tex.html

<h1>Math with \(\TeX\)</h1>

<p>Typesetting with \(\TeX\). This is a list of \(\TeX\) functions supported by Blot. It is sorted into logical groups.</p>

<div class="tex">
<background><pre class="text"><code>Blot will convert equations set in LaTeX. Wrap your LaTeX in two dollar signs ($) like this:

$$ f(x) = 2x^2 + 2/3 $$
</code></pre></background>



<h3 id="accents">Accents</h3>

    <table class="symbol">
    <tr>
      <td>\(a'\)</td>
      <td>a'</td>
      <td>\(\ddot{a}\)</td>
      <td>\ddot{a}</td>
      <td>\(\overleftarrow{AB}\)</td>
      <td>\overleftarrow{AB}</td>
      <td>\(\overrightarrow{AB}\)</td>
      <td>\overrightarrow{AB}</td>
    </tr>
    <tr>
      <td>\(a''\)</td>
      <td>a''</td>
      <td>\(\grave{a}\)</td>
      <td>\grave{a}</td>
      <td>\(\underleftarrow{AB}\)</td>
      <td>\underleftarrow{AB}</td>
      <td>\(\underrightarrow{AB}\)</td>
      <td>\underrightarrow{AB}</td>
    </tr>
    <tr>
      <td>\(a^{\prime}\)</td>
      <td style="white-space: nowrap">a^{\prime}</td>
      <td>\(\hat{\theta}\)</td>
      <td>\hat{\theta}</td>
      <td>\(\overleftrightarrow{AB}\)</td>
      <td style="white-space: nowrap">\overleftrightarrow{AB}</td>
      <td>\(\overbrace{AB}\)</td>
      <td>\overbrace{AB}</td>
    </tr>
    <tr>
      <td>\(\acute{a}\)</td>
      <td>\acute{a}</td>
      <td>\(\widehat{ac}\)</td>
      <td>\widehat{ac}</td>
      <td>\(\underleftrightarrow{AB}\)</td>
      <td style="white-space: nowrap">\underleftrightarrow{AB}</td>
      <td>\(\underbrace{AB}\)</td>
      <td>\underbrace{AB}</td>
    </tr>
    <tr>
      <td>\(\bar{y}\)</td>
      <td>\bar{y}</td>
      <td>\(\tilde{a}\)</td>
      <td>\tilde{a}</td>
      <td>\(\overgroup{AB}\)</td>
      <td>\overgroup{AB}</td>
      <td>\(\overlinesegment{AB}\)</td>
      <td>\overlinesegment{AB}</td>
    </tr>
    <tr>
      <td>\(\breve{a}\)</td>
      <td>\breve{a}</td>
      <td>\(\widetilde{ac}\)</td>
      <td style="white-space: nowrap">\widetilde{ac}</td>
      <td>\(\undergroup{AB}\)</td>
      <td>\undergroup{AB}</td>
      <td>\(\underlinesegment{AB}\)</td>
      <td>\underlinesegment{AB}</td>
    </tr>
    <tr>
      <td>\(\check{a}\)</td>
      <td>\check{a}</td>
      <td>\(\vec{F}\)</td>
      <td>\vec{F}</td>
      <td>\(\overleftharpoon{ac}\)</td>
      <td>\overleftharpoon{ac}</td>
      <td>\(\overrightharpoon{ac}\)</td>
      <td>\overrightharpoon{ac}</td>
    </tr>
    <tr>
      <td>\(\dot{a}\)</td>
      <td>\dot{a}</td>
      <td>\(\overline{AB}\)</td>
      <td>\overline{AB}</td>
      <td>\(\Overrightarrow{AB}\)</td>
      <td>\Overrightarrow{AB}</td>
      <td>\(\utilde{AB}\)</td>
      <td>\utilde{AB}</td>
    </tr>
    <tr>
      <td></td>
      <td></td>
      <td>\(\underline{AB}\)</td>
      <td>\underline{AB}</td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
  </table>
  

  <span class="fr">See also <a href="#other-letters">letters</a>.</span>

  <h4>Accent functions inside <code>\text{…}</code>  </h4>

  <table class="symbol">
    <tr>
      <td>\(\text{\'{a}}\)</td>
      <td>\'{a}</td>
      <td>\(\text{\~{a}}\)</td>
      <td>\~{a}</td>
      <td>\(\text{\.{a}}\)</td>
      <td>\.{a}</td>
      <td>\(\text{\H{a}}\)</td>
      <td>\H{a}</td>
    </tr>
    <tr>
      <td>\(\text{\`{a}}\)</td>
      <td>\`{a}</td>
      <td>\(\text{\={a}}\)</td>
      <td>\={a}</td>
      <td>\(\text{\"{a}}\)</td>
      <td>\"{a}</td>
      <td>\(\text{\v{a}}\)</td>
      <td>\v{a}</td>
    </tr>
    <tr>
      <td>\(\text{\^{a}}\)</td>
      <td>\^{a}</td>
      <td>\(\text{\u{a}}\)</td>
      <td>\u{a}</td>
      <td>\(\text{\r{a}}\)</td>
      <td>\r{a}</td>
      <td></td>
      <td></td>
    </tr>
  </table>
  

<h3 id="delimiters">Delimiters</h3>

    <table class="symbol" id="delim">
        <tr>
            <td>\((\,)\)</td>
            <td>( )</td>
            <td>\(\lgroup\:\rgroup\)</td>
            <td>\lgroup<br>\rgroup</td>
            <td>\(\lceil\:\rceil\)</td>
            <td>\lceil<br>\rceil</td>
            <td>\(\uparrow\)</td>
            <td>\uparrow</td>
        </tr>
        <tr>
            <td>\([\:]\)</td>
            <td>[ ]</td>
            <td>\(\lbrack\:\rbrack\)</td>
            <td>\lbrack<br>\rbrack</td>
            <td>\(\lfloor\:\rfloor\)</td>
            <td>\lfloor<br>\rfloor</td>
            <td>\(\downarrow\)</td>
            <td>\downarrow</td>
        </tr>
        <tr>
            <td>\(\{\,\}\)</td>
            <td>\{&nbsp;\}</td>
            <td>\(\lbrace\:\rbrace\)</td>
            <td>\lbrace<br>\rbrace</td>
            <td>\(\ulcorner \urcorner\)</td>
            <td>\ulcorner<br>\urcorner</td>
            <td>\(\updownarrow\)</td>
            <td>\updownarrow</td>
        </tr>
        <tr>
            <td>\(\langle\:\rangle\)</td>
            <td>\langle<br>\rangle</td>
            <td>\(\lt\:\gt\)</td>
            <td>\lt<br>\gt</td>
            <td>\(\llcorner \lrcorner\)</td>
            <td>\llcorner<br>\lrcorner</td>
            <td>\(\Uparrow\)</td>
            <td>\Uparrow</td>
        </tr>
        <tr>
            <td>\(|\)</td>
            <td>|</td>
            <td>\(\vert\)</td>
            <td>\vert</td>
            <td>\(\backslash\)</td>
            <td>\backslash</td>
            <td>\(\Downarrow\)</td>
            <td>\Downarrow</td>
        </tr>
        <tr>
            <td>\(\|\)</td>
            <td>\|</td>
            <td>\(\Vert\)</td>
            <td>\Vert</td>
            <td>\(\lmoustache\:\rmoustache\)</td>
            <td>\lmoustache<br>\rmoustache</td>
            <td>\(\Updownarrow\)</td>
            <td>\Updownarrow</td>
        </tr>
        <tr>
            <td>\(\lvert\;\rvert\)</td>
            <td>\lvert<br>\rvert</td>
            <td>\(\lVert\;\rVert\)</td>
            <td>\lVert<br>\rVert</td>
            <td></td>
            <td>\left.</td>
            <td></td>
            <td>\right.</td>
        </tr>
    </table>

<h4 id="delimiter-sizing">Delimiter Sizing</h4>

    <table class="all-code">
        <tr>
            <td rowspan="2">\(\left(\LARGE{AB}\right)\)</td>
            <td rowspan="2" >\left( \LARGE{AB} \right)</td>
            <td>\left</td>
            <td>\big</td>
            <td>\bigl</td>
            <td>\bigr</td>
        </tr>
        <tr>
            <td>\middle</td>
            <td>\Big</td>
            <td>\Bigl</td>
            <td>\Bigr</td>
        </tr>
        <tr>
            <td rowspan="2">\(( \big( \Big( \bigg( \Bigg(\)</td>
            <td rowspan="2">( \big( \Big( \bigg( \Bigg(</td>
            <td>\right</td>
            <td>\bigg</td>
            <td>\biggl</td>
            <td>\biggr</td>
        </tr>
        <tr>
            <td></td>
            <td>\Bigg</td>
            <td>\Biggl</td>
            <td>\Biggr</td>
        </tr>
    </table>

<h3 id="environments">Environments</h3>

    <table class="symbol">
        <tr>
            <td>\(\begin{matrix} a & b \\ c & d \end{matrix}\)</td>
            <td>
                <pre><code>\begin{matrix}
   a &amp; b \\
   c &amp; d
\end{matrix}</code></pre>
            </td>
            <td>\(\begin{array}{c|c} a & b \\ c & d \end{array}\)</td>
            <td>
                <pre><code>\begin{array}{c|c}
   a &amp; b \\
   c &amp; d
\end{array}</code></pre>
            </td>
            <td>\(\begin{aligned} a&=b+c \\ d+e&=f \end{aligned}\)</td>
            <td>
                <pre><code>\begin{aligned}
   a&amp;=b+c \\
   d+e&=f
\end{aligned}</code></pre>
            </td>
        </tr>
        <tr>
            <td>\(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)</td>
            <td>
                <pre><code>\begin{pmatrix}
   a &amp; b \\
   c &amp; d
\end{pmatrix}</code></pre>
            </td>
            <td>\(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\)</td>
            <td>
                <pre><code>\begin{bmatrix}
   a &amp; b \\
   c &amp; d
\end{bmatrix}</code></pre>
            </td>
      <td>\(\begin{alignedat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignedat}\)</td>
      <td>
        <pre><code>\begin{alignedat}{2}
   10&x+ &3&y = 2 \\
    3&x+&13&y = 4
\end{alignedat}</code></pre>
      </td>
      </tr>
        <tr>
            <td>\(\begin{vmatrix} a & b \\ c & d \end{vmatrix}\)</td>
            <td>
                <pre><code>\begin{vmatrix}
   a &amp; b \\
   c &amp; d
\end{vmatrix}</code></pre>
            </td>
            <td>\(\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}\)</td>
            <td>
                <pre><code>\begin{Vmatrix}
   a &amp; b \\
   c &amp; d
\end{Vmatrix}</code></pre>
            </td>
            <td>\(\begin{gathered} a=b \\ e=b+c \end{gathered}\)</td>
      <td>
                <pre><code>\begin{gathered}
   a=b \\ 
   e=b+c
\end{gathered}</code></pre>
      </td>
        </tr>
        <tr>
            <td>\(\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}\)</td>
            <td>
                <pre><code>\begin{Bmatrix}
   a &amp; b \\
   c &amp; d
\end{Bmatrix}</code></pre>
            </td>
      <td></td>
      <td></td>
            <td>\(x = \begin{cases} a &\text{if } b \\ c &\text{if } d \end{cases}\)</td>
            <td>
                <pre><code>x = \begin{cases}
   a &amp;\text{if } b  \\
   c &amp;\text{if } d
\end{cases}</code></pre>
            </td>
        </tr>
    </table>

<p class="measure">There is also support for <code>{darray}</code> and <code>{dcases}</code>. Acceptable line separators include: <code>\\</code>, <code>\cr</code>, and <code>\\[<em>distance</em>]</code>. <em>Distance</em> can be written with any of the <a href="#units">units</a>. The <code>{array}</code> environment does not yet support <code>\hline</code>.</p>


<!-- Filed a bug about this here:

https://github.com/Khan/KaTeX/issues/1245

\href doesn't seem to render properly on the server.

<h3>HTML</h3>

  <table>
    <tr>
      <td>\(\href{foo}{bar}\)</td>
      <td>\href{https://wikipedia.org}{Wikipedia}</td>
    </tr>
  </table>
-->


<h3>Letters</h3>
    
    <table class="symbol">
        <tr>
            <td>Γ</td>
            <td>\Gamma</td>
            <td>Δ</td>
            <td>\Delta</td>
            <td>Θ</td>
            <td>\Theta</td>
            <td>Λ</td>
            <td>\Lambda</td>
        </tr>
        <tr>
            <td>Ξ</td>
            <td>\Xi</td>
            <td>Π</td>
            <td>\Pi</td>
            <td>Σ</td>
            <td>\Sigma</td>
            <td>Υ</td>
            <td>\Upsilon</td>
        </tr>
        <tr>
            <td>Φ</td>
            <td>\Phi</td>
            <td>Ψ</td>
            <td>\Psi</td>
            <td>Ω</td>
            <td>\Omega</td>
            <td></td>
            <td></td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">α</span></span></td>
            <td>\alpha</td>
            <td><span class="katex"><span class="mathit">β</span></span></td>
            <td>\beta</td>
            <td><span class="katex"><span class="mathit">γ</span></span></td>
            <td>\gamma</td>
            <td><span class="katex"><span class="mathit">δ</span></span></td>
            <td>\delta</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ϵ</span></span></td>
            <td>\epsilon</td>
            <td><span class="katex"><span class="mathit">ζ</span></span></td>
            <td>\zeta</td>
            <td><span class="katex"><span class="mathit">η</span></span></td>
            <td>\eta</td>
            <td><span class="katex"><span class="mathit">θ</span></span></td>
            <td>\theta</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ι</span></span></td>
            <td>\iota</td>
            <td><span class="katex"><span class="mathit">κ</span></span></td>
            <td>\kappa</td>
            <td><span class="katex"><span class="mathit">λ</span></span></td>
            <td>\lambda</td>
            <td><span class="katex"><span class="mathit">μ</span></span></td>
            <td>\mu</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ν</span></span></td>
            <td>\nu</td>
            <td><span class="katex"><span class="mathit">ξ</span></span></td>
            <td>\xi</td>
            <td><span class="katex"><span class="mathit">o</span></span></td>
            <td>\omicron</td>
            <td><span class="katex"><span class="mathit">π</span></span></td>
            <td>\pi</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ρ</span></span></td>
            <td>\rho</td>
            <td><span class="katex"><span class="mathit">σ</span></span></td>
            <td>\sigma</td>
            <td><span class="katex"><span class="mathit">τ</span></span></td>
            <td>\tau</td>
            <td><span class="katex"><span class="mathit">υ</span></span></td>
            <td>\upsilon</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ϕ</span></span></td>
            <td>\phi</td>
            <td><span class="katex"><span class="mathit">χ</span></span></td>
            <td>\chi</td>
            <td><span class="katex"><span class="mathit">ψ</span></span></td>
            <td>\psi</td>
            <td><span class="katex"><span class="mathit">ω</span></span></td>
            <td>\omega</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ε</span></span></td>
            <td>\varepsilon</td>
            <td><span class="katex"><span class="mathit">ϰ</span></span></td>
            <td>\varkappa</td>
            <td><span class="katex"><span class="mathit">ϑ</span></span></td>
            <td>\vartheta</td>
            <td><span class="katex"><span class="mathit">ϖ</span></span></td>
            <td>\varpi</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathit">ϱ</span></span></td>
            <td>\varrho</td>
            <td><span class="katex"><span class="mathit">ς</span></span></td>
            <td>\varsigma</td>
            <td><span class="katex"><span class="mathit">φ</span></span></td>
            <td>\varphi</td>
            <td>ϝ</td>
            <td>\digamma</td>
        </tr>
            <tr>
      <td class="not-symbol">Direct Input:</td>
      <td class="symbol" colspan="8" style="font-family: KaTeX_Main, KaTeX_AMS;">Γ Δ Θ Λ Ξ Π Σ Υ Φ Ψ Ω<br><span class="katex"><span class="mathit">α β γ δ ϵ ζ η θ ι κ λ μ ν ξ o π ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ</span></span></td>
    </tr>

    </table>

<h4 id="other-letters">Other Letters</h4>
    <table class="symbol">
        <tr>
            <td>\(\imath\)</td>
            <td>\imath</td>
            <td>\(\jmath\)</td>
            <td>\jmath</td>
            <td>ℵ</td>
            <td>\aleph</td>
            <td>ℶ</td>
            <td>\beth</td>
            <td>ℷ</td>
            <td>\gimel</td>
        </tr>
        <tr>
            <td>ℸ</td>
            <td>\daleth</td>
            <td>ð</td>
            <td>\eth</td>
            <td>Ⅎ</td>
            <td>\Finv</td>
            <td>⅁</td>
            <td>\Game</td>
            <td>ℓ</td>
            <td>\ell</td>
        </tr>
        <tr>
            <td>ℏ</td>
            <td>\hbar</td>
            <td>ℏ</td>
            <td>\hslash</td>
            <td>ℑ</td>
            <td>\Im</td>
            <td>ℜ</td>
            <td>\Re</td>
            <td>℘</td>
            <td>\wp</td>
        </tr>
        <tr>
            <td>∂</td>
            <td>\partial</td>
            <td>∇</td>
            <td>\nabla</td>
            <td>\(\Bbbk\)</td>
            <td>\Bbbk</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
        </tr>
    </table>

  <table>
    <tr>
      <td rowspan="2">Direct Input:</td>
      <td>ℂ ℍ ℕ ℙ ℚ ℝ ℤ</td>
      <td style="font-family: KaTeX_Main, KaTeX_AMS;">∂ ð ∇ ℑ ℓ ℘ ℜ Ⅎ ℵ ℶ ℷ ℸ ⅁</td>
    </tr>
    <tr>
      <td colspan="2"><span style="font-family: Times New Roman;">ÀÁÂÃÄÅÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖÙÚÛÜÝÞ<br>àáâãäåçèéêëìíîïðñòóôöùúûüýþÿ</span></td>
    </tr>
  </table>
  
<h4 id="letters-in-text">Letters inside <code>\text{}</code></h4>

    <p><code>\text{…}</code> will accept the functions: <code>\ae</code>, <code>\AE</code>, <code>\oe</code>, <code>\OE</code>, <code>\o</code>, <code>\O</code>, <code>\ss</code>, <code>\i</code>, <code>\j</code>. <code>\text{…}</code> also accepts Unicode characters from:</p>

  <table class="grid">
    <thead>
    <tr>
      <th>Script</th>   <th>Unicode Range</th>   <th>Script</th>   <th>Unicode Range</th>
    </tr>
    </thead>
    <tbody>
      <tr>
        <td>Latin-1</td><td>0080 – 00FF</td>    <td>Sinhala</td><td>0D80 – 0DFF</td>
      </tr>
      <tr>
        <td>Cyrillic</td><td>0400 – 04FF</td>   <td>Thai</td><td>0E00 – 0E7F</td>
      </tr>
      <tr>
        <td>Devanagari</td><td>0900 – 097F</td>   <td>Lao</td><td>0E80 – 0EFF</td>
      </tr>
      <tr>
        <td>Bengali</td><td>0980 – 09FF</td>   <td>Tibetan</td><td>0F00 – 0FFF</td>
      </tr>
      <tr>
        <td>Gurmukhi</td><td>0A00 – 0A7F</td>
        <td>CJK symbols and punctuation</td><td>3000 – 303F</td>
      </tr>
      <tr>
        <td>Gujarati</td><td>0A80 – 0AFF</td>   <td>Hiragana</td><td>3040 – 309F</td>
      </tr>
      <tr>
        <td>Oriya</td><td>0B00 – 0B7F</td>   <td>Katakana</td><td>30A0 – 30FF</td>
      </tr>
      <tr>
        <td>Tamil</td><td>0B80 – 0BFF</td>   <td>CJK ideograms</td><td>4E00 – 9FAF</td>
      </tr>
      <tr>
        <td>Telugu</td><td>0C00 – 0C7F</td>   <td>Hangul</td><td>AC00 – D7AF</td>
      </tr>
      <tr>
        <td>Kannada</td><td>0C80 – 0CFF</td>   <td>Full width punctuation</td><td>FF00 – FF60</td>
      </tr>
      <tr>
        <td>Malayalam</td><td style="white-space: nowrap">0D00 – 0D7F</td>
      </tr>
    </tbody>
  </table>

  <br>

<h3 id="annotation">Annotation</h3>

  <table class="symbol">
    <tr>
      <td>\(\cancel{5}\)</td>
      <td>\cancel{5}</td>
      <td>\(\overbrace{a+b+c}^{\text{note}}\)</td>
      <td>\overbrace{a+b+c}^{\text{note}}</td>
    </tr>
    <tr>
      <td>\(\bcancel{5}\)</td>
      <td>\bcancel{5}</td>
      <td>\(\underbrace{a+b+c}_{\text{note}}\)</td>
      <td style="white-space: nowrap">\underbrace{a+b+c}_{\text{note}}</td>
    </tr>
    <tr>
      <td>\(\xcancel{ABC}\)</td>
      <td style="white-space: nowrap">\xcancel{ABC}</td>
      <td rowspan="2">\(\boxed{\pi = \frac c d}\)</td>
      <td rowspan="2" style="white-space: nowrap">\boxed{\pi=\frac c d}</td>
    </tr>
    <tr>
      <td>\(\sout{abc}\)</td>
      <td>\sout{abc}</td>
    </tr>
    <tr>
            <td>\(\not =\)</td>
            <td>\not =</td>
            <td></td>
            <td></td>
    </tr>
  </table>
  
<h3 id="overlap">Overlap</h3>

    <table class="symbol">
        <tr>
            <td>\({=}\mathllap{/\,}\)</td>
      <td>{=}<strong>\mathllap</strong>{/\,}</td>
      <td>\(\left(x^{\smash{2}}\right)\)</td>
      <td>\left(x^{<strong>\smash</strong>{2}}\right)</td>
        </tr>
        <tr>
            <td>\(\mathrlap{\,/}{=}\)</td>
      <td><strong>\mathrlap</strong>{\,/}{=}&nbsp;&nbsp;&nbsp;</td>
      <td>\(\sqrt{\smash[b]{y}}\)</td>
      <td>\sqrt{<strong>\smash[b]</strong>{y}}</td>
        </tr>
    <tr>
      <td>\( \displaystyle \sum_{\mathclap{1\le i\le j\le n}} x_{ij}\)</td>
      <td colspan="3">\sum_{<strong>\mathclap</strong>{1\le i\le j\le n}} x_{ij}</td>
    </tr>
    </table>
  
  <p>There is also support for <code>\llap</code>, <code>\rlap</code>, and <code>\clap</code>, but they will take only text, not math, as arguments.</p>

<h3 id="spacing">Spacing</h3>

    <table class="explain">
        <thead>
        <tr class="light">
            <th>Function</th>
            <th>Produces</th>
            <th>Function</th>
            <th>Produces</th>
        </tr>
        </thead>
        <tbody>
            <tr>
                <td>\!</td>
        <td style="white-space: nowrap">– ³∕₁₈ em space</td>
                <td>\kern{<em>distance</em>}</td>
                <td>space, width = <em>distance</em></td>
            </tr>
            <tr>
                <td>\,</td>
        <td>³∕₁₈ em space</td>
                <td>\mkern{<em>distance</em>}</td>
                <td>space, width = <em>distance</em></td>
            </tr>
      <tr>
        <td>\thinspace</td>
        <td>³∕₁₈ em space</td>
                <td>\skip{<em>distance</em>}</td>
                <td>space, width = <em>distance</em></td>
      </tr>
            <tr>
                <td>\:</td>
        <td>⁴∕₁₈ em space</td>
                <td>\mskip{<em>distance</em>}</td>
                <td>space, width = <em>distance</em></td>
            </tr>
      <tr>
        <td>\medspace</td>
        <td>⁴∕₁₈ em space</td>
        <td>\hspace{<em>distance</em>}</td>
                <td>space, width = <em>distance</em></td>
      </tr>
            <tr>
                <td>\;</td>
        <td>⁵∕₁₈ em space</td>
        <td>\hspace*{<em>distance</em>}</td>
                <td>space, width = <em>distance</em></td>
            </tr>
      <tr>
        <td>\thickspace</td>
        <td>⁵∕₁₈ em space</td>
                <td>\phantom{<em>content</em>}</td>
                <td style="white-space: nowrap">space the width and height of <em>content</em></td>
      </tr>
            <tr>
                <td>\enspace</td>
        <td>½ em space</td>
                <td>\hphantom{<em>content</em>}</td>
                <td>space the width of <em>content</em></td>
            </tr>
            <tr>
                <td>\quad</td>
        <td>1 em space</td>
                <td>\vphantom{<em>content</em>}</td>
                <td>a strut the height of <em>content</em></td>
            </tr>
            <tr>
                <td>\qquad</td>
        <td>2 em space</td>
        <td></td>
        <td></td>
            </tr>
            <tr>
                <td>~</td>
        <td style="white-space: nowrap">non-breaking space</td>
        <td></td>
        <td></td>
            </tr>
            <tr>
                <td>\space</td>
        <td>non-breaking space</td>
        <td></td>
        <td></td>
            </tr>
            <tr>
                <td>\<em>space</em></td>
                <td>non-breaking space</td>
        <td></td>
        <td></td>
            </tr>
        </tbody>
    </table>
  <table>
    <tr>
      <td>Notes:</td><td>{<em>distance</em>} will accept any of the <a href="#units">units</a>.<br>
      <code>\mkern</code> and <code>\mskip</code> will not work in text mode and both will write a console warning for any unit except <em>mu</em>.</td>
    </tr>
  </table>
  <br>

    <span class="fr">See also <a href="#environments">environments</a></span>
      <h4 id="vertical">Vertical Layout</h4>

    <table class="symbol">
        <tr>
            <td>\(x_n\)</td>
            <td>x_n</td>
            <td>\(\stackrel{!}{=}\)</td>
            <td>\stackrel{!}{=}</td>
            <td>\( a \atop b \)</td>
            <td>a \atop b</td>
        </tr>
        <tr>
            <td>\(e^x\)</td>
            <td>e^x</td>
            <td>\(\overset{!}{=}\)</td>
            <td>\overset{!}{=}</td>
            <td>\(a\raisebox{0.25em}{b}c\)&nbsp;</td>
            <td>a\raisebox{0.25em}{b}c</td>
        </tr>
        <tr>
            <td>\(_u^o\)</td>
            <td>_u^o&nbsp;</td>
            <td>\(\underset{!}{=}\)</td>
            <td>\underset{!}{=}&nbsp;</td>
            <td></td>
            <td></td>
        </tr>
    </table>


        <span class="fr">See also <a href="#relations">relations</a> and <a href="#binary">binary operators</a></span>
        <h3 id="logic">Logic and Set Theory</h3>

    <table class="symbol">
        <tr>
            <td>∀</td>
            <td>\forall</td>
            <td>∁</td>
            <td>\complement</td>
            <td>∴</td>
            <td>\therefore</td>
            <td>¬</td>
            <td>\neg or \lnot</td>
        </tr>
        <tr>
            <td>∃</td>
            <td>\exists</td>
            <td>⊂</td>
            <td>\subset</td>
            <td>∵</td>
            <td>\because</td>
            <td>∅</td>
            <td>\emptyset or \varnothing</td>
        </tr>
        <tr>
            <td>∄</td>
            <td>\nexists</td>
            <td>⊃</td>
            <td>\supset</td>
            <td>↦</td>
            <td>\mapsto</td>
            <td></td>
            <td></td>
        </tr>
        <tr>
            <td>∈</td>
            <td>\in</td>
            <td>∣</td>
            <td>\mid</td>
            <td>→</td>
            <td>\to</td>
            <td>⟹</td>
            <td>\implies</td>
        </tr>
        <tr>
            <td>∉</td>
            <td>\notin</td>
            <td>∧</td>
            <td>\land</td>
            <td>←</td>
            <td>\gets</td>
            <td>⟸</td>
            <td>\impliedby</td>
        </tr>
        <tr>
            <td>∋</td>
            <td>\ni</td>
            <td>∨</td>
            <td>\lor</td>
            <td>↔</td>
            <td>\leftrightarrow</td>
            <td>⟺</td>
            <td>\iff</td>
        </tr>
    <tr>
      <td>\(\notni\)</td>
      <td>\notni</td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
    </table>
  <table>
    <tr>
      <td>Direct Input:</td>
      <td><span style="font-family: KaTeX_Main, KaTeX_AMS;">∀ ∴ ∁ ∵ ∃ ∣ ∈ ∉ ∋ ⊂ ⊃ ∧ ∨ ↦ → ← ↔</span> ℂ ℍ ℕ ℙ ℚ ℝ ℤ</td>
    </tr>
  </table>


<!-- <h3  id="macros">Macros</h3>
  <div>
  <p>Before macros can be used, they must be defined in the KaTeX <a href="https://github.com/Khan/KaTeX#rendering-options">rendering options</a>. Available functions include:</p>
    <div>
    <p><code>\mathchoice \TextOrMath \@ifstar \@ifnextchar \@firstoftwo \@secondoftwo \relax</code></p>
    <p><code>@</code> is a valid character for commands, as if <code>\makeatletter</code> were in effect.</p>
    </div>
  </div> -->

<h3 id="big">Big Operators</h3>

    <table class="symbol big-operator">
        <tr>
            <td>∑</td>
            <td>\sum</td>
            <td>∏</td>
            <td>\prod</td>
            <td>⋁</td>
            <td>\bigvee</td>
            <td>⨂</td>
            <td>\bigotimes</td>
        </tr>
        <tr>
            <td>∫</td>
            <td>\int</td>
            <td>∐</td>
            <td>\coprod</td>
            <td>⋀</td>
            <td>\bigwedge</td>
            <td>⨁</td>
            <td>\bigoplus</td>
        </tr>
        <tr>
            <td>∬</td>
            <td>\iint</td>
            <td>∫</td>
            <td>\intop</td>
            <td>⋂</td>
            <td>\bigcap</td>
            <td>⨀</td>
            <td>\bigodot</td>
        </tr>
        <tr>
            <td>∭</td>
            <td>\iiint</td>
            <td>∫</td>
            <td>\smallint</td>
            <td>⋃</td>
            <td>\bigcup</td>
            <td>⨄</td>
            <td>\biguplus</td>
        </tr>
        <tr>
            <td>∮</td>
            <td>\oint</td>
            <td></td>
            <td></td>
            <td>⨆</td>
            <td>\bigsqcup</td>
            <td></td>
            <td></td>
        </tr>
    </table>
  <table>
    <tr>
      <td>Direct Input:</td>
      <td style="font-family: KaTeX_Size1;">∫ ∬ ∭ ∮ ∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ ⨄ ⨆</td>
    </tr>
  </table>

<h3 id="binary">Binary Operators</h3>

    <!-- Scripts for: \centerdot, \pmod, \pod, and \smallsetminus -->
    <table class="symbol">
        <tr>
            <td>+</td>
            <td>+</td>
            <td>⋅</td>
            <td>\cdot</td>
            <td>⋗</td>
            <td>\gtrdot</td>
            <td>\(x \pmod a\)</td>
            <td>x \pmod a</td>
    </tr>
        <tr>
            <td>−</td>
            <td>-</td>
            <td>⋅</td>
            <td>\cdotp</td>
            <td>⊺</td>
            <td>\intercal</td>
            <td>\(x \pod a\)</td>
            <td>x \pod a</td>
        </tr>
        <tr>
            <td>/</td>
            <td>/</td>
            <td>\(\centerdot\)</td>
            <td>\centerdot</td>
            <td>∧</td>
            <td>\land</td>
            <td>⊳</td>
            <td>\rhd</td>
        </tr>
        <tr>
            <td>∗</td>
            <td>&ast;</td>
            <td>∘</td>
            <td>\circ</td>
            <td>⋋</td>
            <td>\leftthreetimes</td>
            <td>⋌</td>
            <td>\rightthreetimes</td>
        </tr>
        <tr>
            <td>⨿</td>
            <td>\amalg</td>
            <td>⊛</td>
            <td>\circledast</td>
            <td>.</td>
            <td>\ldotp</td>
            <td>⋊</td>
            <td>\rtimes</td>
        </tr>
        <tr>
            <td>&</td>
            <td>\And</td>
            <td>⊚</td>
            <td>\circledcirc</td>
            <td>∨</td>
            <td>\lor</td>
            <td>∖</td>
            <td>\setminus</td>
        </tr>
        <tr>
            <td>∗</td>
            <td>\ast</td>
            <td>⊝</td>
            <td>\circleddash</td>
            <td>⋖</td>
            <td>\lessdot</td>
            <td>\(\smallsetminus\)</td>
            <td>\smallsetminus</td>
        </tr>
        <tr>
            <td>⊼</td>
            <td>\barwedge</td>
            <td>⋓</td>
            <td>\Cup</td>
            <td>⊲</td>
            <td>\lhd</td>
            <td>⊓</td>
            <td>\sqcap</td>
        </tr>
        <tr>
            <td>◯</td>
            <td>\bigcirc</td>
            <td>∪</td>
            <td>\cup</td>
            <td>⋉</td>
            <td>\ltimes</td>
            <td>⊔</td>
            <td>\sqcup</td>
        </tr>
        <tr>
            <td>mod</td>
            <td>\bmod</td>
            <td>⋎</td>
            <td>\curlyvee</td>
            <td>mod</td>
            <td>\mod</td>
            <td>×</td>
            <td>\times</td>
        </tr>
        <tr>
            <td>⊡</td>
            <td>\boxdot</td>
            <td>⋏</td>
            <td>\curlywedge</td>
            <td>∓</td>
            <td>\mp</td>
            <td>⊴</td>
            <td>\unlhd</td>
        </tr>
        <tr>
            <td>⊟</td>
            <td>\boxminus</td>
            <td>÷</td>
            <td>\div</td>
            <td>⊙</td>
            <td>\odot</td>
            <td>⊵</td>
            <td>\unrhd</td>
        </tr>
        <tr>
            <td>⊞</td>
            <td>\boxplus</td>
            <td>⋇</td>
            <td>\divideontimes</td>
            <td>⊖</td>
            <td>\ominus</td>
            <td>⊎</td>
            <td>\uplus</td>
        </tr>
        <tr>
            <td>⊠</td>
            <td>\boxtimes</td>
            <td>∔</td>
            <td>\dotplus</td>
            <td>⊕</td>
            <td>\oplus</td>
            <td>∨</td>
            <td>\vee</td>
        </tr>
        <tr>
            <td>∙</td>
            <td>\bullet</td>
            <td>⩞</td>
            <td>\doublebarwedge</td>
            <td>⊗</td>
            <td>\otimes</td>
            <td>⊻</td>
            <td>\veebar</td>
        </tr>
        <tr>
            <td>⋒</td>
            <td>\Cap</td>
            <td>⋒</td>
            <td>\doublecap</td>
            <td>⊘</td>
            <td>\oslash</td>
            <td>∧</td>
            <td>\wedge</td>
        </tr>
        <tr>
            <td>∩</td>
            <td>\cap</td>
            <td>⋓</td>
            <td>\doublecup</td>
            <td>±</td>
            <td>\pm</td>
            <td>≀</td>
            <td>\wr</td>
        </tr>
    </table>
  <table>
    <tr>
      <td>Direct Input:</td>
      <td style="font-family: KaTeX_Main, KaTeX_AMS;">+ - / * ⋅ ± × ÷ ∓ ∔ ∧ ∨ ∩ ∪ ≀ ⊎ ⊓ ⊔ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊝ ⊞ ⊟ ⊠ ⊡ ⊺ ⊻ ⊼ ⋇ ⋉ ⋊ ⋋ ⋌ ⋎ ⋏ ⋒ ⋓ ⩞</td>
    </tr>
  </table>
  

<h3 id="binomial">Binomial Coefficients</h3>

    <table class="symbol">
        <tr>
            <td>\(\binom{n}{k}\)</td>
            <td>\binom{n}{k}</td>
            <td>\(\dbinom{n}{k}\)</td>
            <td>\dbinom{n}{k}</td>
            <td>\(\left\langle n \atop k \right\rangle\)</td>
            <td>\left\langle<br>n \atop k<br>\right\rangle</td>
        </tr>
        <tr>
            <td>\({n}\choose{k}\)</td>
            <td>{n}\choose{k}</td>
            <td>\(\tbinom{n}{k}\)</td>
            <td>\tbinom{n}{k}</td>
            <td></td>
            <td></td>
        </tr>
    </table>

<h3 id="fractions">Fractions</h3>

    <table class="symbol">
        <tr>
            <td>\(\frac{a}{b}\)</td>
            <td>\frac{a}{b}</td>
            <td>\(\dfrac{a}{b}\)</td>
            <td>\dfrac{a}{b}</td>
            <td>\({a}/{b}\)</td>
            <td>{a}/{b}</td>
        </tr>
        <tr>
            <td>\({a}\over{b}\)</td>
            <td>{a}\over{b}</td>
            <td>\(\tfrac{a}{b}\)</td>
            <td>\tfrac{a}{b}</td>
            <td></td>
            <td></td>
        </tr>
    </table>

<h3 id="math">Math Operators</h3>

    <table class="symbol">
        <tr>
            <td>\(\operatorname{asin} x\)</td>
            <td>\operatorname{asin} x</td>
        </tr>
  </table>
  <table id="math-tbl" class="symbol">
    <tr>
            <td>arcsin</td>
            <td>\arcsin</td>
            <td>cotg</td>
            <td>\cotg</td>
            <td>ln</td>
            <td>\ln</td>
            <td>det</td>
            <td>\det</td>
        </tr>
        <tr>
            <td>arccos</td>
            <td>\arccos</td>
            <td>coth</td>
            <td>\coth</td>
            <td>log</td>
            <td>\log</td>
            <td>gcd</td>
            <td>\gcd</td>
        </tr>
        <tr>
            <td>arctan</td>
            <td>\arctan</td>
            <td>csc</td>
            <td>\csc</td>
            <td>sec</td>
            <td>\sec</td>
            <td>inf</td>
            <td>\inf</td>
        </tr>
        <tr>
            <td>arctg</td>
            <td>\arctg</td>
            <td>ctg</td>
            <td>\ctg</td>
            <td>sin</td>
            <td>\sin</td>
            <td>lim</td>
            <td>\lim</td>
        </tr>
        <tr>
            <td>arcctg</td>
            <td>\arcctg</td>
            <td>cth</td>
            <td>\cth</td>
            <td>sinh</td>
            <td>\sinh</td>
            <td>lim&#x2006;inf</td>
            <td>\liminf</td>
        </tr>
        <tr>
            <td>arg</td>
            <td>\arg</td>
            <td>deg</td>
            <td>\deg</td>
            <td>sh</td>
            <td>\sh</td>
            <td>lim&#x2006;sup</td>
            <td>\limsup</td>
        </tr>
        <tr>
            <td>ch</td>
            <td>\ch</td>
            <td>dim</td>
            <td>\dim</td>
            <td>tan</td>
            <td>\tan</td>
            <td>max</td>
            <td>\max</td>
        </tr>
        <tr>
            <td>cos</td>
            <td>\cos</td>
            <td>exp</td>
            <td>\exp</td>
            <td>tanh</td>
            <td>\tanh</td>
            <td>min</td>
            <td>\min</td>
        </tr>
        <tr>
            <td>cosec</td>
            <td>\cosec</td>
            <td>hom</td>
            <td>\hom</td>
            <td>tg</td>
            <td>\tg</td>
            <td>Pr</td>
            <td>\Pr</td>
        </tr>
        <tr>
            <td>cosh</td>
            <td>\cosh</td>
            <td>ker</td>
            <td>\ker</td>
            <td>th</td>
            <td>\th</td>
            <td>sup</td>
            <td>\sup</td>
        </tr>
        <tr>
            <td>cot</td>
            <td>\cot</td>
            <td>lg</td>
            <td>\lg</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
        </tr>
    </table>

    <div>
        <p>Functions on the right side of this table can take <a href="#limits"><code>\limits</code></a>.<br>
    </div>

<h3 id="sqrt">Sqrt</h3>

    <table class="symbol">
        <tr>
            <td>\(\sqrt{x}\)</td>
            <td>&nbsp;\sqrt{x}</td>
        </tr>
        <tr>
            <td>\(\sqrt[3]{x}\)</td>
            <td>&nbsp;\sqrt[3]{x}</td>
        </tr>
    </table>


<h3  id="relations">Relations</h3>

    <!-- This table has scripts in several cells. -->
    <table class="symbol">
    <tr>
            <td>\(\stackrel{!}{=}\)</td>
            <td colspan="9">\stackrel{!}{=}</td>
    </tr>
    <tr>
      <td>=</td>
      <td>=</td>
      <td>⋟</td>
      <td>\curlyeqsucc</td>
      <td>⪆</td>
      <td>\gtrapprox</td>
      <td>⊥</td>
      <td>\perp</td>
      <td>⪸</td>
      <td>\succapprox</td>
    </tr>
    <tr>
      <td>&lt;</td>
      <td>&lt;</td>
      <td>⊣</td>
      <td>\dashv</td>
      <td>⋛</td>
      <td>\gtreqless</td>
      <td>⋔</td>
      <td>\pitchfork</td>
      <td>≽</td>
      <td>\succcurlyeq</td>
    </tr>
    <tr>
      <td>&gt;</td>
      <td>&gt;</td>
      <td>\(\dblcolon\)</td>
      <td>\dblcolon</td>
      <td>⪌</td>
      <td>\gtreqqless</td>
      <td>≺</td>
      <td>\prec</td>
      <td>⪰</td>
      <td>\succeq</td>
    </tr>
    <tr>
      <td>:</td>
      <td>:</td>
      <td>≐</td>
      <td>\doteq</td>
      <td>≷</td>
      <td>\gtrless</td>
      <td>⪷</td>
      <td>\precapprox</td>
      <td>≿</td>
      <td>\succsim</td>
    </tr>
    <tr>
      <td>≈</td>
      <td>\approx</td>
      <td>≑</td>
      <td>\Doteq</td>
      <td>≳</td>
      <td>\gtrsim</td>
      <td>≼</td>
      <td>\preccurlyeq</td>
      <td>⋑</td>
      <td>\Supset</td>
    </tr>
    <tr>
      <td>≊</td>
      <td>\approxeq</td>
      <td>≑</td>
      <td>\doteqdot</td>
      <td>∈</td>
      <td>\in</td>
      <td>⪯</td>
      <td>\preceq</td>
      <td>⊃</td>
      <td>\supset</td>
    </tr>
    <tr>
      <td>≍</td>
      <td>\asymp</td>
      <td>≖</td>
      <td>\eqcirc</td>
      <td>⋈</td>
      <td>\Join</td>
      <td>≾</td>
      <td>\precsim</td>
      <td>⊇</td>
      <td>\supseteq</td>
    </tr>
    <tr>
      <td>∍</td>
      <td>\backepsilon</td>
      <td>\(\eqcolon\)</td>
      <td>\eqcolon</td>
      <td>≤</td>
      <td>\le</td>
      <td>∝</td>
      <td>\propto</td>
      <td>⫆</td>
      <td>\supseteqq</td>
    </tr>
    <tr>
      <td>∽</td>
      <td>\backsim</td>
      <td>\(\Eqcolon\)</td>
      <td>\Eqcolon</td>
      <td>≤</td>
      <td>\leq</td>
      <td>≓</td>
      <td>\risingdotseq</td>
      <td>≈</td>
      <td>\thickapprox</td>
    </tr>
    <tr>
      <td>⋍</td>
      <td>\backsimeq</td>
      <td>\(\eqqcolon\)</td>
      <td>\eqqcolon</td>
      <td>≦</td>
      <td>\leqq</td>
      <td>∣</td>
      <td>\shortmid</td>
      <td>∼</td>
      <td>\thicksim</td>
    </tr>
    <tr>
      <td>≬</td>
      <td>\between</td>
      <td>\(\Eqqcolon\)</td>
      <td>\Eqqcolon</td>
      <td>⩽</td>
      <td>\leqslant</td>
      <td>∥</td>
      <td>\shortparallel</td>
      <td>⊴</td>
      <td>\trianglelefteq</td>
    </tr>
    <tr>
      <td>⋈</td>
      <td>\bowtie</td>
      <td>≂</td>
      <td>\eqsim</td>
      <td>⪅</td>
      <td>\lessapprox</td>
      <td>∼</td>
      <td>\sim</td>
      <td>≜</td>
      <td>\triangleq</td>
    </tr>
    <tr>
      <td>≏</td>
      <td>\bumpeq</td>
      <td>⪖</td>
      <td>\eqslantgtr</td>
      <td>⋚</td>
      <td>\lesseqgtr</td>
      <td>≃</td>
      <td>\simeq</td>
      <td>⊵</td>
      <td>\trianglerighteq</td>
    </tr>
    <tr>
      <td>≎</td>
      <td>\Bumpeq</td>
      <td>⪕</td>
      <td>\eqslantless</td>
      <td>⪋</td>
      <td>\lesseqqgtr</td>
      <td>\(\smallfrown\)</td>
      <td>\smallfrown</td>
      <td>∝</td>
      <td>\varpropto</td>
    </tr>
    <tr>
      <td>≗</td>
      <td>\circeq</td>
      <td>≡</td>
      <td>\equiv</td>
      <td>≶</td>
      <td>\lessgtr</td>
      <td>\(\smallsmile\)</td>
      <td>\smallsmile</td>
      <td>△</td>
      <td>\vartriangle</td>
    </tr>
    <tr>
      <td>\(\colonapprox\)</td>
      <td>\colonapprox</td>
      <td>≒</td>
      <td>\fallingdotseq</td>
      <td>≲</td>
      <td>\lesssim</td>
      <td>⌣</td>
      <td>\smile</td>
      <td>⊲</td>
      <td>\vartriangleleft</td>
    </tr>
    <tr>
      <td>\(\Colonapprox\)</td>
      <td>\Colonapprox</td>
      <td>⌢</td>
      <td>\frown</td>
      <td>≪</td>
      <td>\ll</td>
      <td>⊏</td>
      <td>\sqsubset</td>
      <td>⊳</td>
      <td>\vartriangleright</td>
    </tr>
    <tr>
      <td>\(\coloneq\)</td>
      <td>\coloneq</td>
      <td>≥</td>
      <td>\ge</td>
      <td>⋘</td>
      <td>\lll</td>
      <td>⊑</td>
      <td>\sqsubseteq</td>
      <td>\(\vcentcolon\)</td>
      <td>\vcentcolon</td>
    </tr>
    <tr>
      <td>\(\Coloneq\)</td>
      <td>\Coloneq</td>
      <td>≥</td>
      <td>\geq</td>
      <td>⋘</td>
      <td>\llless</td>
      <td>⊐</td>
      <td>\sqsupset</td>
      <td>⊢</td>
      <td>\vdash</td>
    </tr>
    <tr>
      <td>\(\coloneqq\)</td>
      <td>\coloneqq</td>
      <td>≧</td>
      <td>\geqq</td>
      <td>&lt;</td>
      <td>\lt</td>
      <td>⊒</td>
      <td>\sqsupseteq</td>
      <td>⊨</td>
      <td>\vDash</td>
    </tr>
    <tr>
      <td>\(\Coloneqq\)</td>
      <td>\Coloneqq</td>
      <td>⩾</td>
      <td>\geqslant</td>
      <td>∣</td>
      <td>\mid</td>
      <td>⋐</td>
      <td>\Subset</td>
      <td>⊩</td>
      <td>\Vdash</td>
    </tr>
    <tr>
      <td>\(\colonsim\)</td>
      <td>\colonsim</td>
      <td>≫</td>
      <td>\gg</td>
      <td>⊨</td>
      <td>\models</td>
      <td>⊂</td>
      <td>\subset</td>
      <td>⊪</td>
      <td>\Vvdash</td>
    </tr>
    <tr>
      <td>\(\Colonsim\)</td>
      <td>\Colonsim</td>
      <td>⋙</td>
      <td>\ggg</td>
      <td>⊸</td>
      <td>\multimap</td>
      <td>⊆</td>
      <td>\subseteq</td>
      <td>\(\)</td>
      <td></td>
    </tr>
    <tr>
      <td>≅</td>
      <td>\cong</td>
      <td>⋙</td>
      <td>\gggtr</td>
      <td>∋</td>
      <td>\owns</td>
      <td>⫅</td>
      <td>\subseteqq</td>
      <td>\(\)</td>
      <td></td>
    </tr>
    <tr>
      <td>⋞</td>
      <td>\curlyeqprec</td>
      <td>&gt;</td>
      <td>\gt</td>
      <td>∥</td>
      <td>\parallel</td>
      <td>≻</td>
      <td>\succ</td>
      <td>\(\)</td>
      <td></td>
    </tr>
  </table>
  <table>
    <tr>
      <td>Direct Input:</td>
      <td style="font-family: KaTeX_Main, KaTeX_AMS;">= &lt; &gt; : ∈ ∋ ∝ ∼ ∽ ≂ ≃ ≅ ≈ ≊ ≍ ≎ ≏ ≐ ≑ ≒ ≓ ≖ ≗ ≜ ≡ ≤ ≥ ≦ ≧ ≫ ≬ ≳ ≷ ≺ ≻ ≼ ≽ ≾ ≿ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ⊩ ⊪ ⊸ ⋈ ⋍ ⋐ ⋑ ⋔ ⋙ ⋛ ⋞ ⋟ ⌢ ⌣ ⩾ ⪆ ⪌ ⪕ ⪖ ⪯ ⪰ ⪷ ⪸ ⫅ ⫆</td>
    </tr>
  </table>


<h4 id="negated-relations">Negated Relations</h4>
  <!-- This table contains one script, \notni-->
    <table class="symbol">
    <tr>
            <td>\(\not =\)</td>
            <td>\not =</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
        </tr>
    <tr>
      <td>⪊</td>
      <td>\gnapprox</td>
      <td></td>
      <td>\ngeqslant</td>
      <td>⊈</td>
      <td>\nsubseteq</td>
      <td>⪵</td>
      <td>\precneqq</td>
    </tr>
    <tr>
      <td>⪈</td>
      <td>\gneq</td>
      <td>≯</td>
      <td>\ngtr</td>
      <td></td>
      <td>\nsubseteqq</td>
      <td>⋨</td>
      <td>\precnsim</td>
    </tr>
    <tr>
      <td>≩</td>
      <td>\gneqq</td>
      <td>≰</td>
      <td>\nleq</td>
      <td>⊁</td>
      <td>\nsucc</td>
      <td>⊊</td>
      <td>\subsetneq</td>
    </tr>
    <tr>
      <td>⋧</td>
      <td>\gnsim</td>
      <td></td>
      <td>\nleqq</td>
      <td>⋡</td>
      <td>\nsucceq</td>
      <td>⫋</td>
      <td>\subsetneqq</td>
    </tr>
    <tr>
      <td></td>
      <td>\gvertneqq</td>
      <td></td>
      <td>\nleqslant</td>
      <td>⊉</td>
      <td>\nsupseteq</td>
      <td>⪺</td>
      <td>\succnapprox</td>
    </tr>
    <tr>
      <td>⪉</td>
      <td>\lnapprox</td>
      <td>≮</td>
      <td>\nless</td>
      <td></td>
      <td>\nsupseteqq</td>
      <td>⪶</td>
      <td>\succneqq</td>
    </tr>
    <tr>
      <td>⪇</td>
      <td>\lneq</td>
      <td>∤</td>
      <td>\nmid</td>
      <td>⋪</td>
      <td>\ntriangleleft</td>
      <td>⋩</td>
      <td>\succnsim</td>
    </tr>
    <tr>
      <td>≨</td>
      <td>\lneqq</td>
      <td>∉</td>
      <td>\notin</td>
      <td>⋬</td>
      <td>\ntrianglelefteq</td>
      <td>⊋</td>
      <td>\supsetneq</td>
    </tr>
    <tr>
      <td>⋦</td>
      <td>\lnsim</td>
      <td>\(\notni\)</td>
      <td>\notni</td>
      <td>⋫</td>
      <td>\ntriangleright</td>
      <td>⫌</td>
      <td>\supsetneqq</td>
    </tr>
    <tr>
      <td></td>
      <td>\lvertneqq</td>
      <td>∦</td>
      <td>\nparallel</td>
      <td>⋭</td>
      <td>\ntrianglerighteq</td>
      <td></td>
      <td>\varsubsetneq</td>
    </tr>
    <tr>
      <td>≆</td>
      <td>\ncong</td>
      <td>⊀</td>
      <td>\nprec</td>
      <td>⊬</td>
      <td>\nvdash</td>
      <td></td>
      <td>\varsubsetneqq</td>
    </tr>
    <tr>
      <td>≠</td>
      <td>\ne</td>
      <td>⋠</td>
      <td>\npreceq</td>
      <td>⊭</td>
      <td>\nvDash</td>
      <td></td>
      <td>\varsupsetneq</td>
    </tr>
    <tr>
      <td>≠</td>
      <td>\neq</td>
      <td></td>
      <td>\nshortmid</td>
      <td>⊯</td>
      <td>\nVDash</td>
      <td></td>
      <td>\varsupsetneqq</td>
    </tr>
    <tr>
      <td>≱</td>
      <td>\ngeq</td>
      <td></td>
      <td>\nshortparallel</td>
      <td>⊮</td>
      <td>\nVdash</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td></td>
      <td>\ngeqq</td>
      <td>≁</td>
      <td>\nsim</td>
      <td>⪹</td>
      <td>\precnapprox</td>
      <td></td>
      <td></td>
    </tr>
  </table>
  <table>
    <tr>
      <td>Direct Input:</td>
      <td style="font-family: KaTeX_Main, KaTeX_AMS;">∉ ∤ ∦ ≁ ≆ ≠ ≨ ≩ ≮ ≯ ≰ ≱ ⊀ ⊁ ⊈ ⊉ ⊊ ⊋ ⊬ ⊭ ⊮ ⊯ ⋠ ⋡ ⋦ ⋧ ⋨ ⋩ ⋬ ⋭ ⪇ ⪈ ⪉ ⪊ ⪵ ⪶ ⪹ ⪺ ⫋ ⫌</td>
    </tr>
  </table>
  
<h3 id="arrows">Arrows</h3>

    <table class="symbol">
        <tr>
            <td>↺</td>
            <td>\circlearrowleft</td>
            <td>⇐</td>
            <td>\Leftarrow</td>
            <td>↬</td>
            <td>\looparrowright</td>
            <td>⇉</td>
            <td>\rightrightarrows</td>
        </tr>
        <tr>
            <td>↻</td>
            <td>\circlearrowright</td>
            <td>↢</td>
            <td>\leftarrowtail</td>
            <td>↰</td>
            <td>\Lsh</td>
            <td>⇝</td>
            <td>\rightsquigarrow</td>
        </tr>
        <tr>
            <td>↶</td>
            <td>\curvearrowleft</td>
            <td>↽</td>
            <td>\leftharpoondown</td>
            <td>↦</td>
            <td>\mapsto</td>
            <td>⇛</td>
            <td>\Rrightarrow</td>
        </tr>
        <tr>
            <td>↷</td>
            <td>\curvearrowright</td>
            <td>↼</td>
            <td>\leftharpoonup</td>
            <td>↗</td>
            <td>\nearrow</td>
            <td>↱</td>
            <td>\Rsh</td>
        </tr>
        <tr>
            <td>⇠</td>
            <td>\dashleftarrow</td>
            <td>⇇</td>
            <td>\leftleftarrows</td>
            <td>↚</td>
            <td>\nleftarrow</td>
            <td>↘</td>
            <td>\searrow</td>
        </tr>
        <tr>
            <td>⇢</td>
            <td>\dashrightarrow</td>
            <td>↔</td>
            <td>\leftrightarrow</td>
            <td>⇍</td>
            <td>\nLeftarrow</td>
            <td>↙</td>
            <td>\swarrow</td>
        </tr>
        <tr>
            <td>↓</td>
            <td>\downarrow</td>
            <td>⇔</td>
            <td>\Leftrightarrow</td>
            <td>↮</td>
            <td>\nleftrightarrow</td>
            <td>→</td>
            <td>\to</td>
        </tr>
        <tr>
            <td>⇓</td>
            <td>\Downarrow</td>
            <td>⇆</td>
            <td>\leftrightarrows</td>
            <td>⇎</td>
            <td>\nLeftrightarrow</td>
            <td>↞</td>
            <td>\twoheadleftarrow</td>
        </tr>
        <tr>
            <td>⇊</td>
            <td>\downdownarrows</td>
            <td>⇋</td>
            <td>\leftrightharpoons</td>
            <td>↛</td>
            <td>\nrightarrow</td>
            <td>↠</td>
            <td>\twoheadrightarrow</td>
        </tr>
        <tr>
            <td>⇃</td>
            <td>\downharpoonleft</td>
            <td>↭</td>
            <td>\leftrightsquigarrow</td>
            <td>⇏</td>
            <td>\nRightarrow</td>
            <td>↑</td>
            <td>\uparrow</td>
        </tr>
        <tr>
            <td>⇂</td>
            <td>\downharpoonright</td>
            <td>⇚</td>
            <td>\Lleftarrow</td>
            <td>↖</td>
            <td>\nwarrow</td>
            <td>⇑</td>
            <td>\Uparrow</td>
        </tr>
        <tr>
            <td>←</td>
            <td>\gets</td>
            <td>⟵</td>
            <td>\longleftarrow</td>
            <td>↾</td>
            <td>\restriction</td>
            <td>↕</td>
            <td>\updownarrow</td>
        </tr>
        <tr>
            <td>↩</td>
            <td>\hookleftarrow</td>
            <td>⟸</td>
            <td>\Longleftarrow</td>
            <td>→</td>
            <td>\rightarrow</td>
            <td>⇕</td>
            <td>\Updownarrow</td>
        </tr>
        <tr>
            <td>↪</td>
            <td>\hookrightarrow</td>
            <td>⟷</td>
            <td>\longleftrightarrow</td>
            <td>⇒</td>
            <td>\Rightarrow</td>
            <td>↿</td>
            <td>\upharpoonleft</td>
        </tr>
        <tr>
            <td>⟺</td>
            <td>\iff</td>
            <td>⟺</td>
            <td>\Longleftrightarrow</td>
            <td>↣</td>
            <td>\rightarrowtail</td>
            <td>↾</td>
            <td>\upharpoonright</td>
        </tr>
        <tr>
            <td>⟸</td>
            <td>\impliedby</td>
            <td>⟼</td>
            <td>\longmapsto</td>
            <td>⇁</td>
            <td>\rightharpoondown</td>
            <td>⇈</td>
            <td>\upuparrows</td>
        </tr>
        <tr>
            <td>⟹</td>
            <td>\implies</td>
            <td>⟶</td>
            <td>\longrightarrow</td>
            <td>⇀</td>
            <td>\rightharpoonup</td>
            <td></td>
            <td></td>
        </tr>
        <tr>
            <td>⇝</td>
            <td>\leadsto</td>
            <td>⟹</td>
            <td>\Longrightarrow</td>
            <td>⇄</td>
            <td>\rightleftarrows</td>
            <td></td>
            <td></td>
        </tr>
        <tr>
            <td>←</td>
            <td>\leftarrow</td>
            <td>↫</td>
            <td>\looparrowleft</td>
            <td>⇌</td>
            <td>\rightleftharpoons</td>
            <td></td>
            <td></td>
        </tr>
    </table>
  <table>
    <tr>
      <td>Direct Input:</td>
      <td style="font-family: KaTeX_Main, KaTeX_AMS;">← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↞ ↠ ↢ ↣ ↦ ↩ ↪ ↫ ↬ ↭ ↮ ↰ ↱ ↶ ↷ ↺ ↻ ↼ ↽ ↾ ↾ ↿ ⇀ ⇁ ⇂ ⇃ ⇄ ⇆ ⇇ ⇈ ⇉ ⇊ ⇋ ⇌ ⇍ ⇎ ⇏ ⇐ ⇑ ⇒ ⇓ ⇔ ⇕ ⇚ ⇛ ⇝ ⇠ ⇢ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟼</td>
    </tr>
  </table>
  
<h4 id="extensible-arrows">Extensible Arrows</h4>

  <table class="symbol">
    <tr>
      <td>\(\xrightarrow{over}\)</td>
      <td>\xrightarrow{over}</td>
      <td>\(\xRightarrow{abc}\)</td>
      <td>\xRightarrow{abc}</td>
      <td>\(\xrightharpoonup{abc}\)</td>
      <td>\xrightharpoonup{abc}</td>
    </tr>
    <tr>
      <td>\(\xrightarrow[under]{over}\)</td>
      <td style="white-space: nowrap">\xrightarrow[under]{over}</td>
      <td>\(\xmapsto{abc}\)</td>
      <td>\xmapsto{abc}</td>
      <td>\(\xrightharpoondown{abc}\)</td>
      <td>\xrightharpoondown{abc}</td>
    </tr>
    <tr>
      <td>\(\xleftarrow{abc}\)</td>
      <td>\xleftarrow{abc}</td>
      <td>\(\xLeftarrow{abc}\)</td>
      <td>\xLeftarrow{abc}</td>
      <td>\(\xleftharpoonup{abc}\)</td>
      <td>\xleftharpoonup{abc}</td>
    </tr>
    <tr>
      <td>\(\xleftrightarrow{abc}\)</td>
      <td>\xleftrightarrow{abc}</td>
      <td>\(\xLeftrightarrow{abc}\)</td>
      <td>\xLeftrightarrow{abc}</td>
      <td>\(\xleftharpoondown{abc}\)</td>
      <td>\xleftharpoondown{abc}</td>
    </tr>
    <tr>
      <td>\(\xhookleftarrow{abc}\)</td>
      <td>\xhookleftarrow{abc}</td>
      <td>\(\xhookrightarrow{abc}\)</td>
      <td style="white-space: nowrap">\xhookrightarrow{abc}</td>
      <td>\(\xrightleftharpoons{abc}\)</td>
      <td style="white-space: nowrap">\xrightleftharpoons{abc}</td>
    </tr>
    <tr>
      <td>\(\xtwoheadrightarrow{abc}\)</td>
      <td>\xtwoheadrightarrow{abc}</td>
      <td>\(\xlongequal{abc}\)</td>
      <td>\xlongequal{abc}</td>
      <td>\(\xleftrightharpoons{abc}\)</td>
      <td>\xleftrightharpoons{abc}</td>
    </tr>
    <tr>
      <td>\(\xtwoheadleftarrow{abc}\)</td>
      <td>\xtwoheadleftarrow{abc}</td>
      <td>\(\xtofrom{abc}\)</td>
      <td>\xtofrom{abc}</td>
      <td></td>
      <td></td>
    </tr>
  </table>

  <p>Extensible arrows all can take an optional argument in the same manner as <code>\xrightarrow[under]{over}</code>.</p>


<h3  id="class">Class Assignment</h3>

    <table class="all-code">
        <tr>
            <td>\mathbin</td>
            <td>\mathclose</td>
            <td>\mathinner</td>
            <td>\mathop</td>
        </tr>
        <tr>
            <td>\mathopen</td>
            <td>\mathord</td>
            <td>\mathpunct</td>
            <td>\mathrel</td>
        </tr>
    </table>

<h3 id="color">Color</h3>

    <p>The color function behaves like a switch.</p>

    <table class="symbol">
      <tr>
      <td>\(\color{blue} F=ma\)</td>
      <td>\color{blue} F=ma</td>
      </tr>
      <tr>
      <td>\(\color{#fc625d} F=ma \)</td>
      <td>\color{#fc625d} F=ma</td>
    </tr>
    </table>

<!--   <p>As of KaTeX 0.8.1, the behavior of <code>\color</code> depends on the setting of <a href="https://github.com/Khan/KaTeX#rendering-options">rendering option</a> <code>colorIsTextColor</code>.</p>

  <table class="grid">
    <tr>
      <td>When <code>colorIsTextColor</code> is set to:</td>
      <td colspan="2"><code>false</code> (default)</td>
      <td colspan="2"><code>true</code></td>
    </tr>
    <tr>
      <td><code>\color</code> behaves as it does in:</td>
      <td colspan="2">LaTeX</td>
      <td colspan="2">MathJax<br><span style="font-size:85%;">(or KaTeX pre 0.8.1)</span></td>
    </tr>
    <tr>
      <td>That is, <code>\color</code>:</td>
      <td colspan="2">… acts like a switch.</td>
      <td colspan="2">… expects content to be a function argument.</td>
    </tr>
    <tr>
      <td rowspan="2">Examples:</td>
      <td>\(\color{blue} F=ma\)</td>
      <td>\color{blue} F=ma</td>
      <td>\(\textcolor{blue}{F=ma}\)</td>
      <td>\color{blue}{F=ma}</td>
    </tr>
    <tr>
      <td>\(\color{#fc625d} F=ma \)</td>
      <td style="white-space: nowrap">\color{#fc625d} F=ma</td>
      <td>\(\textcolor{#228B22}{F=ma}\)</td>
      <td style="white-space: nowrap">\color{#228B22}{F=ma}</td>
    </tr>
  </table>
  
    <div> -->
    <p>Other color functions always expect the content to be a function argument.</p>

    <table class="symbol">
      <tr>
        <td>\(\textcolor{forestgreen}{F=ma}\)</td>
        <td>\textcolor{forestgreen}{F=ma}</td>
      </tr>
      <tr>
        <td>\(\textcolor{#fc625d}{F=ma}\)</td>
        <td>\textcolor{#fc625d}{F=ma}</td>
      </tr>
      <tr>
        <td>\(\colorbox{gold}{A}\)</td>
        <td>\colorbox{gold}{A}</td>
      </tr>
      <tr>
        <td>\(\fcolorbox{black}{gold}{A}\)</td>
        <td>\fcolorbox{black}{gold}{A}</td>
      </tr>
    </table>
  
<p>For color definition, color functions will accept the standard HTML <a href="https://www.w3schools.com/colors/colors_names.asp">predefined color names</a>. They will also accept an RGB argument in CSS hexa­decimal style.</p>

<h3 id="font">Font</h3>

    <table class="symbol tall">
        <tr>
            <td><span class="katex"><span class="mathrm">AB</span></span></td>
            <td>\mathrm{AB}</td>
            <td><span class="katex"><span class="mathbf">AB</span></span></td>
            <td>\mathbf{AB}</td>
            <td><span class="katex"><span class="mathit">AB</span></span></td>
            <td>\mathit{AB}</td>
            <td><span class="katex"><span class="mathsf">AB</span></span></td>
            <td>\mathsf{AB}</td>
            <td><span class="katex"><span class="mathtt">AB</span></span></td>
            <td>\mathtt{AB}</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathrm">AB</span></span></td>
            <td>\textrm{AB}</td>
            <td><span class="katex"><span class="mathbf">AB</span></span></td>
            <td>\textbf{AB}</td>
            <td><span class="katex"><span class="mathit">AB</span></span></td>
            <td>\textit{AB}</td>
            <td><span class="katex"><span class="mathsf">AB</span></span></td>
            <td>\textsf{AB}</td>
            <td><span class="katex"><span class="mathtt">AB</span></span></td>
            <td>\texttt{AB}</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathrm">AB</span></span></td>
            <td>\rm{AB}</td>
            <td><span class="katex"><span class="mathbf">AB</span></span></td>
            <td>\bf{AB}</td>
            <td><span class="katex"><span class="mathit">AB</span></span></td>
            <td>\it{AB}</td>
            <td><span class="katex"><span class="mathsf">AB</span></span></td>
            <td>\sf{AB}</td>
            <td><span class="katex"><span class="mathtt">AB</span></span></td>
            <td>\tt{AB}</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathrm">AB</span></span></td>
            <td style="white-space: nowrap">\textnormal{AB}</td>
            <td><span class="katex"><span class="mathbf">AB</span></span></td>
            <td>\bold{AB}</td>
            <td><span class="katex"><span class="mathbb">AB</span></span></td>
            <td>\Bbb{AB}</td>
            <td><span class="katex"><span class="mathcal">AB</span></span></td>
            <td style="white-space: nowrap">\mathcal{AB}</td>
            <td><span class="katex"><span class="mathfrak">AB</span></span></td>
            <td>\frak{AB}</td>
        </tr>
        <tr>
            <td><span class="katex"><span class="mathrm">AB</span></span></td>
            <td>\text{AB}</td>
            <td><span class="katex"><span class="boldsymbol">AB</span></span></td>
            <td style="white-space: nowrap">\boldsymbol{AB}</td>
            <td><span class="katex"><span class="mathbb">AB</span></span></td>
            <td style="white-space: nowrap">\mathbb{AB}</td>
      <td><span class="katex"><span class="mathscr">AB</span></span></td>
      <td style="white-space: nowrap">\mathscr{AB}</td>
            <td><span class="katex"><span class="mathfrak">AB</span></span></td>
            <td style="white-space: nowrap">\mathfrak{AB}</td>
        </tr>
    <tr>
      <td></td>
      <td></td>
      <td><span class="katex"><span class="boldsymbol">AB</span></span></td>
      <td style="white-space: nowrap">\bm{AB}</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
    </tr>
    </table>
  
  <p>One can stack font family, font weight, and font shape by using the <code>\textXX</code> versions of the font functions. So <code>\textsf{\textbf{H}}</code> will produce \(\textsf{\textbf{H}}\).  The other versions so not stack, e.g., <code>\mathsf{\mathbf{H}}</code> will produce \(\mathsf{\mathbf{H}}\).</p>

<h4 id="size">Size</h4>

    <table class="symbol">
        <tr>
            <td>\(\Huge AB\)</td>
            <td>\Huge AB</td>
            <td>\(\normalsize AB\)</td>
            <td>\normalsize AB</td>
        </tr>
        <tr>
            <td>\(\huge AB\)</td>
            <td>\huge AB</td>
            <td>\(\small AB\)</td>
            <td>\small AB</td>
        </tr>
        <tr>
            <td>\(\LARGE AB\)</td>
            <td>\LARGE AB</td>
            <td>\(\footnotesize AB\)</td>
            <td>\footnotesize AB</td>
        </tr>
        <tr>
            <td>\(\Large AB\)</td>
            <td>\Large AB</td>
            <td>\(\scriptsize AB\)</td>
            <td>\scriptsize AB</td>
        </tr>
        <tr>
            <td>\(\large AB\)</td>
            <td>\large AB</td>
            <td>\(\tiny AB\)</td>
            <td>\tiny AB</td>
        </tr>
    </table>

<h4 id="style">Style</h4>

    <table id="style-tbl" class="symbol">
        <tr>
            <td>\(\displaystyle\sum_{i=1}^n\)</td>
            <td style="white-space: nowrap"><strong>\displaystyle</strong>\sum_{i=1}^n</td>
            <td></td>
        </tr>
        <tr>
            <td>\(\textstyle\sum_{i=1}^n\)</td>
            <td><strong>\textstyle</strong>\sum_{i=1}^n</td>
            <td></td>
        </tr>
        <tr>
            <td>\(\scriptstyle x\)</td>
            <td><strong>\scriptstyle</strong> x</td>
            <td>The size of a first sub/superscript</td>
        </tr>
        <tr>
            <td>\(\scriptscriptstyle x\)</td>
            <td><strong>\scriptscriptstyle</strong> x</td>
            <td>The size of subsequent sub/superscripts</td>
        </tr>
        <tr id="limits">
            <td>\(\lim\limits_x\)</td>
            <td>\lim<strong>\limits</strong>_x</td>
            <td></td>
        </tr>
        <tr>
            <td>\(\lim\nolimits_x\)</td>
            <td>\lim<strong>\nolimits</strong>_x</td>
            <td></td>
        </tr>
        <tr>
            <td>\(\verb! x^2 !\)</td>
            <td><strong>\verb!</strong>x^2<strong>!</strong></td>
            <td></td>
        </tr>
        <tr>
            <td>\(\text{x}\)</td>
            <td><strong>\text</strong>{x}</td>
            <td></td>
        </tr>
    </table>
  
  <div>    
    <p><code>\text{…}</code> will accept nested <code>$…$</code> fragments and render them in math mode.</p>
    
    <p><code>\text{…}</code> will render an extended range of characters. See <a href="#letters-in-text">Letters inside \text</a>.</p>
  </div>

<h3  id="symbols">Symbols and Punctuation</h3>

    <table class="symbol">
    <tr>
      <td></td>
      <td>% comment</td>
      <td>□</td>
      <td>\Box</td>
      <td>…</td>
      <td>\dots</td>
      <td>✓</td>
      <td>\checkmark</td>
    </tr>
    <tr>
      <td>%</td>
      <td>\%</td>
      <td>□</td>
      <td>\square</td>
      <td>⋯</td>
      <td>\cdots</td>
      <td>†</td>
      <td>\dag</td>
    </tr>
    <tr>
      <td>#</td>
      <td>\#</td>
      <td>■</td>
      <td>\blacksquare</td>
      <td>⋱</td>
      <td>\ddots</td>
      <td>†</td>
      <td>\dagger</td>
    </tr>
    <tr>
      <td>&amp;</td>
      <td>\&amp;</td>
      <td>\(\triangle\)</td>
      <td>\triangle</td>
      <td>…</td>
      <td>\ldots</td>
      <td>†</td>
      <td>\textdagger</td>
    </tr>
    <tr>
      <td>_</td>
      <td>\_</td>
      <td>\(\triangledown\)</td>
      <td>\triangledown</td>
      <td>⋮</td>
      <td>\vdots</td>
      <td>‡</td>
      <td>\ddag</td>
    </tr>
    <tr>
      <td>_</td>
      <td>\textunderscore</td>
      <td>\(\triangleleft\)</td>
      <td>\triangleleft</td>
      <td>…</td>
      <td>\mathellipsis</td>
      <td>‡</td>
      <td>\ddagger</td>
    </tr>
    <tr>
      <td>–</td>
      <td>--</td>
      <td>\(\triangleright\)</td>
      <td>\triangleright</td>
      <td>…</td>
      <td>\textellipsis</td>
      <td>‡</td>
      <td>\textdaggerdbl</td>
    </tr>
    <tr>
      <td>–</td>
      <td>\textendash</td>
      <td>\(\bigtriangledown\)</td>
      <td>\bigtriangledown</td>
      <td>♭</td>
      <td>\flat</td>
      <td>$</td>
      <td>\$</td>
    </tr>
    <tr>
      <td>—</td>
      <td>---</td>
      <td>\(\bigtriangleup\)</td>
      <td>\bigtriangleup</td>
      <td>♮</td>
      <td>\natural</td>
      <td>$</td>
      <td>\textdollar</td>
    </tr>
    <tr>
      <td>—</td>
      <td>\textemdash</td>
      <td>▲</td>
      <td>\blacktriangle</td>
      <td>♯</td>
      <td>\sharp</td>
      <td>£</td>
      <td>\pounds</td>
    </tr>
    <tr>
      <td>‘</td>
      <td>`</td>
      <td>▼</td>
      <td>\blacktriangledown</td>
      <td>®</td>
      <td>\circledR</td>
      <td>£</td>
      <td>\textsterling</td>
    </tr>
    <tr>
      <td>‘</td>
      <td>\textquoteleft</td>
      <td>◀</td>
      <td>\blacktriangleleft</td>
      <td>Ⓢ</td>
      <td>\circledS</td>
      <td>¥</td>
      <td>\yen</td>
    </tr>
    <tr>
      <td>’</td>
      <td>\textquoteright</td>
      <td>▶</td>
      <td>\blacktriangleright</td>
      <td>♣</td>
      <td>\clubsuit</td>
      <td>√</td>
      <td>\surd</td>
    </tr>
    <tr>
      <td>“</td>
      <td>\textquotedblleft</td>
      <td>⋄</td>
      <td>\diamond</td>
      <td>♢</td>
      <td>\diamondsuit</td>
      <td>°</td>
      <td>\degree</td>
    </tr>
    <tr>
      <td>&quot;</td>
      <td>&quot;</td>
      <td>◊</td>
      <td>\Diamond</td>
      <td>♡</td>
      <td>\heartsuit</td>
      <td>╲</td>
      <td>\diagdown</td>
    </tr>
    <tr>
      <td>”</td>
      <td>\textquotedblright</td>
      <td>◊</td>
      <td>\lozenge</td>
      <td>♠</td>
      <td>\spadesuit</td>
      <td>╱</td>
      <td>\diagup</td>
    </tr>
    <tr>
      <td>:</td>
      <td>\colon</td>
      <td>⧫</td>
      <td>\blacklozenge</td>
      <td>∠</td>
      <td>\angle</td>
      <td>℧</td>
      <td>\mho</td>
    </tr>
    <tr>
      <td>‵</td>
      <td>\backprime</td>
      <td>⋆</td>
      <td>\star</td>
      <td>∡</td>
      <td>\measuredangle</td>
      <td>✠</td>
      <td>\maltese</td>
    </tr>
    <tr>
      <td>′</td>
      <td>\prime</td>
      <td>★</td>
      <td>\bigstar</td>
      <td>∢</td>
      <td>\sphericalangle</td>
      <td>∇</td>
      <td>\nabla</td>
    </tr>
    <tr>
      <td>&lt;</td>
      <td>\textless</td>
      <td>|</td>
      <td>\textbar</td>
      <td>⊤</td>
      <td>\top</td>
      <td>∞</td>
      <td>\infty</td>
    </tr>
    <tr>
      <td>&gt;</td>
      <td>\textgreater</td>
      <td>∥</td>
      <td>\textbardbl</td>
      <td>⊥</td>
      <td>\bot</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>{</td>
      <td>\textbraceleft</td>
      <td>}</td>
      <td>\textbraceright</td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
  </table>
    <table class="symbol">
        <tr>
            <td>\(\KaTeX\)</td>
            <td>\KaTeX</td>
            <td>\(\LaTeX\)</td>
            <td>\LaTeX</td>
            <td>\(\TeX\)</td>
            <td>\TeX</td>
        </tr>
    </table>

  <table>
    <tr>
      <td>Direct Input:</td>
      <td style="font-family: KaTeX_Main, KaTeX_AMS;">£ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓</td>
    </tr>
  </table>  
    
  
  <h3  id="units">Units</h3>

  <p>Units are proportioned as they are in TeX instead of CSS.</p>

  <table class="grid units">
    <thead>
    <tr>
      <th>Unit</th>
      <th>Value</th>
      <th>Unit</th>
      <th>Value</th>
    </tr>
    </thead>
    <tbody>
      <tr>
        <td>em</td>
        <td>CSS em</td>
        <td>bp</td>
        <td>\(\frac 1{72}\) inch × <em>F</em> × <em>G</em></td>
      </tr>
      <tr>
        <td>ex</td>
        <td>CSS ex</td>
        <td>pc</td>
        <td>12 \(\TeX\)pt</td>
      </tr>
      <tr>
        <td>mu</td>
        <td>\(\frac 1{18}\) CSS em</td>
        <td>dd</td>
        <td>\(\frac{1238}{1157}\) \(\TeX\)pt</td>
      </tr>
      <tr>
        <td>pt</td>
        <td>\(\frac 1{72.27}\) inch × <em>F</em> × <em>G</em>&nbsp;&nbsp;&nbsp;</td>
        <td>cc</td>
        <td>\(\frac{14856}{1157}\) \(\TeX\)pt</td>
      </tr>
      <tr>
        <td>mm</td>
        <td>1 mm × <em>F</em> × <em>G</em></td>
        <td>nd</td>
        <td>\(\frac{685}{642}\) \(\TeX\)pt</td>
      </tr>
      <tr>
        <td>cm</td>
        <td>1 cm × <em>F</em> × <em>G</em></td>
        <td>nc</td>
        <td>\(\frac{1370}{107}\) \(\TeX\)pt</td>
      </tr>
      <tr>
        <td>in</td>
        <td>1 inch × <em>F</em> × <em>G</em></td>
        <td>sp</td>
        <td>\(\frac 1{65536}\) \(\TeX\)pt</td>
      </tr>
    </tbody>
  </table>

  <table>
    <tr>
      <td style="padding-right:0;">where:</td>
      <td><em>F</em> = \(\large \frac{\text{font size of surrounding HTML text}}{10\text{ pt}}\)</td>
    </tr>
    <tr>
      <td></td>
      <td><em>G</em> = 1.21 by default, because \(\TeX\) font-size is normally 1.21 × the surrounding font size. This value can be over-ridden by the CSS of an HTML page. For example, on this page, <em>G</em> = 1.0.</td>
    </tr>
  </table>
  
  <br>
  
  <p>The effect of style and size:</p>
  <table>
    <thead>
    <tr>
      <th>Unit</th>
      <th>textstyle</th>
      <th>scriptscript</th>
      <th>huge</th>
    </tr>
    </thead>
    <tbody>
    <tr>
      <td>em or ex</td>
      <td>\(\rule{1em}{1em}\)</td>
      <td>\(\scriptscriptstyle\rule{1em}{1em}\)</td>
      <td>\(\huge\rule{1em}{1em}\)</td>
    </tr>

    <tr>
      <td>mu</td>
      <td>\(\rule{18mu}{18mu}\)</td>
      <td>\(\scriptscriptstyle\rule{18mu}{18mu}\)</td>
      <td>\(\huge\rule{18mu}{18mu}\)</td>
    </tr>
    <tr>
      <td>others</td>
      <td>\(\rule{10pt}{10pt}\)</td>
      <td>\(\scriptscriptstyle\rule{10pt}{10pt}\)</td>
      <td>\(\huge\rule{10pt}{10pt}\)</td>
    </tr>
    </tbody>
  </table>

</div>

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