイン

\sinh x
sinh𝑥


  • ハイパボリックコサイン

\cosh x
cosh𝑥


  • ハイパボリックタンジェント

\tanh x
tanh𝑥


  • ハイパボリックコタンジェント

\coth x
coth𝑥

 

複素数

  • 複素数

a+bi
𝑎+𝑏𝑖


  • 実部

\Re x
Re{𝑥}


  • 実部2

\require{physics} \Re x
Re{𝑥}


  • 虚部

\Im x
Im{𝑥}


  • 虚部2

\require{physics} \Im x
Im{𝑥}


  • 共役複素数

\bar{z}
𝑧¯


  • 偏角

\arg (z)
arg(𝑧)


  • 1の3乗根

\omega
𝜔


  • 複素数サンプル

\begin{eqnarray}
z\bar{z} = |z|^2
\end{eqnarray}
𝑧𝑧¯=|𝑧|2

 

極限

  • 極限

\lim_{ x \to +0 } \frac{1}{x} = \infty
lim𝑥+01𝑥=


  • 極限(大)

\displaystyle \lim_{ n \to \infty } f_n(x) = f(x)
lim𝑛𝑓𝑛(𝑥)=𝑓(𝑥)


  • 上極限

\limsup_{ n \to \infty } a_n
lim sup𝑛𝑎𝑛


  • 上極限(簡略)

\varlimsup_{ n \to \infty } a_n
lim𝑛𝑎𝑛


  • 下極限

\liminf_{ n \to \infty } a_n
lim inf𝑛𝑎𝑛


  • 下極限(簡略)

\varliminf_{ n \to \infty } a_n
lim𝑛𝑎𝑛


  • 上極限サンプル

\begin{eqnarray}
\varlimsup_{ n \to \infty } a_n
 = \lim_{ n \to \infty } \sup_{ k \geqq n } a_k
\end{eqnarray}
lim𝑛𝑎𝑛=lim𝑛sup𝑘𝑛𝑎𝑘


  • 下極限サンプル

\begin{eqnarray}
\varliminf_{ n \to \infty } A_n
 = \bigcup_{ n = 1 }^{ \infty } \bigcap_{ k = n }^{ \infty } A_k
 = \bigcup_{ n \in \mathbb{ N } } \bigcap_{ k \geqq n } A_k
\end{eqnarray}
lim𝑛𝐴𝑛=𝑛=1𝑘=𝑛𝐴𝑘=𝑛𝑘𝑛𝐴𝑘


  • ランダウの記号

\mathcal{O}
O

 

微分

  • 微分(ライプニッツ)

\frac{ dy }{ dx }
𝑑𝑦𝑑𝑥


  • 微分(ライプニッツ)2

\frac{ \mathrm{ d } y }{ \mathrm{ d } x }
d𝑦d𝑥


  • 微分(ライプニッツ)3

\require{physics} \dv{y}{x}
d𝑦d𝑥


  • n階微分(ライプニッツ)

\frac{ d^n y }{ dx^n }
𝑑𝑛𝑦𝑑𝑥𝑛


  • n階微分(ライプニッツ)2

\require{physics} \dv[n]{f}{x}
d[d𝑛]𝑓𝑥


  • ある点での微分(ライプニッツ)

\left. \frac{dy}{dx} \right|_{x=a}
𝑑𝑦𝑑𝑥|𝑥=𝑎


  • ある点での微分(ライプニッツ)2

\require{physics} \eval{\dv{y}{x}}_{x=a}
d𝑦d𝑥|𝑥=𝑎


  • 微分(ラグランジュ)

f'
𝑓


  • 2階微分(ラグランジュ)

f^{\prime\prime}
𝑓


  • n階微分(ラグランジュ)

f^{ ( n ) }
𝑓(𝑛)


  • 微分(オイラー)

Df
𝐷𝑓


  • 微分(オイラー)2

D_x f
𝐷𝑥𝑓


  • n階微分(オイラー)

D^n f
𝐷𝑛𝑓


  • 微分(ニュートン)

\dot{y} = \frac{dy}{dt}
𝑦˙=𝑑𝑦𝑑𝑡


  • 4階微分(ニュートン)

\ddddot{ y } = \frac{ d^4 y }{ dt^4 }
𝑦⃜ =𝑑4𝑦𝑑𝑡4


  • 微分サンプル

\begin{eqnarray}
f'(x)
 = \frac{ df }{ dx }
 = \lim_{ \Delta x \to 0 } \frac{ f(x + \Delta x) - f(x) }{ \Delta x }
\end{eqnarray}
𝑓(𝑥)=𝑑𝑓𝑑𝑥=limΔ𝑥0𝑓(𝑥+Δ𝑥)𝑓(𝑥)Δ𝑥


  • 偏微分

\frac{ \partial f }{ \partial x }
𝑓𝑥


  • 2階偏微分

\frac{ \partial }{ \partial y } \frac{ \partial }{ \partial x } z
𝑦𝑥𝑧


  • n階偏微分

\frac{ \partial^n f}{ \partial x^n }
𝑛𝑓𝑥𝑛


  • 偏微分2

\require{physics} \pdv{f}{x}
𝑓𝑥


  • 2階偏微分2

\require{physics} \pdv{f}{x}{y}
𝑓𝑥𝑦


  • n階偏微分2

\require{physics} \pdv[n]{f}{x}
[𝑛]𝑓𝑥


  • 偏微分(簡略)

f_x
𝑓𝑥


  • 2階偏微分(簡略)

f_{ xy }
𝑓𝑥𝑦


  • ナブラ

\nabla f
𝑓


  • ラプラシアン

\Delta f
Δ𝑓


  • ラプラシアン サンプル

\begin{eqnarray}
\Delta \varphi
 = \nabla^2 \varphi
 = \frac{ \partial^2 \varphi }{ \partial x^2 }
   + \frac{ \partial^2 \varphi }{ \partial y^2 }
   + \frac{ \partial^2 \varphi }{ \partial z^2 }
\end{eqnarray}
Δ𝜑=2𝜑=2𝜑𝑥2+2𝜑𝑦2+2𝜑𝑧2


  • 増減表

\begin{array}{c|ccccc}
  x     & \cdots & -1 & \cdots & 1 & \cdots \\ 
  \hline
  f’(x) & + & 0 & – & 0 & + \\ 
  \hline
  f(x)  & \nearrow & e & \searrow & -e & \nearrow
\end{array}
𝑥𝑓(𝑥)𝑓(𝑥)+10𝑒10𝑒+

 

積分

  • 積分

\int_0^1 f(x) dx
10𝑓(𝑥)𝑑𝑥


  • 積分(大)

\displaystyle \int_{-\infty}^{ \infty } f(x) dx
𝑓(𝑥)𝑑𝑥


  • 積分サンプル

\begin{eqnarray}
\int_0^1 x dx
= \left[ \frac{x^2}{2} \right]_0^1
= \frac{1}{2}
\end{eqnarray}
10𝑥𝑑𝑥=[𝑥22]10=12


  • 2重積分

\iint_D f(x,y) dxdy
𝐷𝑓(𝑥,𝑦)𝑑𝑥𝑑𝑦


  • 多重積分

\idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n
𝐷𝑓(𝑥1,𝑥2,,𝑥𝑛)𝑑𝑥1𝑑𝑥𝑛


  • 周回積分

\oint_C f(z) dz
𝐶𝑓(𝑧)𝑑𝑧

 

ベクトル

  • ベクトル

\vec{ a }
𝑎⃗ 


  • ベクトル2文字

\overrightarrow{ AB }
𝐴𝐵


  • ベクトル太文字

\boldsymbol{ A }
𝑨


  • 横ベクトル

( a_1, a_2, \ldots, a_n )
(𝑎1,𝑎2,,𝑎𝑛)


  • 縦ベクトル

\left(
  \begin{array}{c}
    a_1 \\
    a_2 \\
    \vdots \\
    a_n
  \end{array}
\right)
𝑎1𝑎2𝑎𝑛


  • ベクトルサンプル

\begin{eqnarray}
\boldsymbol{ 1 }
=( \underbrace{ 1, 1, \ldots, 1 }_{ n } )^{ \mathrm{ T } }
=\left(
   \begin{array}{c}
     1 \\
     1 \\
     \vdots \\
     1
   \end{array}
 \right)
\end{eqnarray}
𝟏=(1,1,,1𝑛)T=111


  • 単位ベクトルサンプル

\boldsymbol{ \rm{ e } }_k
=( 0, \ldots, 0, \stackrel{k}{ 1 }, 0, \ldots, 0 )^{\mathrm{T}}
𝐞𝑘=(0,,0,1𝑘,0,,0)T


  • ノルム

\| x \|
𝑥


  • ノルム2

\require{physics} \norm{ \dfrac{1}{2} }
12


  • 内積

\vec{ a } \cdot \vec{ b }
𝑎⃗ 𝑏⃗ 


  • 外積

\vec{ a } \times \vec{ b }
𝑎⃗ ×𝑏⃗ 

 

行列

  • 行列(丸かっこ)

\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
(𝑎𝑐𝑏𝑑)


  • 行列(角かっこ)

\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
[𝑎𝑐𝑏𝑑]


  • 行列(縦線)

\begin{vmatrix}
a & b \\
c & d
\end{vmatrix}
|𝑎𝑐𝑏𝑑|


  • 転置行列

A^{ \mathrm{ T } }
𝐴T


  • 転置行列2

{}^t \! A
𝑡𝐴


  • 次元

\dim
dim


  • 行列の階数

\mathrm{ rank } A
rank𝐴


  • 対角和

\mathrm{ Tr } A
Tr𝐴


  • 行列式

\mathrm{ det }A
det𝐴


  • 行列式サンプル

\begin{eqnarray}
\mathrm{ det }A
 = | A |
 = \begin{vmatrix} a & b \\ c & d \end{vmatrix}
 = ad - bc
\end{eqnarray}
det𝐴=|𝐴|=|𝑎𝑐𝑏𝑑|=𝑎𝑑𝑏𝑐


  • 行列(大)

\begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & I
\end{pmatrix}
𝑎𝑑𝑔𝑏𝑒𝑐𝑓𝐼


  • 行列(大)

\begin{eqnarray}
\left(
  \begin{array}{ccc}
    a & b & c \\
    d & e & f \\
    g & h & i
  \end{array}
\right)
\end{eqnarray}
𝑎𝑑𝑔𝑏𝑒𝑐𝑓𝑖


  • 行列(右寄せ)

\begin{eqnarray}
\left(
  \begin{array}{rrr}
    111 & 111 & 111 \\
    22 & 0.2 & -2 \\
    3 & 3 & 3
  \end{array}
\right)
\end{eqnarray}
1112231110.2311123


  • 行列(m行n列)

\begin{eqnarray}
A = \left(
  \begin{array}{cccc}
    a_{ 11 } & a_{ 12 } & \ldots & a_{ 1n } \\
    a_{ 21 } & a_{ 22 } & \ldots & a_{ 2n } \\
    \vdots & \vdots & \ddots & \vdots \\
    a_{ m1 } & a_{ m2 } & \ldots & a_{ mn }
  \end{array}
\right)
\end{eqnarray}
𝐴=𝑎11𝑎21𝑎𝑚1𝑎12𝑎22𝑎𝑚2𝑎1𝑛𝑎2𝑛𝑎𝑚𝑛


  • ブロック行列

\begin{eqnarray}
\left(
  \begin{array}{cc|cc}
    a & b & 0 & 0 \\
    c & d & 0 & 0 \\
    \hline
    x & y & 1 & 0 \\
    z & w & 0 & 1 \\
  \end{array}
\right)
\end{eqnarray}
𝑎𝑐𝑥𝑧𝑏𝑑𝑦𝑤00100001


  • ジョルダン細胞

\begin{eqnarray}
\begin{pmatrix}
  \lambda & 1 &   &  & 0 \\
    & \lambda & 1 &   &   \\
    &   & \ddots & \ddots &   \\
    &   &   & \lambda & 1  \\
  0 &   &   &   & \lambda
\end{pmatrix}
\end{eqnarray}
𝜆01𝜆1𝜆01𝜆


  • 余因子

\begin{eqnarray}
& & (-1)^{ i+j } \times \\[5pt]
& & \quad
\begin{vmatrix}
  a_{1,1} & \ldots & a_{1,j-1} & a_{1,j+1} & \ldots & a_{1,n} \\
  \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\
  a_{i-1,1} & \ldots & a_{i-1, j-1} & a_{i-1, j+1} & \ldots & a_{i-1, n} \\
  a_{i+1,1} & \ldots & a_{i+1, j-1} & a_{i+1, j+1} & \ldots & a_{i+1, n} \\
  \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\
  a_{n,1} & \ldots & a_{n, j-1} & a_{n, j+1} & \ldots & a_{n, n}
\end{vmatrix}
\end{eqnarray}
(1)𝑖+𝑗×𝑎1,1𝑎𝑖1,1𝑎𝑖+1,1𝑎𝑛,1𝑎1,𝑗1𝑎𝑖1,𝑗1𝑎𝑖+1,𝑗1𝑎𝑛,𝑗1𝑎1,𝑗+1𝑎𝑖1,𝑗+1𝑎𝑖+1,𝑗+1𝑎𝑛,𝑗+1𝑎1,𝑛𝑎𝑖1,𝑛𝑎𝑖+1,𝑛𝑎𝑛,𝑛

 

\begin{array}{ccc}
  xxx & yyy & zzz \\
  1   & 2   & 3
\end{array}
𝑥𝑥𝑥1𝑦𝑦𝑦2𝑧𝑧𝑧3


  • 表(縦線付)

\begin{array}{|c|c|c|}
  xxx & yyy & zzz \\
  1   & 2   & 3 \\
\end{array}
𝑥𝑥𝑥1𝑦𝑦𝑦2𝑧𝑧𝑧3


  • 表(横線付)

\begin{array}{ccc}
  \hline
  xxx & yyy & zzz \\
  \hline
  1   & 2   & 3 \\
  \hline
\end{array}
𝑥𝑥𝑥1𝑦𝑦𝑦2𝑧𝑧𝑧3


  • 表サンプル

\begin{array}{c|ccccc}
  x     & \cdots & -1 & \cdots & 1 & \cdots \\ 
  \hline
  f’(x) & + & 0 & – & 0 & + \\ 
  \hline
  f(x)  & \nearrow & e & \searrow & -e & \nearrow
\end{array}
𝑥𝑓(𝑥)𝑓(𝑥)+10𝑒10𝑒+

 

可換図式

  • 可換図式サンプル

\require{AMScd}
\begin{CD}
A @>{f}>> B\\
@V{gg}VV {\large\circlearrowleft} @VV{hh}V\\
C @>>{k}> D
\end{CD}
𝐴𝑔𝑔𝐶𝑓𝑘𝐵𝐷

 

  • 縦線

| x |
|𝑥|


  • 縦線2

\vert x \vert
|𝑥|


  • 縦線3

\{ x \mid x \in A \}
{𝑥𝑥𝐴}


  • 2重縦線

\Vert x \Vert
𝑥


  • 2重縦線2

AB \parallel CD
𝐴𝐵𝐶𝐷


  • 上線

\overline{ A }
𝐴


  • 上線2

\bar{ A }
𝐴¯


  • 下線

\underline{ A }
𝐴


  • スラッシュ

/
/


  • バックスラッシュ

\backslash


  • 斜線(下)

\diagdown


  • 斜線(上)

\diagup


  • キャンセル

\cancel{a}
𝑎


  • バックキャンセル

\bcancel{a}
𝑎


  • ×印キャンセル

\xcancel{a}
𝑎


  • キャンセルと矢印

\cancelto{A}{a}
𝑎𝐴


  • キャンセルサンプル

\begin{eqnarray}
\frac{\cancel{2}}{\cancel{6}}=\frac{1}{3}
\end{eqnarray}
26=13


  • キャンセルと矢印サンプル

\begin{eqnarray}
\frac{1}{\cancel{3}} \times \frac{\cancelto{2}{6}}{5}
\end{eqnarray}
13×625


  • 左下の角

\llcorner


  • 右下の角

\lrcorner


  • 左上の角

\ulcorner


  • 右上の角

\urcorner

 

矢印

  • 左矢印

\leftarrow


  • 左矢印(長い)

\longleftarrow


  • 右矢印

\rightarrow


  • 右矢印(長い)

\longrightarrow


  • 上矢印

\uparrow


  • 下矢印

\downarrow


  • 左右矢印

\leftrightarrow


  • 左右矢印(長い)

\longleftrightarrow


  • 上下矢印

\updownarrow


  • 2重左矢印

\Leftarrow


  • 2重左矢印(長い)

\Longleftarrow


  • 2重右矢印

\Rightarrow


  • 2重右矢印(長い)

\Longrightarrow


  • 2重上矢印

\Uparrow


  • 2重下矢印

\Downarrow


  • 2重左右矢印

\Leftrightarrow


  • 2重左右矢印(長い)

\Longleftrightarrow


  • 2重上下矢印

\Updownarrow


  • 右上矢印

\nearrow


  • 右下矢印

\searrow


  • 左上矢印

\nwarrow


  • 左下矢印

\swarrow


  • 棒付矢印

\mapsto


  • 棒付矢印(長い)

\longmapsto


  • 頭に矢印

\vec{ a }
𝑎⃗ 


  • 頭に矢印2

\overrightarrow{ AB }
𝐴𝐵


  • 頭に矢印(左向き)

\overleftarrow{ AB }
𝐴𝐵


  • 時計回り矢印

\circlearrowright


  • 反時計回り矢印

\circlearrowleft

 

括弧

  • 丸括弧

( x )
(𝑥)


  • 角括弧

[ x ]
[𝑥]


  • 角括弧2

\lbrack x \rbrack
[𝑥]


  • かぎ括弧

\lceil x \rfloor
𝑥


  • かぎ括弧2

\lfloor x \rceil
𝑥


  • 波括弧

\{ x \}
{𝑥}


  • 波括弧2

\lbrace x \rbrace
{𝑥}


  • 山括弧

\langle x \rangle
𝑥


  • 大きい括弧

\left[ \dfrac{ 1 }{ 2 } \right]
[12]


  • 上括弧

\overbrace{ x + y + z }
𝑥+𝑦+𝑧


  • 上括弧と文字

\overbrace{ a_1 + \cdots + a_n }^{ n }
𝑎1++𝑎𝑛𝑛


  • 下括弧

\underbrace{ x + y + z }
𝑥+𝑦+𝑧


  • 下括弧と文字

\underbrace{ a_1 + \cdots + a_n }_{ n }
𝑎1++𝑎𝑛𝑛

 

  • 点(中央)

\cdot


  • 複数の点(中央横向き)

\cdots


  • 複数の点(下側横向き)

\ldots


  • 複数の点(中央縦向き)

\vdots


  • 複数の点(斜め)

\ddots


  • 頭に点

\dot{ a }
𝑎˙


  • 頭に2つの点

\ddot{ a }
𝑎¨

 

  • 白丸

\circ


  • 黒丸

\bullet


  • 大きい丸

\bigcirc


  • 丸にプラス

\oplus


  • 丸にマイナス

\ominus


  • 丸に掛ける

\otimes


  • 丸に点

\odot

 

三角形

  • 三角形

\triangle


  • 下向き三角形

\triangledown


  • 大きな上向き三角形

\bigtriangleup


  • 大きな下向き三角形

\bigtriangledown


  • 左向き三角形

\triangleleft


  • 左向き三角形2

\lhd


  • 右向き三角形

\triangleright


  • 右向き三角形2

\rhd


  • 左向き三角形と下線

\unlhd


  • 右向き三角形と下線

\unrhd


  • 黒い三角形

\blacktriangle

 

四角形

  • 正方形

\square


  • 四角形

\Box


  • 四角形と十字

\boxplus


  • 四角形と横線

\boxminus


  • 四角形と×

\boxtimes


  • 四角形と点

\boxdot


  • 黒い正方形

\blacksquare


  • ダイヤモンド

\diamond


  • ダイヤモンド2

\Diamond


  • ひし形

\lozenge


  • 黒いひし形

\blacklozenge


  • 枠付きテキスト

\boxed{ abc }
𝑎𝑏𝑐


  • 枠付きテキスト2

\fbox{ abc }
 abc 


  • 枠付きテキスト3

\bbox[yellow, 5pt, border: 2px dotted red]{abc}
𝑎𝑏𝑐

 

二項演算

  • アスタリスク

\ast


  • スター

\star


  • 左線と掛ける

\ltimes


  • 右線と掛ける

\rtimes


  • 自然結合

\Join

 

一般的な記号

  • ドル記号

\$
$


  • &記号

\And
&


  • 円マーク

\yen
¥


  • チェックマーク

\checkmark


  • ダイヤモンド

\diamondsuit


  • ハート

\heartsuit


  • クラブ

\clubsuit


  • スペード

\spadesuit


  • フラット

\flat


  • ナチュラル

\natural


  • シャープ

\sharp


  • ダガー

\dagger


  • ダガー2

\ddagger

 

空白

  • 空白

aaa \ bbb
𝑎𝑎𝑎 𝑏𝑏𝑏


  • 広い空白

aaa \quad bbb
𝑎𝑎𝑎𝑏𝑏𝑏


  • 広い空白2

aaa \qquad bbb
𝑎𝑎𝑎𝑏𝑏𝑏


  • 空白(サイズ指定)

aaa \hspace{ 10pt } bbb
𝑎𝑎𝑎𝑏𝑏𝑏


  • 空白をなくす

aaa \! bbb
𝑎𝑎𝑎𝑏𝑏𝑏


  • 改行

\begin{eqnarray} 
aaa \\ bbb
\end{eqnarray}
𝑎𝑎𝑎𝑏𝑏𝑏


  • 改行(サイズ指定)

\begin{eqnarray} 
aaa \\[5pt] bbb
\end{eqnarray}
𝑎𝑎𝑎𝑏𝑏𝑏


  • 改行(サイズ指定)サンプル

\begin{eqnarray}
& & \frac{1}{2} +\frac{1}{3} +\frac{1}{6} \\[ 5pt ]
&=& \frac{3}{6} +\frac{2}{6} +\frac{1}{6} \\
&=& 1
\end{eqnarray}
==12+13+1636+26+161

 

文字サイズ

  • 極小サイズ

\tiny{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 小さいサイズ

\scriptsize{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 小さいサイズ2

\small{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • ノーマルサイズ

\normalsize{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 大きいサイズ

\large{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 大きいサイズ2

\Large{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 大きいサイズ3

\LARGE{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 極大サイズ

\huge{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶


  • 極大サイズ2

\Huge{ abc ABC }
𝑎𝑏𝑐𝐴𝐵𝐶

 

フォント

  • ローマン体

\mathrm{ ABC }
ABC


  • タイプライターフォント

\mathtt{ ABC }
𝙰𝙱𝙲


  • サンセリフ

\mathsf{ ABC }
𝖠𝖡𝖢


  • カリグラフィーフォント

\mathcal{ ABC }
ABC


  • 太文字

\mathbf{ ABC }
𝐀𝐁𝐂


  • イタリック

\mathit{ ABC }
ABC


  • 中抜き文字

\mathbb{ ABC }
𝔸𝔹


  • スクリプトフォント

\mathscr{ ABC }
𝒜𝒞


  • フラクトゥール

\mathfrak{ ABC }
𝔄𝔅


  • ローマン体 サンプル

\mathrm{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
abcdefghijklmnopqrstuvwxyz }
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz


  • タイプライターフォント サンプル

\mathtt{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
abcdefghijklmnopqrstuvwxyz }
𝙰𝙱𝙲𝙳𝙴𝙵𝙶𝙷𝙸𝙹𝙺𝙻𝙼𝙽𝙾𝙿𝚀𝚁𝚂𝚃𝚄𝚅𝚆𝚇𝚈𝚉𝚊𝚋𝚌𝚍𝚎𝚏𝚐𝚑𝚒𝚓𝚔𝚕𝚖𝚗𝚘𝚙𝚚𝚛𝚜𝚝𝚞𝚟𝚠𝚡𝚢𝚣


  • サンセリフ サンプル

\mathsf{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
abcdefghijklmnopqrstuvwxyz }
𝖠𝖡𝖢𝖣𝖤𝖥𝖦𝖧𝖨𝖩𝖪𝖫𝖬𝖭𝖮𝖯𝖰𝖱𝖲𝖳𝖴𝖵𝖶𝖷𝖸𝖹𝖺𝖻𝖼𝖽𝖾𝖿𝗀𝗁𝗂𝗃𝗄𝗅𝗆𝗇𝗈𝗉𝗊𝗋𝗌𝗍𝗎𝗏𝗐𝗑𝗒𝗓


  • カリグラフィーフォント サンプル

\mathcal{ ABCDEFGHIJKLM \\
NOPQRSTUVWXYZ }
ABCDEFGHIJKLMNOPQRSTUVWXYZ


  • 太文字 サンプル

\mathbf{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
abcdefghijklmnopqrstuvwxyz }
𝐀𝐁𝐂𝐃𝐄𝐅𝐆𝐇𝐈𝐉𝐊𝐋𝐌𝐍𝐎𝐏𝐐𝐑𝐒𝐓𝐔𝐕𝐖𝐗𝐘𝐙𝐚𝐛𝐜𝐝𝐞𝐟𝐠𝐡𝐢𝐣𝐤𝐥𝐦𝐧𝐨𝐩𝐪𝐫𝐬𝐭𝐮𝐯𝐰𝐱𝐲𝐳


  • イタリック サンプル

\mathit{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
abcdefghijklmnopqrstuvwxyz }
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz


  • 中抜き文字 サンプル

\mathbb{ ABCDEFGHIJKLM \\
NOPQRSTUVWXYZ }
𝔸𝔹𝔻𝔼𝔽𝔾𝕀𝕁𝕂𝕃𝕄𝕆𝕊𝕋𝕌𝕍𝕎𝕏𝕐


  • スクリプトフォント サンプル

\mathscr{ ABCDEFGHIJKLM \\
NOPQRSTUVWXYZ }
𝒜𝒞𝒟𝒢𝒥𝒦𝒩𝒪𝒫𝒬𝒮𝒯𝒰𝒱𝒲𝒳𝒴𝒵


  • フラクトゥール サンプル

\mathfrak{ ABCDEFGHIJKLMNOPQRSTUVWXYZ \\
abcdefghijklmnopqrstuvwxyz }
𝔄𝔅𝔇𝔈𝔉𝔊𝔍𝔎𝔏𝔐𝔑𝔒𝔓𝔔𝔖𝔗𝔘𝔙𝔚𝔛𝔜𝔞𝔟𝔠𝔡𝔢𝔣𝔤𝔥𝔦𝔧𝔨𝔩𝔪𝔫𝔬𝔭𝔮𝔯𝔰𝔱𝔲𝔳𝔴𝔵𝔶𝔷

 

上付き・下付き

  • 上付き文字

a^{ xy }
𝑎𝑥𝑦


  • 上付き文字(左)

{}^{ xy } a
𝑥𝑦𝑎


  • 下付き文字

a_{ xy }
𝑎𝑥𝑦


  • 下付き文字(左)

{}_{ xy } a
𝑥𝑦𝑎


  • 下付きサンプル

\begin{eqnarray}
a_n^2 + a_{ n + 1 }^2 = a_{ 2n + 1 }
\end{eqnarray}
𝑎2𝑛+𝑎2𝑛+1=𝑎2𝑛+1

 

アクセント

  • ハット

\hat{ a }
𝑎̂ 


  • グレイブ

\grave{ a }
𝑎̀ 


  • アキュート

\acute{ a }
𝑎́ 


  • ドット

\dot{ a }
𝑎˙


  • ダブルドット

\ddot{ a }
𝑎¨


  • バー

\bar{ a }
𝑎¯


  • 矢印

\vec{ a }
𝑎⃗ 


  • チェック

\check{ a }
𝑎ˇ


  • チルダ

\tilde{ a }
𝑎̃ 


  • ブリーブ

\breve{ a }
𝑎˘


  • 広いハット

\widehat{ AAA }
𝐴𝐴𝐴̂


  • 広いチルダ

\widetilde{ AAA }
𝐴𝐴𝐴̃

 

アルファベット

  • さかさまの A

\forall


  • さかさまの E

\exists


  • さかさまの F

\Finv


  • バー付きの h

\hbar


  • 点なしの i

\imath
ı


  • 点なしの j

\jmath
ȷ


  • 中抜き文字の k

\Bbbk
𝕜


  • 筆記体の l

\ell


  • 丸付きの R

\circledR
®


  • 丸付きの S

\circledS

 

ギリシャ文字

  • アルファ

\alpha
𝛼


  • ベータ

\beta
𝛽


  • ガンマ

\gamma
𝛾


  • デルタ

\delta
𝛿


  • イプシロン

\epsilon
𝜖


  • イプシロン2

\varepsilon
𝜀


  • ゼータ

\zeta
𝜁


  • イータ

\eta
𝜂


  • シータ

\theta
𝜃


  • シータ2

\vartheta
𝜗


  • イオタ

\iota
𝜄


  • カッパ

\kappa
𝜅


  • ラムダ

\lambda
𝜆


  • ミュー

\mu
𝜇


  • ニュー

\nu
𝜈


  • クシー

\xi
𝜉


  • オミクロン

o
𝑜


  • パイ

\pi
𝜋


  • パイ2

\varpi
𝜛


  • ロー

\rho
𝜌


  • ロー2

\varrho
𝜚


  • シグマ

\sigma
𝜎


  • シグマ2

\varsigma
𝜍


  • タウ

\tau
𝜏


  • ユプシロン

\upsilon
𝜐


  • ファイ

\phi
𝜙


  • ファイ2

\varphi
𝜑


  • カイ

\chi
𝜒


  • プシー

\psi
𝜓


  • オメガ

\omega
𝜔


  • アルファ(大)

A
𝐴


  • ベータ(大)

B
𝐵


  • ガンマ(大)

\Gamma
Γ


  • ガンマ(大)2

\varGamma
𝛤


  • デルタ(大)

\Delta
Δ


  • デルタ(大)2

\varDelta
𝛥


  • イプシロン(大)

E
𝐸


  • ゼータ(大)

Z
𝑍


  • イータ(大)

H
𝐻


  • シータ(大)

\Theta
Θ


  • シータ(大)2

\varTheta
𝛩


  • イオタ(大)

I
𝐼


  • カッパ(大)

K
𝐾


  • ラムダ(大)

\Lambda
Λ


  • ラムダ(大)2

\varLambda
𝛬


  • ミュー(大)

M
𝑀


  • ニュー(大)

N
𝑁


  • クシー(大)

\Xi
Ξ


  • クシー(大)2

\varXi
𝛯


  • オミクロン(大)

O
𝑂


  • パイ(大)

\Pi
Π


  • パイ(大)2

\varPi
𝛱


  • ロー(大)

P
𝑃


  • シグマ(大)

\Sigma
Σ


  • シグマ(大)2

\varSigma
𝛴


  • タウ(大)

T
𝑇


  • ユプシロン(大)

\Upsilon
Υ


  • ユプシロン(大)2

\varUpsilon
𝛶


  • ファイ(大)

\Phi
Φ


  • ファイ(大)2

\varPhi
𝛷


  • カイ(大)

X
𝑋


  • プシー(大)

\Psi
Ψ


  • プシー(大)2

\varPsi
𝛹


  • オメガ(大)

\Omega
Ω


  • オメガ(大)2

\varOmega
𝛺

 

HTML

  • 色付きの文字

\color{red}{a \times b}
𝑎×𝑏


  • 色付きの文字2

\color{ #ff0000 }{a \times b}
𝑎×𝑏


  • 色付きの箱

\colorbox{red}{ Important! }
 Important! 


  • 色付きの箱2

\colorbox{red}{$a \times b$}
𝑎×𝑏


  • 枠線と色のついた箱

\fcolorbox{black}{ #00ff00 }{$a \times b$}
𝑎×𝑏


  • 枠線と色のついた箱 2

\bbox[yellow, 5pt, border: 2px dotted red]{abc}
𝑎𝑏𝑐


  • ユニコード

\unicode{x0041}
A


  • ユニコードサンプル

\begin{eqnarray}
\unicode{x5F45}\text{は、弓へんに剪。}
\end{eqnarray}

 

特殊文字

  • セクション

\S
§


  • アレフ

\aleph


  • ベート

\beth


  • ギメル

\gimel


  • ダレット

\daleth

 

ロゴ

  • tex

\TeX
𝑇𝐸𝑋


  • latex

\LaTeX
𝐿𝐴𝑇𝐸𝑋

 

Mathjax 2.7に戻る。