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<table style="max-width: 60vw; margin: auto;"><tr><th colspan="2">Accents And Diacritics</th></tr><tr><td>\dot{a}, \ddot{a}, \acute{a}, \grave{a}</td><td style="position: relative"><math display="block"><mover><mrow><mi>a</mi></mrow><mi>Ë™</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>¨</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>´</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>`</mi></mover></math></td></tr><tr><td>\check{a}, \breve{a}, \tilde{a}, \bar{a}</td><td style="position: relative"><math display="block"><mover><mrow><mi>a</mi></mrow><mi>ˇ</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>˘</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>~</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>‾</mi></mover></math></td></tr><tr><td>\hat{a}, \widehat{a}, \vec{a}</td><td style="position: relative"><math display="block"><mover><mrow><mi>a</mi></mrow><mi>^</mi></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mo stretchy="true">^</mo></mover><mo>,</mo><mover><mrow><mi>a</mi></mrow><mi>→</mi></mover></math></td></tr><tr><th colspan="2">Angle Brackets</th></tr><tr><td>\left \langle \frac{a}{b} \right \rangle</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">⟨</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">⟩</mo></mrow></math></td></tr><tr><th colspan="2">Arc</th></tr><tr><td>\overset{\frown} {AB}</td><td style="position: relative"><math display="block"><mover><mrow><mi>A</mi><mi>B</mi></mrow><mrow><mo>⌢</mo></mrow></mover></math></td></tr><tr><th colspan="2">Area Of Quadrilateral</th></tr><tr><td>S=dD\sin\alpha</td><td style="position: relative"><math display="block"><mi>S</mi><mo>=</mo><mi>d</mi><mi>D</mi><mspace width="0.1667em" /><mi>sin</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>α</mi></math></td></tr><tr><th colspan="2">Arrays</th></tr><tr><td>\begin{array}{||c|c::c|c||}
A & B & C & D \\ \hdashline
1 & 2 & 3 & 4 \\ \hline
5 & 6 & 7 & 8 \\
9 & 10 & 11 & 12
\end{array}</td><td style="position: relative"><math display="block"><mtable class="menv-arraylike"><mtr><mtd class="menv-left-solid menv-border-only"></mtd><mtd class="menv-left-solid menv-right-solid"><mi>A</mi></mtd><mtd class="menv-right-dashed"><mi>B</mi></mtd><mtd class="menv-right-dashed menv-border-only"></mtd><mtd class="menv-right-solid"><mi>C</mi></mtd><mtd class="menv-right-solid"><mi>D</mi></mtd><mtd class="menv-right-solid menv-border-only"></mtd></mtr><mtr class="menv-hdashline"><mtd class="menv-left-solid menv-border-only"></mtd><mtd class="menv-left-solid menv-right-solid"><mn>1</mn></mtd><mtd class="menv-right-dashed"><mn>2</mn></mtd><mtd class="menv-right-dashed menv-border-only"></mtd><mtd class="menv-right-solid"><mn>3</mn></mtd><mtd class="menv-right-solid"><mn>4</mn></mtd><mtd class="menv-right-solid menv-border-only"></mtd></mtr><mtr class="menv-hline"><mtd class="menv-left-solid menv-border-only"></mtd><mtd class="menv-left-solid menv-right-solid"><mn>5</mn></mtd><mtd class="menv-right-dashed"><mn>6</mn></mtd><mtd class="menv-right-dashed menv-border-only"></mtd><mtd class="menv-right-solid"><mn>7</mn></mtd><mtd class="menv-right-solid"><mn>8</mn></mtd><mtd class="menv-right-solid menv-border-only"></mtd></mtr><mtr><mtd class="menv-left-solid menv-border-only"></mtd><mtd class="menv-left-solid menv-right-solid"><mn>9</mn></mtd><mtd class="menv-right-dashed"><mn>10</mn></mtd><mtd class="menv-right-dashed menv-border-only"></mtd><mtd class="menv-right-solid"><mn>11</mn></mtd><mtd class="menv-right-solid"><mn>12</mn></mtd><mtd class="menv-right-solid menv-border-only"></mtd></mtr></mtable></math></td></tr><tr><th colspan="2">Arrows</th></tr><tr><td>\Rrightarrow, \Lleftarrow</td><td style="position: relative"><math display="block"><mo>⇛</mo><mo>,</mo><mo>⇚</mo></math></td></tr><tr><td>\Rightarrow, \nRightarrow, \Longrightarrow, \implies</td><td style="position: relative"><math display="block"><mo>⇒</mo><mo>,</mo><mo>â‡</mo><mo>,</mo><mo>⟹</mo><mo>,</mo><mo>⟹</mo></math></td></tr><tr><td>\Leftarrow, \nLeftarrow, \Longleftarrow</td><td style="position: relative"><math display="block"><mo>â‡</mo><mo>,</mo><mo>â‡</mo><mo>,</mo><mo>⟸</mo></math></td></tr><tr><td>\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff</td><td style="position: relative"><math display="block"><mo>⇔</mo><mo>,</mo><mo>⇎</mo><mo>,</mo><mo>⟺</mo><mo>,</mo><mo>⟺</mo></math></td></tr><tr><td>\Uparrow, \Downarrow, \Updownarrow</td><td style="position: relative"><math display="block"><mo>⇑</mo><mo>,</mo><mo>⇓</mo><mo>,</mo><mo>⇕</mo></math></td></tr><tr><td>\rightarrow, \to, \nrightarrow, \longrightarrow</td><td style="position: relative"><math display="block"><mo>→</mo><mo>,</mo><mo>→</mo><mo>,</mo><mo>↛</mo><mo>,</mo><mo>⟶</mo></math></td></tr><tr><td>\leftarrow, \gets, \nleftarrow, \longleftarrow</td><td style="position: relative"><math display="block"><mo>â†</mo><mo>,</mo><mo>â†</mo><mo>,</mo><mo>↚</mo><mo>,</mo><mo>⟵</mo></math></td></tr><tr><td>\leftrightarrow, \nleftrightarrow, \longleftrightarrow</td><td style="position: relative"><math display="block"><mo>↔</mo><mo>,</mo><mo>↮</mo><mo>,</mo><mo>⟷</mo></math></td></tr><tr><td>\uparrow, \downarrow, \updownarrow</td><td style="position: relative"><math display="block"><mo>↑</mo><mo>,</mo><mo>↓</mo><mo>,</mo><mo>↕</mo></math></td></tr><tr><td>\nearrow, \swarrow, \nwarrow, \searrow</td><td style="position: relative"><math display="block"><mo>↗</mo><mo>,</mo><mo>↙</mo><mo>,</mo><mo>↖</mo><mo>,</mo><mo>↘</mo></math></td></tr><tr><td>\mapsto, \longmapsto</td><td style="position: relative"><math display="block"><mo>↦</mo><mo>,</mo><mo>⟼</mo></math></td></tr><tr><td>\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons</td><td style="position: relative"><math display="block"><mo>⇀</mo><mo>â‡</mo><mo>↼</mo><mo>↽</mo><mo>↿</mo><mo>↾</mo><mo>⇃</mo><mo>⇂</mo><mo>⇌</mo><mo>⇋</mo></math></td></tr><tr><td>\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright</td><td style="position: relative"><math display="block"><mo>↶</mo><mo>↺</mo><mo>↰</mo><mo>⇈</mo><mo>⇉</mo><mo>⇄</mo><mo>↣</mo><mo>↬</mo></math></td></tr><tr><td>\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft</td><td style="position: relative"><math display="block"><mo>↷</mo><mo>↻</mo><mo>↱</mo><mo>⇊</mo><mo>⇇</mo><mo>⇆</mo><mo>↢</mo><mo>↫</mo></math></td></tr><tr><td>\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow</td><td style="position: relative"><math display="block"><mo>↪</mo><mo>↩</mo><mo>⊸</mo><mo>â†</mo><mo>â‡</mo><mo>↠</mo><mo>↞</mo></math></td></tr><tr><th colspan="2">Arrows Example</th></tr><tr><td>A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</td><td style="position: relative"><math display="block"><mi>A</mi><mover><mo>â†</mo><mrow><mi>n</mi><mo>+</mo><mi>µ</mi><mo>−</mo><mn>1</mn></mrow></mover><mi>B</mi><munderover><mo>→</mo><mrow><mi>T</mi></mrow><mrow><mi>n</mi><mo>±</mo><mi>i</mi><mo>−</mo><mn>1</mn></mrow></munderover><mi>C</mi></math></td></tr><tr><th colspan="2">Bars And Double Bars</th></tr><tr><td>\left | \frac{a}{b} \right \vert</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">|</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">|</mo></mrow></math></td></tr><tr><td>\left \| \frac{a}{b} \right \Vert</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">‖</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">‖</mo></mrow></math></td></tr><tr><th colspan="2">Basic</th></tr><tr><td>\alpha</td><td style="position: relative"><math display="block"><mi>α</mi></math></td></tr><tr><td>f(x) = x^2</td><td style="position: relative"><math display="block"><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math></td></tr><tr><td>\{1,e,\pi\}</td><td style="position: relative"><math display="block"><mo symmetric="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>Ï€</mi><mo symmetric="false" stretchy="false">}</mo></math></td></tr><tr><td>|z| \leq 2</td><td style="position: relative"><math display="block"><mi>|</mi><mi>z</mi><mi>|</mi><mo>≤</mo><mn>2</mn></math></td></tr><tr><th colspan="2">Binomials</th></tr><tr><td>\binom{n}{k}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">(</mo><mfrac linethickness="0em"><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></mfrac><mo stretchy="true">)</mo></mrow></math></td></tr><tr><td>\tbinom{n}{k}</td><td style="position: relative"><math display="block"><mrow displaystyle="false" scriptlevel="0"><mo stretchy="true">(</mo><mfrac linethickness="0em"><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></mfrac><mo stretchy="true">)</mo></mrow></math></td></tr><tr><td>\dbinom{n}{k}</td><td style="position: relative"><math display="block"><mrow displaystyle="true" scriptlevel="0"><mo stretchy="true">(</mo><mfrac linethickness="0em"><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></mfrac><mo stretchy="true">)</mo></mrow></math></td></tr><tr><th colspan="2">Blackboard Bold</th></tr><tr><td>\mathbb{ABCDEFGHI}</td><td style="position: relative"><math display="block"><mrow><mi>ð”¸</mi><mi>ð”¹</mi><mi>â„‚</mi><mi>ð”»</mi><mi>ð”¼</mi><mi>ð”½</mi><mi>ð”¾</mi><mi>â„</mi><mi>ð•€</mi></mrow></math></td></tr><tr><td>\mathbb{JKLMNOPQR}</td><td style="position: relative"><math display="block"><mrow><mi>ð•</mi><mi>ð•‚</mi><mi>ð•ƒ</mi><mi>ð•„</mi><mi>â„•</mi><mi>ð•†</mi><mi>â„™</mi><mi>â„š</mi><mi>â„</mi></mrow></math></td></tr><tr><td>\mathbb{STUVWXYZ}</td><td style="position: relative"><math display="block"><mrow><mi>ð•Š</mi><mi>ð•‹</mi><mi>ð•Œ</mi><mi>ð•</mi><mi>ð•Ž</mi><mi>ð•</mi><mi>ð•</mi><mi>ℤ</mi></mrow></math></td></tr><tr><th colspan="2">Boldface</th></tr><tr><td>\mathbf{ABCDEFGHI}</td><td style="position: relative"><math display="block"><mrow><mi>ð€</mi><mi>ð</mi><mi>ð‚</mi><mi>ðƒ</mi><mi>ð„</mi><mi>ð…</mi><mi>ð†</mi><mi>ð‡</mi><mi>ðˆ</mi></mrow></math></td></tr><tr><td>\mathbf{JKLMNOPQR}</td><td style="position: relative"><math display="block"><mrow><mi>ð‰</mi><mi>ðŠ</mi><mi>ð‹</mi><mi>ðŒ</mi><mi>ð</mi><mi>ðŽ</mi><mi>ð</mi><mi>ð</mi><mi>ð‘</mi></mrow></math></td></tr><tr><td>\mathbf{STUVWXYZ}</td><td style="position: relative"><math display="block"><mrow><mi>ð’</mi><mi>ð“</mi><mi>ð”</mi><mi>ð•</mi><mi>ð–</mi><mi>ð—</mi><mi>ð˜</mi><mi>ð™</mi></mrow></math></td></tr><tr><td>\mathbf{abcdefghijklm}</td><td style="position: relative"><math display="block"><mrow><mi>ðš</mi><mi>ð›</mi><mi>ðœ</mi><mi>ð</mi><mi>ðž</mi><mi>ðŸ</mi><mi>ð </mi><mi>ð¡</mi><mi>ð¢</mi><mi>ð£</mi><mi>ð¤</mi><mi>ð¥</mi><mi>ð¦</mi></mrow></math></td></tr><tr><td>\mathbf{nopqrstuvwxyz}</td><td style="position: relative"><math display="block"><mrow><mi>ð§</mi><mi>ð¨</mi><mi>ð©</mi><mi>ðª</mi><mi>ð«</mi><mi>ð¬</mi><mi>ð</mi><mi>ð®</mi><mi>ð¯</mi><mi>ð°</mi><mi>ð±</mi><mi>ð²</mi><mi>ð³</mi></mrow></math></td></tr><tr><td>\mathbf{0123456789}</td><td style="position: relative"><math display="block"><mrow><mn>ðŸŽðŸðŸðŸ‘ðŸ’ðŸ“ðŸ”ðŸ•ðŸ–ðŸ—</mn></mrow></math></td></tr><tr><th colspan="2">Boldface Greek</th></tr><tr><td>\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}</td><td style="position: relative"><math display="block"><mrow><mi>ðš¨</mi><mi>ðš©</mi><mi>ðšª</mi><mi>ðš«</mi><mi>ðš¬</mi><mi>ðš</mi><mi>ðš®</mi><mi>ðš¯</mi></mrow></math></td></tr><tr><td>\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}</td><td style="position: relative"><math display="block"><mrow><mi>ðš°</mi><mi>ðš±</mi><mi>ðš²</mi><mi>ðš³</mi><mi>ðš´</mi><mi>ðšµ</mi><mi>ðš¶</mi><mi>ðš·</mi></mrow></math></td></tr><tr><td>\boldsymbol{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}</td><td style="position: relative"><math display="block"><mrow><mi>ðš¸</mi><mi>ðšº</mi><mi>ðš»</mi><mi>ðš¼</mi><mi>ðš½</mi><mi>ðš¾</mi><mi>ðš¿</mi><mi>ð›€</mi></mrow></math></td></tr><tr><td>\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta}</td><td style="position: relative"><math display="block"><mrow><mi>ð›‚</mi><mi>ð›ƒ</mi><mi>ð›„</mi><mi>ð›…</mi><mi>ð›œ</mi><mi>ð›‡</mi><mi>ð›ˆ</mi><mi>ð›‰</mi></mrow></math></td></tr><tr><td>\boldsymbol{\iota \kappa \lambda \mu \nu \xi \omicron \pi}</td><td style="position: relative"><math display="block"><mrow><mi>ð›Š</mi><mi>ð›‹</mi><mi>ð›Œ</mi><mi>µ</mi><mi>ð›Ž</mi><mi>ð›</mi><mi>ð›</mi><mi>ð›‘</mi></mrow></math></td></tr><tr><td>\boldsymbol{\rho \sigma \tau \upsilon \phi \chi \psi \omega}</td><td style="position: relative"><math display="block"><mrow><mi>ð›’</mi><mi>ð›”</mi><mi>ð›•</mi><mi>ð›–</mi><mi>ð›Ÿ</mi><mi>ð›˜</mi><mi>ð›™</mi><mi>ð›š</mi></mrow></math></td></tr><tr><td>\boldsymbol{\varepsilon\digamma\varkappa\varpi}</td><td style="position: relative"><math display="block"><mrow><mi>ð›†</mi><mi>ð®§</mi><mi>ð›ž</mi><mi>ð›¡</mi></mrow></math></td></tr><tr><td>\boldsymbol{\varrho\varsigma\vartheta\varphi}</td><td style="position: relative"><math display="block"><mrow><mi>ð› </mi><mi>ð›“</mi><mi>ð›</mi><mi>ð›—</mi></mrow></math></td></tr><tr><th colspan="2">Bounds</th></tr><tr><td>\min x, \max y, \inf s, \sup t</td><td style="position: relative"><math display="block"><mi>min</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>x</mi><mo>,</mo><mi>max</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>y</mi><mo>,</mo><mi>inf</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>s</mi><mo>,</mo><mi>sup</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>t</mi></math></td></tr><tr><td>\lim u, \liminf v, \limsup w</td><td style="position: relative"><math display="block"><mi>lim</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>u</mi><mo>,</mo><mi>lim inf</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>v</mi><mo>,</mo><mi>lim sup</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>w</mi></math></td></tr><tr><td>\dim p, \deg q, \det m, \ker\phi</td><td style="position: relative"><math display="block"><mi>dim</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>p</mi><mo>,</mo><mi>deg</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>q</mi><mo>,</mo><mi>det</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>m</mi><mo>,</mo><mi>ker</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>Ï•</mi></math></td></tr><tr><th colspan="2">Braces</th></tr><tr><td>\left \{ \frac{a}{b} \right \}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">{</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">}</mo></mrow></math></td></tr><tr><td>\left \lbrace \frac{a}{b} \right \rbrace</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">{</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">}</mo></mrow></math></td></tr><tr><th colspan="2">Brackets</th></tr><tr><td>\left [ \frac{a}{b} \right ]</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">[</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">]</mo></mrow></math></td></tr><tr><td>\left \lbrack \frac{a}{b} \right \rbrack</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">[</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">]</mo></mrow></math></td></tr><tr><th colspan="2">Calligraphiy</th></tr><tr><td>\mathcal{ABCDEFGHI}</td><td style="position: relative"><math display="block"><mrow><mi>ð’œ</mi><mi>ℬ</mi><mi>ð’ž</mi><mi>ð’Ÿ</mi><mi>â„°</mi><mi>ℱ</mi><mi>ð’¢</mi><mi>â„‹</mi><mi>â„</mi></mrow></math></td></tr><tr><td>\mathcal{JKLMNOPQR}</td><td style="position: relative"><math display="block"><mrow><mi>ð’¥</mi><mi>ð’¦</mi><mi>â„’</mi><mi>ℳ</mi><mi>ð’©</mi><mi>ð’ª</mi><mi>ð’«</mi><mi>ð’¬</mi><mi>â„›</mi></mrow></math></td></tr><tr><td>\mathcal{STUVWXYZ}</td><td style="position: relative"><math display="block"><mrow><mi>ð’®</mi><mi>ð’¯</mi><mi>ð’°</mi><mi>ð’±</mi><mi>ð’²</mi><mi>ð’³</mi><mi>ð’´</mi><mi>ð’µ</mi></mrow></math></td></tr><tr><td>\mathcal{abcdefghi}</td><td style="position: relative"><math display="block"><mrow><mi>ð’¶</mi><mi>ð’·</mi><mi>ð’¸</mi><mi>ð’¹</mi><mi>ℯ</mi><mi>ð’»</mi><mi>â„Š</mi><mi>ð’½</mi><mi>ð’¾</mi></mrow></math></td></tr><tr><td>\mathcal{jklmnopqr}</td><td style="position: relative"><math display="block"><mrow><mi>ð’¿</mi><mi>ð“€</mi><mi>ð“</mi><mi>ð“‚</mi><mi>ð“ƒ</mi><mi>â„´</mi><mi>ð“…</mi><mi>ð“†</mi><mi>ð“‡</mi></mrow></math></td></tr><tr><td>\mathcal{stuvwxyz}</td><td style="position: relative"><math display="block"><mrow><mi>ð“ˆ</mi><mi>ð“‰</mi><mi>ð“Š</mi><mi>ð“‹</mi><mi>ð“Œ</mi><mi>ð“</mi><mi>ð“Ž</mi><mi>ð“</mi></mrow></math></td></tr><tr><th colspan="2">Cases</th></tr><tr><td>f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}</td><td style="position: relative"><math display="block"><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>n</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="true">{</mo><mtable class="menv-cells-left menv-cases"><mtr><mtd><mi>n</mi><mo>/</mo><mn>2</mn><mo>,</mo></mtd><mtd><mtext>if </mtext><mi>n</mi><mtext> is even</mtext></mtd></mtr><mtr><mtd><mn>3</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo></mtd><mtd><mtext>if </mtext><mi>n</mi><mtext> is odd</mtext></mtd></mtr></mtable></mrow></math></td></tr><tr><td>\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">{</mo><mtable class="menv-cells-left menv-cases"><mtr><mtd><mn>3</mn><mi>x</mi><mo>+</mo><mn>5</mn><mi>y</mi><mo>+</mo><mi>z</mi></mtd></mtr><mtr><mtd><mn>7</mn><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>4</mn><mi>z</mi></mtd></mtr><mtr><mtd><mi>−</mi><mn>6</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi></mtd></mtr></mtable></mrow></math></td></tr><tr><th colspan="2">Closed Line Or Path Integral</th></tr><tr><td>\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy</td><td style="position: relative"><math display="block"><msub><mo movablelimits="false">∮</mo><mrow><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mo>∈</mo><mi>C</mi></mrow></msub><msup><mi>x</mi><mn>3</mn></msup><mspace width="0.16666667em" /><mi>d</mi><mi>x</mi><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi></math></td></tr><tr><th colspan="2">Color</th></tr><tr><td>{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}</td><td style="position: relative"><math display="block"><mrow style="color: rgb(0 0 255)"><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow style="color: rgb(255 165 0)"><mn>2</mn><mi>x</mi></mrow><mo>−</mo><mrow style="color: rgb(50 205 50)"><mn>1</mn></mrow></math></td></tr><tr><td>x=\frac{{\color{Blue}-b}\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}2a}</td><td style="position: relative"><math display="block"><mi>x</mi><mo>=</mo><mfrac><mrow><mrow style="color: rgb(0 0 255)"><mi>−</mi><mi>b</mi></mrow><mo>±</mo><msqrt><mrow style="color: rgb(255 0 0)"><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow style="color: rgb(0 128 0)"><mn>2</mn><mi>a</mi></mrow></mfrac></math></td></tr><tr><td>x\color{red}\neq y=z</td><td style="position: relative"><math display="block"><mi>x</mi><mo style="color: rgb(255 0 0)">≠</mo><mi style="color: rgb(255 0 0)">y</mi><mo style="color: rgb(255 0 0)">=</mo><mi style="color: rgb(255 0 0)">z</mi></math></td></tr><tr><td>x{\color{red}\neq} y=z</td><td style="position: relative"><math display="block"><mi>x</mi><mrow style="color: rgb(255 0 0)"><mo>≠</mo></mrow><mi>y</mi><mo>=</mo><mi>z</mi></math></td></tr><tr><td>x\color{red}\neq\color{black} y=z</td><td style="position: relative"><math display="block"><mi>x</mi><mo style="color: rgb(255 0 0)">≠</mo><mi style="color: rgb(0 0 0)">y</mi><mo style="color: rgb(0 0 0)">=</mo><mi style="color: rgb(0 0 0)">z</mi></math></td></tr><tr><td>\frac{-b\color{Green}\pm\sqrt{b^2\color{Blue}-4{\color{Red}a}c}}{2a}=x</td><td style="position: relative"><math display="block"><mfrac><mrow><mi>−</mi><mi>b</mi><mo style="color: rgb(0 128 0)">±</mo><msqrt style="color: rgb(0 128 0)"><mrow style="color: rgb(0 128 0)"><msup><mi>b</mi><mn>2</mn></msup><mo style="color: rgb(0 0 255)">−</mo><mn style="color: rgb(0 0 255)">4</mn><mrow style="color: rgb(255 0 0)"><mi>a</mi></mrow><mi style="color: rgb(0 0 255)">c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>=</mo><mi>x</mi></math></td></tr><tr><td>{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}</td><td style="position: relative"><math display="block"><mrow style="color: rgb(0 0 255)"><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow style="color: rgb(255 165 0)"><mn>2</mn><mi>x</mi></mrow><mo>−</mo><mrow style="color: rgb(50 205 50)"><mn>1</mn></mrow></math></td></tr><tr><td>\color{Blue}x^2\color{Black}+\color{Orange}2x\color{Black}-\color{LimeGreen}1</td><td style="position: relative"><math display="block"><msup style="color: rgb(0 0 255)"><mi style="color: rgb(0 0 255)">x</mi><mn style="color: rgb(0 0 255)">2</mn></msup><mo style="color: rgb(0 0 0)">+</mo><mn style="color: rgb(255 165 0)">2</mn><mi style="color: rgb(255 165 0)">x</mi><mo style="color: rgb(0 0 0)">−</mo><mn style="color: rgb(50 205 50)">1</mn></math></td></tr><tr><th colspan="2">Combined Sub Superscript</th></tr><tr><td>x_2^3</td><td style="position: relative"><math display="block"><msubsup><mi>x</mi><mn>2</mn><mn>3</mn></msubsup></math></td></tr><tr><td>{x_2}^3</td><td style="position: relative"><math display="block"><msup><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><mn>3</mn></msup></math></td></tr><tr><th colspan="2">Complex Numbers</th></tr><tr><td>|\bar{z}| = |z|,
|(\bar{z})^n| = |z|^n,
\arg(z^n) = n \arg(z)</td><td style="position: relative"><math display="block"><mi>|</mi><mover><mrow><mi>z</mi></mrow><mi>‾</mi></mover><mi>|</mi><mo>=</mo><mi>|</mi><mi>z</mi><mi>|</mi><mo>,</mo><mi>|</mi><mo symmetric="false" stretchy="false">(</mo><mover><mrow><mi>z</mi></mrow><mi>‾</mi></mover><msup><mo symmetric="false" stretchy="false">)</mo><mi>n</mi></msup><mi>|</mi><mo>=</mo><mi>|</mi><mi>z</mi><msup><mi>|</mi><mi>n</mi></msup><mo>,</mo><mi>arg</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><msup><mi>z</mi><mi>n</mi></msup><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mi>n</mi><mspace width="0.1667em" /><mi>arg</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mi>z</mi><mo symmetric="false" stretchy="false">)</mo></math></td></tr><tr><th colspan="2">Continuation And Cases</th></tr><tr><td>f(x) =
\begin{cases}
1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\
1 - x^2 & \text{otherwise}
\end{cases}</td><td style="position: relative"><math display="block"><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="true">{</mo><mtable class="menv-cells-left menv-cases"><mtr><mtd><mn>1</mn></mtd><mtd><mi>−</mi><mn>1</mn><mo>≤</mo><mi>x</mi><mo><</mo><mn>0</mn></mtd></mtr><mtr><mtd><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mtd><mtd><mi>x</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>−</mo><msup><mi>x</mi><mn>2</mn></msup></mtd><mtd><mtext>otherwise</mtext></mtd></mtr></mtable></mrow></math></td></tr><tr><th colspan="2">Coproduct</th></tr><tr><td>\coprod_{i=1}^N x_i</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">âˆ</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>x</mi><mi>i</mi></msub></math></td></tr><tr><td>\textstyle \coprod_{i=1}^N x_i</td><td style="position: relative"><math display="block"><msubsup displaystyle="false" scriptlevel="0"><mo displaystyle="false" scriptlevel="0" movablelimits="false">âˆ</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><msub displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">x</mi><mi>i</mi></msub></math></td></tr><tr><th colspan="2">Delimiter Sizes</th></tr><tr><td>( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]</td><td style="position: relative"><math display="block"><mo symmetric="false" stretchy="false">(</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">(</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">(</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">(</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">(</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">]</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">]</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">]</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">]</mo><mo symmetric="false" stretchy="false">]</mo></math></td></tr><tr><td>\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots \Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle</td><td style="position: relative"><math display="block"><mo symmetric="false" stretchy="false">{</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">{</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">{</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">{</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">{</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">⟩</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">⟩</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">⟩</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">⟩</mo><mo symmetric="false" stretchy="false">⟩</mo></math></td></tr><tr><td>\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |</td><td style="position: relative"><math display="block"><mi>∥</mi><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">‖</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">‖</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">‖</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">‖</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">|</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">|</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">|</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">|</mo><mi>|</mi></math></td></tr><tr><td>\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil</td><td style="position: relative"><math display="block"><mo symmetric="false" stretchy="false">⌊</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">⌊</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">⌊</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">⌊</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">⌊</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">⌉</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">⌉</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">⌉</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">⌉</mo><mo symmetric="false" stretchy="false">⌉</mo></math></td></tr><tr><td>\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow</td><td style="position: relative"><math display="block"><mo>↑</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">↑</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">↑</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">↑</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">↑</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">⇓</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">⇓</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">⇓</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">⇓</mo><mo>⇓</mo></math></td></tr><tr><td>\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow</td><td style="position: relative"><math display="block"><mo>↕</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">↕</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">↕</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">↕</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">↕</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">⇕</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">⇕</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">⇕</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">⇕</mo><mo>⇕</mo></math></td></tr><tr><td>/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash</td><td style="position: relative"><math display="block"><mi>/</mi><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">/</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">/</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">/</mo><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">/</mo><mi>⋯</mi><mo symmetric="true" stretchy="true"minsize="3em" maxsize="3em">\</mo><mo symmetric="true" stretchy="true"minsize="2.4em" maxsize="2.4em">\</mo><mo symmetric="true" stretchy="true"minsize="1.8em" maxsize="1.8em">\</mo><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">\</mo><mi>\</mi></math></td></tr><tr><th colspan="2">Derivative Dots</th></tr><tr><td>\dot{x}, \ddot{x}</td><td style="position: relative"><math display="block"><mover><mrow><mi>x</mi></mrow><mi>Ë™</mi></mover><mo>,</mo><mover><mrow><mi>x</mi></mrow><mi>¨</mi></mover></math></td></tr><tr><th colspan="2">Derivatives</th></tr><tr><td>x', y'', f', f''</td><td style="position: relative"><math display="block"><mi>x</mi><mi>′</mi><mo>,</mo><mi>y</mi><mi>′</mi><mi>′</mi><mo>,</mo><mi>f</mi><mi>′</mi><mo>,</mo><mi>f</mi><mi>′</mi><mi>′</mi></math></td></tr><tr><td>x^\prime, y^{\prime\prime}</td><td style="position: relative"><math display="block"><msup><mi>x</mi><mi>′</mi></msup><mo>,</mo><msup><mi>y</mi><mrow><mi>′</mi><mi>′</mi></mrow></msup></math></td></tr><tr><th colspan="2">Differential And Derivatives</th></tr><tr><td>dt, \mathrm{d}t, \partial t, \nabla\psi</td><td style="position: relative"><math display="block"><mi>d</mi><mi>t</mi><mo>,</mo><mrow><mi mathvariant="normal">d</mi></mrow><mi>t</mi><mo>,</mo><mi>∂</mi><mi>t</mi><mo>,</mo><mi>∇</mi><mi>ψ</mi></math></td></tr><tr><td>dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}</td><td style="position: relative"><math display="block"><mi>d</mi><mi>y</mi><mo>/</mo><mi>d</mi><mi>x</mi><mo>,</mo><mrow><mi mathvariant="normal">d</mi></mrow><mi>y</mi><mo>/</mo><mrow><mi mathvariant="normal">d</mi></mrow><mi>x</mi><mo>,</mo><mfrac><mrow><mi>d</mi><mi>y</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mrow><mi mathvariant="normal">d</mi></mrow><mi>y</mi></mrow><mrow><mrow><mi mathvariant="normal">d</mi></mrow><mi>x</mi></mrow></mfrac></math></td></tr><tr><td>\frac{\partial^2}{\partial x_1\partial x_2}y, \left.\frac{\partial^3 f}{\partial^2 x \partial y}\right\vert_{p_0}</td><td style="position: relative"><math display="block"><mfrac><mrow><msup><mi>∂</mi><mn>2</mn></msup></mrow><mrow><mi>∂</mi><msub><mi>x</mi><mn>1</mn></msub><mi>∂</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mfrac><mi>y</mi><mo>,</mo><msub><mrow><mfrac><mrow><msup><mi>∂</mi><mn>3</mn></msup><mi>f</mi></mrow><mrow><msup><mi>∂</mi><mn>2</mn></msup><mi>x</mi><mi>∂</mi><mi>y</mi></mrow></mfrac><mo stretchy="true">|</mo></mrow><mrow><msub><mi>p</mi><mn>0</mn></msub></mrow></msub></math></td></tr><tr><td>\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y</td><td style="position: relative"><math display="block"><mi>′</mi><mo>,</mo><mi>‵</mi><mo>,</mo><msup><mi>f</mi><mi>′</mi></msup><mo>,</mo><mi>f</mi><mi>′</mi><mo>,</mo><mi>f</mi><mi>′</mi><mi>′</mi><mo>,</mo><msup><mi>f</mi><mrow><mo symmetric="false" stretchy="false">(</mo><mn>3</mn><mo symmetric="false" stretchy="false">)</mo></mrow></msup><mo>,</mo><mover><mi>y</mi><mi>Ë™</mi></mover><mo>,</mo><mover><mi>y</mi><mi>¨</mi></mover></math></td></tr><tr><th colspan="2">Differential Equations</th></tr><tr><td>u'' + p(x)u' + q(x)u=f(x),\quad x>a</td><td style="position: relative"><math display="block"><mi>u</mi><mi>′</mi><mi>′</mi><mo>+</mo><mi>p</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo><mi>u</mi><mi>′</mi><mo>+</mo><mi>q</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo><mi>u</mi><mo>=</mo><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo><mo>,</mo><mspace width="1em" /><mi>x</mi><mo>></mo><mi>a</mi></math></td></tr><tr><th colspan="2">Double Integral</th></tr><tr><td>\iint\limits_{D} dx\,dy</td><td style="position: relative"><math display="block"><munder><mo movablelimits="false">∬</mo><mrow><mi>D</mi></mrow></munder><mi>d</mi><mi>x</mi><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi></math></td></tr><tr><th colspan="2">Floor And Ceiling</th></tr><tr><td>\left \lfloor \frac{a}{b} \right \rfloor</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">⌊</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">⌋</mo></mrow></math></td></tr><tr><td>\left \lceil \frac{a}{b} \right \rceil</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">⌈</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">⌉</mo></mrow></math></td></tr><tr><th colspan="2">Fraction And Small Fraction</th></tr><tr><td>\frac{a}{b}\ \tfrac{a}{b}</td><td style="position: relative"><math display="block"><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mtext> </mtext><mrow displaystyle="false" scriptlevel="0"><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mrow></math></td></tr><tr><th colspan="2">Fractions</th></tr><tr><td>\frac{2}{4} = 0.5</td><td style="position: relative"><math display="block"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mn>0.5</mn></math></td></tr><tr><td>\tfrac{2}{4} = 0.5</td><td style="position: relative"><math display="block"><mrow displaystyle="false" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mo>=</mo><mn>0.5</mn></math></td></tr><tr><td>\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a</td><td style="position: relative"><math display="block"><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mo>=</mo><mn>0.5</mn><mspace width="2em" /><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mi>c</mi><mo>+</mo><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mi>d</mi><mo>+</mo><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mrow></mfrac></mrow></mrow></mfrac></mrow><mo>=</mo><mi>a</mi></math></td></tr><tr><td>\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a</td><td style="position: relative"><math display="block"><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mi>c</mi><mo>+</mo><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mi>d</mi><mo>+</mo><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mrow></mfrac></mrow></mrow></mfrac></mrow><mo>=</mo><mi>a</mi></math></td></tr><tr><td>\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}</td><td style="position: relative"><math display="block"><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>x</mi></mrow><mrow><mn>1</mn><mo>+</mo><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mrow class="mop-negated"><mrow><mi>y</mi></mrow></mrow></mrow><mrow><mrow class="mop-negated"><mrow><mi>y</mi></mrow></mrow></mrow></mfrac></mrow></mrow></mfrac></mrow><mo>=</mo><mrow displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></td></tr><tr><th colspan="2">Fraktur</th></tr><tr><td>\mathfrak{ABCDEFGHI}</td><td style="position: relative"><math display="block"><mrow><mi>ð”„</mi><mi>ð”…</mi><mi>â„</mi><mi>ð”‡</mi><mi>ð”ˆ</mi><mi>ð”‰</mi><mi>ð”Š</mi><mi>â„Œ</mi><mi>â„</mi></mrow></math></td></tr><tr><td>\mathfrak{JKLMNOPQR}</td><td style="position: relative"><math display="block"><mrow><mi>ð”</mi><mi>ð”Ž</mi><mi>ð”</mi><mi>ð”</mi><mi>ð”‘</mi><mi>ð”’</mi><mi>ð”“</mi><mi>ð””</mi><mi>â„œ</mi></mrow></math></td></tr><tr><td>\mathfrak{STUVWXYZ}</td><td style="position: relative"><math display="block"><mrow><mi>ð”–</mi><mi>ð”—</mi><mi>ð”˜</mi><mi>ð”™</mi><mi>ð”š</mi><mi>ð”›</mi><mi>ð”œ</mi><mi>ℨ</mi></mrow></math></td></tr><tr><td>\mathfrak{abcdefghijklm}</td><td style="position: relative"><math display="block"><mrow><mi>ð”ž</mi><mi>ð”Ÿ</mi><mi>ð” </mi><mi>ð”¡</mi><mi>ð”¢</mi><mi>ð”£</mi><mi>ð”¤</mi><mi>ð”¥</mi><mi>ð”¦</mi><mi>ð”§</mi><mi>ð”¨</mi><mi>ð”©</mi><mi>ð”ª</mi></mrow></math></td></tr><tr><td>\mathfrak{nopqrstuvwxyz}</td><td style="position: relative"><math display="block"><mrow><mi>ð”«</mi><mi>ð”¬</mi><mi>ð”</mi><mi>ð”®</mi><mi>ð”¯</mi><mi>ð”°</mi><mi>ð”±</mi><mi>ð”²</mi><mi>ð”³</mi><mi>ð”´</mi><mi>ð”µ</mi><mi>ð”¶</mi><mi>ð”·</mi></mrow></math></td></tr><tr><td>\mathfrak{0123456789}</td><td style="position: relative"><math display="block"><mrow><mn>0123456789</mn></mrow></math></td></tr><tr><th colspan="2">Geometric</th></tr><tr><td>\parallel, \nparallel, \shortparallel, \nshortparallel</td><td style="position: relative"><math display="block"><mo>∥</mo><mo>,</mo><mo>∦</mo><mo>,</mo><mo class="small">∥</mo><mo>,</mo><mo class="small">∦</mo></math></td></tr><tr><td>\perp, \angle, \sphericalangle, \measuredangle, 45^\circ</td><td style="position: relative"><math display="block"><mo>⟂</mo><mo>,</mo><mi>∠</mi><mo>,</mo><mi>∢</mi><mo>,</mo><mi>∡</mi><mo>,</mo><msup><mn>45</mn><mi>∘</mi></msup></math></td></tr><tr><td>\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar</td><td style="position: relative"><math display="block"><mi>â–¡</mi><mo>,</mo><mi>â–¡</mi><mo>,</mo><mi>â– </mi><mo>,</mo><mi>â‹„</mi><mo>,</mo><mi>â—Š</mi><mo>,</mo><mi>â—Š</mi><mo>,</mo><mi>⧫</mi><mo>,</mo><mi>★</mi></math></td></tr><tr><td>\bigcirc, \triangle, \bigtriangleup, \bigtriangledown</td><td style="position: relative"><math display="block"><mi>â—¯</mi><mo>,</mo><mi>â–³</mi><mo>,</mo><mi>â–³</mi><mo>,</mo><mi>â–½</mi></math></td></tr><tr><td>\vartriangle, \triangledown</td><td style="position: relative"><math display="block"><mi>â–³</mi><mo>,</mo><mi>â–½</mi></math></td></tr><tr><td>\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright</td><td style="position: relative"><math display="block"><mi>â–²</mi><mo>,</mo><mi>â–¼</mi><mo>,</mo><mi>â—€</mi><mo>,</mo><mi>â–¶</mi></math></td></tr><tr><th colspan="2">Greek Alphabet</th></tr><tr><td>\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta</td><td style="position: relative"><math display="block"><mi mathvariant="normal">Α</mi><mi mathvariant="normal">Î’</mi><mi mathvariant="normal">Γ</mi><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ε</mi><mi mathvariant="normal">Ζ</mi><mi mathvariant="normal">Η</mi><mi mathvariant="normal">Θ</mi></math></td></tr><tr><td>\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi</td><td style="position: relative"><math display="block"><mi mathvariant="normal">Ι</mi><mi mathvariant="normal">Κ</mi><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">Îœ</mi><mi mathvariant="normal">Î</mi><mi mathvariant="normal">Ξ</mi><mi mathvariant="normal">Ο</mi><mi mathvariant="normal">Î </mi></math></td></tr><tr><td>\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega</td><td style="position: relative"><math display="block"><mi mathvariant="normal">Ρ</mi><mi mathvariant="normal">Σ</mi><mi mathvariant="normal">Τ</mi><mi mathvariant="normal">Î¥</mi><mi mathvariant="normal">Φ</mi><mi mathvariant="normal">Χ</mi><mi mathvariant="normal">Ψ</mi><mi mathvariant="normal">Ω</mi></math></td></tr><tr><td>\alpha \beta \gamma \delta \epsilon \zeta \eta \theta</td><td style="position: relative"><math display="block"><mi>α</mi><mi>β</mi><mi>γ</mi><mi>δ</mi><mi>ϵ</mi><mi>ζ</mi><mi>η</mi><mi>θ</mi></math></td></tr><tr><td>\iota \kappa \lambda \mu \nu \xi \omicron \pi</td><td style="position: relative"><math display="block"><mi>ι</mi><mi>κ</mi><mi>λ</mi><mi>µ</mi><mi>ν</mi><mi>ξ</mi><mi>ο</mi><mi>Ï€</mi></math></td></tr><tr><td>\rho \sigma \tau \upsilon \phi \chi \psi \omega</td><td style="position: relative"><math display="block"><mi>Ï</mi><mi>σ</mi><mi>Ï„</mi><mi>Ï…</mi><mi>Ï•</mi><mi>χ</mi><mi>ψ</mi><mi>ω</mi></math></td></tr><tr><td>\varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega</td><td style="position: relative"><math display="block"><mi mathvariant="normal">ð›¤</mi><mi mathvariant="normal">ð›¥</mi><mi mathvariant="normal">ð›©</mi><mi mathvariant="normal">ð›¬</mi><mi mathvariant="normal">ð›¯</mi><mi mathvariant="normal">ð›±</mi><mi mathvariant="normal">ð›´</mi><mi mathvariant="normal">ð›·</mi><mi mathvariant="normal">ð›¶</mi><mi mathvariant="normal">ð›º</mi></math></td></tr><tr><td>\varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi</td><td style="position: relative"><math display="block"><mi>ε</mi><mi>Ï</mi><mi>Ï°</mi><mi>Ï–</mi><mi>ϱ</mi><mi>Ï‚</mi><mi>Ï‘</mi><mi>φ</mi></math></td></tr><tr><th colspan="2">Greek Italics</th></tr><tr><td>\mathit{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}</td><td style="position: relative"><math display="block"><mrow><mi>ð›¢</mi><mi>ð›£</mi><mi>ð›¤</mi><mi>ð›¥</mi><mi>ð›¦</mi><mi>ð›§</mi><mi>ð›¨</mi><mi>ð›©</mi></mrow></math></td></tr><tr><td>\mathit{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}</td><td style="position: relative"><math display="block"><mrow><mi>ð›ª</mi><mi>ð›«</mi><mi>ð›¬</mi><mi>ð›</mi><mi>ð›®</mi><mi>ð›¯</mi><mi>ð›°</mi><mi>ð›±</mi></mrow></math></td></tr><tr><td>\mathit{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}</td><td style="position: relative"><math display="block"><mrow><mi>ð›²</mi><mi>ð›´</mi><mi>ð›µ</mi><mi>ð›¶</mi><mi>ð›·</mi><mi>ð›¸</mi><mi>ð›¹</mi><mi>ð›º</mi></mrow></math></td></tr><tr><th colspan="2">Greek Uppercase Boldface Italics</th></tr><tr><td>\boldsymbol{\varGamma \varDelta \varTheta \varLambda}</td><td style="position: relative"><math display="block"><mrow><mi>ð›¤</mi><mi>ð›¥</mi><mi>ð›©</mi><mi>ð›¬</mi></mrow></math></td></tr><tr><td>\boldsymbol{\varXi \varPi \varSigma \varUpsilon \varOmega}</td><td style="position: relative"><math display="block"><mrow><mi>ð›¯</mi><mi>ð›±</mi><mi>ð›´</mi><mi>ð›¶</mi><mi>ð›º</mi></mrow></math></td></tr><tr><th colspan="2">Grouping</th></tr><tr><td>10^{30} a^{2+2}</td><td style="position: relative"><math display="block"><msup><mn>10</mn><mrow><mn>30</mn></mrow></msup><msup><mi>a</mi><mrow><mn>2</mn><mo>+</mo><mn>2</mn></mrow></msup></math></td></tr><tr><td>a_{i,j} b_{f'}</td><td style="position: relative"><math display="block"><msub><mi>a</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>b</mi><mrow><mi>f</mi><mi>′</mi></mrow></msub></math></td></tr><tr><th colspan="2">Hebrew Symbols</th></tr><tr><td>\aleph \beth \gimel \daleth</td><td style="position: relative"><math display="block"><mi>ℵ</mi><mi>ℶ</mi><mi>â„·</mi><mi>ℸ</mi></math></td></tr><tr><th colspan="2">Integral</th></tr><tr><td>\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">∫</mo><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></munderover><mfrac><mrow><msup><mi>e</mi><mn>3</mn></msup><mo>/</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac><mspace width="0.16666667em" /><mi>d</mi><mi>x</mi></math></td></tr><tr><td>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</td><td style="position: relative"><math display="block"><msubsup><mo movablelimits="false">∫</mo><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></msubsup><mfrac><mrow><msup><mi>e</mi><mn>3</mn></msup><mo>/</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac><mspace width="0.16666667em" /><mi>d</mi><mi>x</mi></math></td></tr><tr><td>\textstyle \int\limits_{-N}^{N} e^x dx</td><td style="position: relative"><math display="block"><munderover displaystyle="false" scriptlevel="0"><mo displaystyle="false" scriptlevel="0" movablelimits="false">∫</mo><mrow><mi>−</mi><mi>N</mi></mrow><mrow><mi>N</mi></mrow></munderover><msup displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">e</mi><mi>x</mi></msup><mi displaystyle="false" scriptlevel="0">d</mi><mi displaystyle="false" scriptlevel="0">x</mi></math></td></tr><tr><td>\textstyle \int_{-N}^{N} e^x dx</td><td style="position: relative"><math display="block"><msubsup displaystyle="false" scriptlevel="0"><mo displaystyle="false" scriptlevel="0" movablelimits="false">∫</mo><mrow><mi>−</mi><mi>N</mi></mrow><mrow><mi>N</mi></mrow></msubsup><msup displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">e</mi><mi>x</mi></msup><mi displaystyle="false" scriptlevel="0">d</mi><mi displaystyle="false" scriptlevel="0">x</mi></math></td></tr><tr><th colspan="2">Integral Equation</th></tr><tr><td>\phi_n(\kappa) =
\frac{1}{4\pi^2\kappa^2} \int_0^\infty
\frac{\sin(\kappa R)}{\kappa R}
\frac{\partial}{\partial R}
\left [ R^2\frac{\partial D_n(R)}{\partial R} \right ] \,dR</td><td style="position: relative"><math display="block"><msub><mi>Ï•</mi><mi>n</mi></msub><mo symmetric="false" stretchy="false">(</mo><mi>κ</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn><msup><mi>Ï€</mi><mn>2</mn></msup><msup><mi>κ</mi><mn>2</mn></msup></mrow></mfrac><msubsup><mo movablelimits="false">∫</mo><mn>0</mn><mi>∞</mi></msubsup><mfrac><mrow><mi>sin</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mi>κ</mi><mi>R</mi><mo symmetric="false" stretchy="false">)</mo></mrow><mrow><mi>κ</mi><mi>R</mi></mrow></mfrac><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><mi>R</mi></mrow></mfrac><mrow><mo stretchy="true">[</mo><msup><mi>R</mi><mn>2</mn></msup><mfrac><mrow><mi>∂</mi><msub><mi>D</mi><mi>n</mi></msub><mo symmetric="false" stretchy="false">(</mo><mi>R</mi><mo symmetric="false" stretchy="false">)</mo></mrow><mrow><mi>∂</mi><mi>R</mi></mrow></mfrac><mo stretchy="true">]</mo></mrow><mspace width="0.16666667em" /><mi>d</mi><mi>R</mi></math></td></tr><tr><th colspan="2">Integrals</th></tr><tr><td>\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</td><td style="position: relative"><math display="block"><msubsup><mo movablelimits="false">∫</mo><mi>a</mi><mi>x</mi></msubsup><msubsup><mo movablelimits="false">∫</mo><mi>a</mi><mi>s</mi></msubsup><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi><mspace width="0.16666667em" /><mi>d</mi><mi>s</mi><mo>=</mo><msubsup><mo movablelimits="false">∫</mo><mi>a</mi><mi>x</mi></msubsup><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi></math></td></tr><tr><td>\int_e^{\infty}\frac {1}{t(\ln t)^2}dt = \left. \frac{-1}{\ln t} \right\vert_e^\infty = 1</td><td style="position: relative"><math display="block"><msubsup><mo movablelimits="false">∫</mo><mi>e</mi><mrow><mi>∞</mi></mrow></msubsup><mfrac><mrow><mn>1</mn></mrow><mrow><mi>t</mi><mo symmetric="false" stretchy="false">(</mo><mi>ln</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>t</mi><msup><mo symmetric="false" stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac><mi>d</mi><mi>t</mi><mo>=</mo><msubsup><mrow><mfrac><mrow><mi>−</mi><mn>1</mn></mrow><mrow><mi>ln</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>t</mi></mrow></mfrac><mo stretchy="true">|</mo></mrow><mi>e</mi><mi>∞</mi></msubsup><mo>=</mo><mn>1</mn></math></td></tr><tr><th colspan="2">Intersections</th></tr><tr><td>\bigcap_{i=1}^n E_i</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">â‹‚</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>E</mi><mi>i</mi></msub></math></td></tr><tr><th colspan="2">Italics</th></tr><tr><td>\mathit{0123456789}</td><td style="position: relative"><math display="block"><mrow><mn>0123456789</mn></mrow></math></td></tr><tr><th colspan="2">Letter Like Symbols Or Constants</th></tr><tr><td>\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar</td><td style="position: relative"><math display="block"><mi>∞</mi><mo>,</mo><mi>ℵ</mi><mo>,</mo><mi>âˆ</mi><mo>,</mo><mi>϶</mi><mo>,</mo><mi>ð</mi><mo>,</mo><mi mathvariant="normal">Ⅎ</mi><mo>,</mo><mi>â„</mi></math></td></tr><tr><td>\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P</td><td style="position: relative"><math display="block"><mi mathvariant="normal">â„‘</mi><mo>,</mo><mi>ı</mi><mo>,</mo><mi>È·</mi><mo>,</mo><mi>ð•œ</mi><mo>,</mo><mi>â„“</mi><mo>,</mo><mi>℧</mi><mo>,</mo><mi>℘</mi><mo>,</mo><mi mathvariant="normal">â„œ</mi><mo>,</mo><mi mathvariant="normal">Ⓢ</mi><mo>,</mo><mi>§</mi><mo>,</mo><mi>¶</mi></math></td></tr><tr><th colspan="2">Limit</th></tr><tr><td>\lim_{x \to \infty} x_n</td><td style="position: relative"><math display="block"><munder><mi>lim</mi><mrow><mi>x</mi><mo>→</mo><mi>∞</mi></mrow></munder><mo>â¡</mo><mspace width="0.1667em" /><msub><mi>x</mi><mi>n</mi></msub></math></td></tr><tr><td>\textstyle \lim_{x \to \infty} x_n</td><td style="position: relative"><math display="block"><msub displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">lim</mi><mrow><mi>x</mi><mo>→</mo><mi>∞</mi></mrow></msub><mo>â¡</mo><mspace width="0.1667em" /><msub displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">x</mi><mi>n</mi></msub></math></td></tr><tr><th colspan="2">Limits</th></tr><tr><td>\lim_{z\to z_0} f(z)=f(z_0)</td><td style="position: relative"><math display="block"><munder><mi>lim</mi><mrow><mi>z</mi><mo>→</mo><msub><mi>z</mi><mn>0</mn></msub></mrow></munder><mo>â¡</mo><mspace width="0.1667em" /><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>z</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><msub><mi>z</mi><mn>0</mn></msub><mo symmetric="false" stretchy="false">)</mo></math></td></tr><tr><th colspan="2">Line Or Path Integral</th></tr><tr><td>\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy</td><td style="position: relative"><math display="block"><msub><mo movablelimits="false">∫</mo><mrow><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mo>∈</mo><mi>C</mi></mrow></msub><msup><mi>x</mi><mn>3</mn></msup><mspace width="0.16666667em" /><mi>d</mi><mi>x</mi><mo>+</mo><mn>4</mn><msup><mi>y</mi><mn>2</mn></msup><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi></math></td></tr><tr><th colspan="2">Logic</th></tr><tr><td>\forall, \exists, \nexists</td><td style="position: relative"><math display="block"><mi>∀</mi><mo>,</mo><mi>∃</mi><mo>,</mo><mi>∄</mi></math></td></tr><tr><td>\therefore, \because, \And</td><td style="position: relative"><math display="block"><mo>∴</mo><mo>,</mo><mo>∵</mo><mo>,</mo><mi>&</mi></math></td></tr><tr><td>\lor, \vee, \curlyvee, \bigvee</td><td style="position: relative"><math display="block"><mi>∨</mi><mo>,</mo><mi>∨</mi><mo>,</mo><mi>â‹Ž</mi><mo>,</mo><mo movablelimits="false">â‹</mo></math></td></tr><tr><td>\land, \wedge, \curlywedge, \bigwedge</td><td style="position: relative"><math display="block"><mi>∧</mi><mo>,</mo><mi>∧</mi><mo>,</mo><mi>â‹</mi><mo>,</mo><mo movablelimits="false">â‹€</mo></math></td></tr><tr><td>\bar{q}, \bar{abc}, \overline{q}, \overline{abc}</td><td style="position: relative"><math display="block"><mover><mrow><mi>q</mi></mrow><mi>‾</mi></mover><mo>,</mo><mover><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow><mi>‾</mi></mover><mo>,</mo><mover><mrow><mi>q</mi></mrow><mi>‾</mi></mover><mo>,</mo><mover><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow><mi>‾</mi></mover></math></td></tr><tr><td>\lnot, \neg, \not\operatorname{R}, \bot, \to</td><td style="position: relative"><math display="block"><mi>¬</mi><mo>,</mo><mi>¬</mi><mo>,</mo><mrow class="mop-negated"><mi mathvariant="normal">R</mi><mo>â¡</mo></mrow><mo>,</mo><mi>⊥</mi><mo>,</mo><mo>→</mo></math></td></tr><tr><td>\vdash, \dashv, \vDash, \Vdash, \models</td><td style="position: relative"><math display="block"><mo>⊢</mo><mo>,</mo><mo>⊣</mo><mo>,</mo><mo>⊨</mo><mo>,</mo><mo>⊩</mo><mo>,</mo><mo>⊨</mo></math></td></tr><tr><td>\Vvdash, \nvdash, \nVdash, \nvDash, \nVDash</td><td style="position: relative"><math display="block"><mo>⊪</mo><mo>,</mo><mo>⊬</mo><mo>,</mo><mo>⊮</mo><mo>,</mo><mo>âŠ</mo><mo>,</mo><mo>⊯</mo></math></td></tr><tr><td>\ulcorner, \urcorner, \llcorner, \lrcorner</td><td style="position: relative"><math display="block"><mo symmetric="false" stretchy="false">┌</mo><mo>,</mo><mo symmetric="false" stretchy="false">â”</mo><mo>,</mo><mo symmetric="false" stretchy="false">â””</mo><mo>,</mo><mo symmetric="false" stretchy="false">┘</mo></math></td></tr><tr><th colspan="2">Matrices</th></tr><tr><td>\begin{matrix}
-x & y \\
z & -v
\end{matrix}</td><td style="position: relative"><math display="block"><mtable class="menv-arraylike"><mtr><mtd><mi>−</mi><mi>x</mi></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>−</mi><mi>v</mi></mtd></mtr></mtable></math></td></tr><tr><td>\begin{vmatrix}
-x & y \\
z & -v
\end{vmatrix}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">|</mo><mtable class="menv-arraylike"><mtr><mtd><mi>−</mi><mi>x</mi></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>−</mi><mi>v</mi></mtd></mtr></mtable><mo stretchy="true">|</mo></mrow></math></td></tr><tr><td>\begin{Vmatrix}
-x & y \\
z & -v
\end{Vmatrix}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">‖</mo><mtable class="menv-arraylike"><mtr><mtd><mi>−</mi><mi>x</mi></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>−</mi><mi>v</mi></mtd></mtr></mtable><mo stretchy="true">‖</mo></mrow></math></td></tr><tr><td>\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">[</mo><mtable class="menv-arraylike"><mtr><mtd><mn>0</mn></mtd><mtd><mi>⋯</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>⋮</mi></mtd><mtd><mi>⋱</mi></mtd><mtd><mi>⋮</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>⋯</mi></mtd><mtd><mn>0</mn></mtd></mtr></mtable><mo stretchy="true">]</mo></mrow></math></td></tr><tr><td>\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">{</mo><mtable class="menv-arraylike"><mtr><mtd><mi>x</mi></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>v</mi></mtd></mtr></mtable><mo stretchy="true">}</mo></mrow></math></td></tr><tr><td>\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">(</mo><mtable class="menv-arraylike"><mtr><mtd><mi>x</mi></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>v</mi></mtd></mtr></mtable><mo stretchy="true">)</mo></mrow></math></td></tr><tr><td>\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)</td><td style="position: relative"><math display="block"><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">(</mo><mtable class="menv-arraylike"><mtr><mtd><mi displaystyle="false" scriptlevel="0">a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable><mo symmetric="true" stretchy="true"minsize="1.2em" maxsize="1.2em">)</mo></math></td></tr><tr><th colspan="2">Matrices And Determinants</th></tr><tr><td>\det(\mathsf{A}-\lambda\mathsf{I}) = 0</td><td style="position: relative"><math display="block"><mi>det</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mrow><mi>ð– </mi></mrow><mo>−</mo><mi>λ</mi><mrow><mi>ð–¨</mi></mrow><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mn>0</mn></math></td></tr><tr><th colspan="2">Mixed</th></tr><tr><td>\left [ 0,1 \right )</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">[</mo><mn>0,1</mn><mo stretchy="true">)</mo></mrow></math></td></tr><tr><td>\left \langle \psi \right |</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">⟨</mo><mi>ψ</mi><mo stretchy="true">|</mo></mrow></math></td></tr><tr><th colspan="2">Mixed Faces</th></tr><tr><td>x y z</td><td style="position: relative"><math display="block"><mi>x</mi><mi>y</mi><mi>z</mi></math></td></tr><tr><td>\text{x y z}</td><td style="position: relative"><math display="block"><mtext>x y z</mtext></math></td></tr><tr><td>\text{if} n \text{is even}</td><td style="position: relative"><math display="block"><mtext>if</mtext><mi>n</mi><mtext>is even</mtext></math></td></tr><tr><td>\text{if }n\text{ is even}</td><td style="position: relative"><math display="block"><mtext>if </mtext><mi>n</mi><mtext> is even</mtext></math></td></tr><tr><td>\text{if}~n\ \text{is even}</td><td style="position: relative"><math display="block"><mtext>if</mtext><mtext> </mtext><mi>n</mi><mtext> </mtext><mtext>is even</mtext></math></td></tr><tr><th colspan="2">Modular Arithmetic</th></tr><tr><td>s_k \equiv 0 \pmod{m}</td><td style="position: relative"><math display="block"><msub><mi>s</mi><mi>k</mi></msub><mo>≡</mo><mn>0</mn><mspace width="1em" /><mrow><mo symmetric="false" stretchy="false">(</mo><mi>mod</mi><mo>â¡</mo><mspace width="0.1667em" /><mrow><mi>m</mi></mrow></mrow><mo symmetric="false" stretchy="false">)</mo></math></td></tr><tr><td>a \bmod b</td><td style="position: relative"><math display="block"><mi>a</mi><mspace width="0.1667em" /><mi>mod</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>b</mi></math></td></tr><tr><td>\gcd(m, n), \operatorname{lcm}(m, n)</td><td style="position: relative"><math display="block"><mi>gcd</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo symmetric="false" stretchy="false">)</mo><mo>,</mo><mi>lcm</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo symmetric="false" stretchy="false">)</mo></math></td></tr><tr><td>\mid, \nmid, \shortmid, \nshortmid</td><td style="position: relative"><math display="block"><mo>∣</mo><mo>,</mo><mo>∤</mo><mo>,</mo><mo class="small">∣</mo><mo>,</mo><mo class="small">∤</mo></math></td></tr><tr><th colspan="2">Multiline Equations</th></tr><tr><td>\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-align menv-with-eqn"><mtr><mtd><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd><mo>=</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mo symmetric="false" stretchy="false">)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></math></td></tr><tr><td>\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-with-eqn"><mtr><mtd><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd><mo>=</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>−</mo><mi>b</mi><msup><mo symmetric="false" stretchy="false">)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></math></td></tr><tr><td>\begin{align}
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\
\end{align}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-align menv-with-eqn"><mtr><mtd><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd><mo>=</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mo symmetric="false" stretchy="false">)</mo><mn>2</mn></msup></mtd><mtd></mtd><mtd><mo>=</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo symmetric="false" stretchy="false">)</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo symmetric="false" stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>a</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd><mtd></mtd><mtd><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></math></td></tr><tr><td>\begin{alignat}{3}
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\
\end{alignat}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-with-eqn"><mtr><mtd><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd><mo>=</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mo symmetric="false" stretchy="false">)</mo><mn>2</mn></msup></mtd><mtd></mtd><mtd><mo>=</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo symmetric="false" stretchy="false">)</mo><mo symmetric="false" stretchy="false">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo symmetric="false" stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>a</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd><mtd></mtd><mtd><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></math></td></tr><tr><td>\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}</td><td style="position: relative"><math display="block"><mtable class="menv-arraylike"><mtr><mtd class="cell-left"><mi>z</mi></mtd><mtd><mo>=</mo></mtd><mtd class="cell-left"><mi>a</mi></mtd></mtr><mtr><mtd class="cell-left"><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd><mo>=</mo></mtd><mtd class="cell-left"><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi></mtd></mtr></mtable></math></td></tr><tr><td>\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}</td><td style="position: relative"><math display="block"><mtable class="menv-arraylike"><mtr><mtd class="cell-left"><mi>z</mi></mtd><mtd><mo>=</mo></mtd><mtd class="cell-right"><mi>a</mi></mtd></mtr><mtr><mtd class="cell-left"><mi>f</mi><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd><mo>=</mo></mtd><mtd class="cell-right"><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi></mtd></mtr></mtable></math></td></tr><tr><td>\begin{alignat}{4}
F:\; && C(X) && \;\to\; & C(X) \\
&& g && \;\mapsto\; & g^2
\end{alignat}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-with-eqn"><mtr><mtd><mi>F</mi><mo>:</mo><mspace width="0.2777778em" /></mtd><mtd></mtd><mtd><mi>C</mi><mo symmetric="false" stretchy="false">(</mo><mi>X</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd></mtd><mtd><mspace width="0.2777778em" /><mo>→</mo><mspace width="0.2777778em" /></mtd><mtd><mi>C</mi><mo symmetric="false" stretchy="false">(</mo><mi>X</mi><mo symmetric="false" stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd><mi>g</mi></mtd><mtd></mtd><mtd><mspace width="0.2777778em" /><mo>↦</mo><mspace width="0.2777778em" /></mtd><mtd><msup><mi>g</mi><mn>2</mn></msup></mtd></mtr></mtable></math></td></tr><tr><td>\begin{alignat}{4}
F:\; && C(X) && \;\to\; && C(X) \\
&& g && \;\mapsto\; && g^2
\end{alignat}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-with-eqn"><mtr><mtd><mi>F</mi><mo>:</mo><mspace width="0.2777778em" /></mtd><mtd></mtd><mtd><mi>C</mi><mo symmetric="false" stretchy="false">(</mo><mi>X</mi><mo symmetric="false" stretchy="false">)</mo></mtd><mtd></mtd><mtd><mspace width="0.2777778em" /><mo>→</mo><mspace width="0.2777778em" /></mtd><mtd></mtd><mtd><mi>C</mi><mo symmetric="false" stretchy="false">(</mo><mi>X</mi><mo symmetric="false" stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd><mi>g</mi></mtd><mtd></mtd><mtd><mspace width="0.2777778em" /><mo>↦</mo><mspace width="0.2777778em" /></mtd><mtd></mtd><mtd><msup><mi>g</mi><mn>2</mn></msup></mtd></mtr></mtable></math></td></tr><tr><th colspan="2">Multiple Equations</th></tr><tr><td>\begin{align}
u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\[0.6ex]
v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
\end{align}</td><td style="position: relative"><math display="block"><mtable class="menv-alignlike menv-align menv-with-eqn"><mtr><mtd><mi>u</mi></mtd><mtd><mo>=</mo><mrow displaystyle="false" scriptlevel="0"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></mfrac></mrow><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mspace width="2em" /></mtd><mtd><mi>x</mi></mtd><mtd><mo>=</mo><mrow displaystyle="false" scriptlevel="0"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></mfrac></mrow><mo symmetric="false" stretchy="false">(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo symmetric="false" stretchy="false">)</mo></mtd></mtr><mtr style="height: 0.6ex"><mtd class="menv-nonumber"></mtd></mtr><mtr><mtd><mi>v</mi></mtd><mtd><mo>=</mo><mrow displaystyle="false" scriptlevel="0"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></mfrac></mrow><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mspace width="2em" /></mtd><mtd><mi>y</mi></mtd><mtd><mo>=</mo><mrow displaystyle="false" scriptlevel="0"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></mfrac></mrow><mo symmetric="false" stretchy="false">(</mo><mi>u</mi><mo>−</mo><mi>v</mi><mo symmetric="false" stretchy="false">)</mo></mtd></mtr></mtable></math></td></tr><tr><th colspan="2">No Delimiter</th></tr><tr><td>\left . \frac{A}{B} \right \} \to X</td><td style="position: relative"><math display="block"><mrow><mfrac><mrow><mi>A</mi></mrow><mrow><mi>B</mi></mrow></mfrac><mo stretchy="true">}</mo></mrow><mo>→</mo><mi>X</mi></math></td></tr><tr><th colspan="2">Operators</th></tr><tr><td>+, -, \pm, \mp, \dotplus</td><td style="position: relative"><math display="block"><mi>+</mi><mo>,</mo><mi>−</mi><mo>,</mo><mi>±</mi><mo>,</mo><mi>∓</mi><mo>,</mo><mi>∔</mi></math></td></tr><tr><td>\times, \div, \divideontimes, /, \backslash</td><td style="position: relative"><math display="block"><mi>×</mi><mo>,</mo><mi>÷</mi><mo>,</mo><mi>⋇</mi><mo>,</mo><mi>/</mi><mo>,</mo><mi>\</mi></math></td></tr><tr><td>\cdot, * \ast, \star, \circ, \bullet</td><td style="position: relative"><math display="block"><mi>â‹…</mi><mo>,</mo><mi>∗</mi><mi>*</mi><mo>,</mo><mi>⋆</mi><mo>,</mo><mi>∘</mi><mo>,</mo><mi>∙</mi></math></td></tr><tr><td>\boxplus, \boxminus, \boxtimes, \boxdot</td><td style="position: relative"><math display="block"><mi>⊞</mi><mo>,</mo><mi>⊟</mi><mo>,</mo><mi>⊠</mi><mo>,</mo><mi>⊡</mi></math></td></tr><tr><td>\oplus, \ominus, \otimes, \oslash, \odot</td><td style="position: relative"><math display="block"><mi>⊕</mi><mo>,</mo><mi>⊖</mi><mo>,</mo><mi>⊗</mi><mo>,</mo><mi>⊘</mi><mo>,</mo><mi>⊙</mi></math></td></tr><tr><td>\circleddash, \circledcirc, \circledast</td><td style="position: relative"><math display="block"><mi>âŠ</mi><mo>,</mo><mi>⊚</mi><mo>,</mo><mi>⊛</mi></math></td></tr><tr><td>\bigoplus, \bigotimes, \bigodot</td><td style="position: relative"><math display="block"><mo movablelimits="false">â¨</mo><mo>,</mo><mo movablelimits="false">⨂</mo><mo>,</mo><mo movablelimits="false">⨀</mo></math></td></tr><tr><th colspan="2">Overbraces</th></tr><tr><td>\overbrace{ 1+2+\cdots+100 }^{5050}</td><td style="position: relative"><math display="block"><mover><mover><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mi>⋯</mi><mo>+</mo><mn>100</mn></mrow><mo stretchy="true">âž</mo></mover><mrow><mn>5050</mn></mrow></mover></math></td></tr><tr><td>\underbrace{ a+b+\cdots+z }_{26}</td><td style="position: relative"><math display="block"><munder><munder><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>⋯</mi><mo>+</mo><mi>z</mi></mrow><mo stretchy="true">âŸ</mo></munder><mrow><mn>26</mn></mrow></munder></math></td></tr><tr><th colspan="2">Parentheses</th></tr><tr><td>\left ( \frac{a}{b} \right )</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">(</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">)</mo></mrow></math></td></tr><tr><th colspan="2">Preceding And Or Additional</th></tr><tr><td>{}_1^2\!\Omega_3^4</td><td style="position: relative"><math display="block"><msubsup><mrow></mrow><mn>1</mn><mn>2</mn></msubsup><mspace width="-0.16666667em" style="margin-left: -0.16666667em" /><msubsup><mi mathvariant="normal">Ω</mi><mn>3</mn><mn>4</mn></msubsup></math></td></tr><tr><th colspan="2">Prefixed Subscript</th></tr><tr><td>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
= \sum_{n=0}^\infty
\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
\frac{z^n}{n!}</td><td style="position: relative"><math display="block"><msub><mrow></mrow><mi>p</mi></msub><msub><mi>F</mi><mi>q</mi></msub><mo symmetric="false" stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><mo>,</mo><mi>…</mi><mo>,</mo><msub><mi>a</mi><mi>p</mi></msub><mo>;</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><mi>…</mi><mo>,</mo><msub><mi>c</mi><mi>q</mi></msub><mo>;</mo><mi>z</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><munderover><mo movablelimits="false">∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mi>∞</mi></munderover><mfrac><mrow><mo symmetric="false" stretchy="false">(</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mo symmetric="false" stretchy="false">)</mo><mi>n</mi></msub><mi>⋯</mi><mo symmetric="false" stretchy="false">(</mo><msub><mi>a</mi><mi>p</mi></msub><msub><mo symmetric="false" stretchy="false">)</mo><mi>n</mi></msub></mrow><mrow><mo symmetric="false" stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><msub><mo symmetric="false" stretchy="false">)</mo><mi>n</mi></msub><mi>⋯</mi><mo symmetric="false" stretchy="false">(</mo><msub><mi>c</mi><mi>q</mi></msub><msub><mo symmetric="false" stretchy="false">)</mo><mi>n</mi></msub></mrow></mfrac><mfrac><mrow><msup><mi>z</mi><mi>n</mi></msup></mrow><mrow><mi>n</mi><mi>!</mi></mrow></mfrac></math></td></tr><tr><th colspan="2">Product</th></tr><tr><td>\prod_{i=1}^N x_i</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">âˆ</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>x</mi><mi>i</mi></msub></math></td></tr><tr><td>\textstyle \prod_{i=1}^N x_i</td><td style="position: relative"><math display="block"><msubsup displaystyle="false" scriptlevel="0"><mo displaystyle="false" scriptlevel="0" movablelimits="false">âˆ</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><msub displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">x</mi><mi>i</mi></msub></math></td></tr><tr><th colspan="2">Projections</th></tr><tr><td>\Pr j, \hom l, \lVert z \rVert, \arg z</td><td style="position: relative"><math display="block"><mi>Pr</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>j</mi><mo>,</mo><mi>hom</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>l</mi><mo>,</mo><mo symmetric="false" stretchy="false">‖</mo><mi>z</mi><mo symmetric="false" stretchy="false">‖</mo><mo>,</mo><mi>arg</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>z</mi></math></td></tr><tr><th colspan="2">Quadratic Formula</th></tr><tr><td>x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}</td><td style="position: relative"><math display="block"><mi>x</mi><mo>=</mo><mfrac><mrow><mi>−</mi><mi>b</mi><mo>±</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></math></td></tr><tr><th colspan="2">Quadratic Polynomial</th></tr><tr><td>ax^2 + bx + c = 0</td><td style="position: relative"><math display="block"><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></td></tr><tr><th colspan="2">Quadruple Integral</th></tr><tr><td>\iiiint\limits_{D} dx\,dy\,dz\,dt</td><td style="position: relative"><math display="block"><munder><mo movablelimits="false">⨌</mo><mrow><mi>D</mi></mrow></munder><mi>d</mi><mi>x</mi><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi><mspace width="0.16666667em" /><mi>d</mi><mi>z</mi><mspace width="0.16666667em" /><mi>d</mi><mi>t</mi></math></td></tr><tr><th colspan="2">Radicals</th></tr><tr><td>\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}}</td><td style="position: relative"><math display="block"><msqrt><mspace width="0em" height="0.7em" /></msqrt><mo>,</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>,</mo><mroot><mrow><mn>2</mn></mrow><mi>n</mi></mroot><mo>,</mo><mroot><mrow><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mn>3</mn></mroot></math></td></tr><tr><th colspan="2">Relations</th></tr><tr><td>=, \ne, \neq, \equiv, \not\equiv</td><td style="position: relative"><math display="block"><mo>=</mo><mo>,</mo><mo>≠</mo><mo>,</mo><mo>≠</mo><mo>,</mo><mo>≡</mo><mo>,</mo><mo>≢</mo></math></td></tr><tr><td>\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=</td><td style="position: relative"><math display="block"><mo>â‰</mo><mo>,</mo><mo>≑</mo><mo>,</mo><mover><mrow><mo>=</mo></mrow><mrow><munder><mrow></mrow><mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi></mrow></mrow></munder></mrow></mover><mo>,</mo><mo>:</mo><mo>=</mo></math></td></tr><tr><td>\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong</td><td style="position: relative"><math display="block"><mo>∼</mo><mo>,</mo><mo>â‰</mo><mo>,</mo><mo>∽</mo><mo>,</mo><mo>∼</mo><mo>,</mo><mo>≃</mo><mo>,</mo><mo>â‹</mo><mo>,</mo><mo>≂</mo><mo>,</mo><mo>≅</mo><mo>,</mo><mo>≆</mo></math></td></tr><tr><td>\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto</td><td style="position: relative"><math display="block"><mo>≈</mo><mo>,</mo><mo>≈</mo><mo>,</mo><mo>≊</mo><mo>,</mo><mi>â‰</mi><mo>,</mo><mo>âˆ</mo><mo>,</mo><mo>âˆ</mo></math></td></tr><tr><td><, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot</td><td style="position: relative"><math display="block"><mo><</mo><mo>,</mo><mo>≮</mo><mo>,</mo><mo>≪</mo><mo>,</mo><mo>≪̸</mo><mo>,</mo><mo>⋘</mo><mo>,</mo><mo>⋘̸</mo><mo>,</mo><mi>â‹–</mi></math></td></tr><tr><td>>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot</td><td style="position: relative"><math display="block"><mo>></mo><mo>,</mo><mo>≯</mo><mo>,</mo><mo>≫</mo><mo>,</mo><mo>≫̸</mo><mo>,</mo><mo>â‹™</mo><mo>,</mo><mo>⋙̸</mo><mo>,</mo><mi>â‹—</mi></math></td></tr><tr><td>\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq</td><td style="position: relative"><math display="block"><mo>≤</mo><mo>,</mo><mo>≤</mo><mo>,</mo><mo>⪇</mo><mo>,</mo><mo>≦</mo><mo>,</mo><mo>≰</mo><mo>,</mo><mo>≰</mo><mo>,</mo><mo>≨</mo><mo>,</mo><mo>≨︀</mo></math></td></tr><tr><td>\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq</td><td style="position: relative"><math display="block"><mo>≥</mo><mo>,</mo><mo>≥</mo><mo>,</mo><mo>⪈</mo><mo>,</mo><mo>≧</mo><mo>,</mo><mo>≱</mo><mo>,</mo><mo>≱</mo><mo>,</mo><mo>≩</mo><mo>,</mo><mo>≩︀</mo></math></td></tr><tr><td>\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless</td><td style="position: relative"><math display="block"><mo>≶</mo><mo>,</mo><mo>â‹š</mo><mo>,</mo><mo>⪋</mo><mo>,</mo><mo>≷</mo><mo>,</mo><mo>â‹›</mo><mo>,</mo><mo>⪌</mo></math></td></tr><tr><td>\leqslant, \nleqslant, \eqslantless</td><td style="position: relative"><math display="block"><mo>⩽</mo><mo>,</mo><mo>≰</mo><mo>,</mo><mo>⪕</mo></math></td></tr><tr><td>\geqslant, \ngeqslant, \eqslantgtr</td><td style="position: relative"><math display="block"><mo>⩾</mo><mo>,</mo><mo>≱</mo><mo>,</mo><mo>⪖</mo></math></td></tr><tr><td>\lesssim, \lnsim, \lessapprox, \lnapprox</td><td style="position: relative"><math display="block"><mo>≲</mo><mo>,</mo><mo>⋦</mo><mo>,</mo><mo>⪅</mo><mo>,</mo><mo>⪉</mo></math></td></tr><tr><td>\gtrsim, \gnsim, \gtrapprox, \gnapprox</td><td style="position: relative"><math display="block"><mo>≳</mo><mo>,</mo><mo>⋧</mo><mo>,</mo><mo>⪆</mo><mo>,</mo><mo>⪊</mo></math></td></tr><tr><td>\prec, \nprec, \preceq, \npreceq, \precneqq</td><td style="position: relative"><math display="block"><mo>≺</mo><mo>,</mo><mo>⊀</mo><mo>,</mo><mo>⪯</mo><mo>,</mo><mo>â‹ </mo><mo>,</mo><mo>⪵</mo></math></td></tr><tr><td>\succ, \nsucc, \succeq, \nsucceq, \succneqq</td><td style="position: relative"><math display="block"><mo>≻</mo><mo>,</mo><mo>âŠ</mo><mo>,</mo><mo>⪰</mo><mo>,</mo><mo>â‹¡</mo><mo>,</mo><mo>⪶</mo></math></td></tr><tr><td>\preccurlyeq, \curlyeqprec</td><td style="position: relative"><math display="block"><mo>≼</mo><mo>,</mo><mo>â‹ž</mo></math></td></tr><tr><td>\succcurlyeq, \curlyeqsucc</td><td style="position: relative"><math display="block"><mo>≽</mo><mo>,</mo><mo>â‹Ÿ</mo></math></td></tr><tr><td>\precsim, \precnsim, \precapprox, \precnapprox</td><td style="position: relative"><math display="block"><mo>≾</mo><mo>,</mo><mo>⋨</mo><mo>,</mo><mo>⪷</mo><mo>,</mo><mo>⪹</mo></math></td></tr><tr><td>\succsim, \succnsim, \succapprox, \succnapprox</td><td style="position: relative"><math display="block"><mo>≿</mo><mo>,</mo><mo>â‹©</mo><mo>,</mo><mo>⪸</mo><mo>,</mo><mo>⪺</mo></math></td></tr><tr><th colspan="2">Roman Typeface</th></tr><tr><td>\mathrm{ABCDEFGHI}</td><td style="position: relative"><math display="block"><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">B</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">F</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">I</mi></mrow></math></td></tr><tr><td>\mathrm{JKLMNOPQR}</td><td style="position: relative"><math display="block"><mrow><mi mathvariant="normal">J</mi><mi mathvariant="normal">K</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">M</mi><mi mathvariant="normal">N</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">Q</mi><mi mathvariant="normal">R</mi></mrow></math></td></tr><tr><td>\mathrm{STUVWXYZ}</td><td style="position: relative"><math display="block"><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">U</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">W</mi><mi mathvariant="normal">X</mi><mi mathvariant="normal">Y</mi><mi mathvariant="normal">Z</mi></mrow></math></td></tr><tr><td>\mathrm{abcdefghijklm}</td><td style="position: relative"><math display="block"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">j</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">m</mi></mrow></math></td></tr><tr><td>\mathrm{nopqrstuvwxyz}</td><td style="position: relative"><math display="block"><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">q</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">z</mi></mrow></math></td></tr><tr><td>\mathrm{0123456789}</td><td style="position: relative"><math display="block"><mrow><mn>0123456789</mn></mrow></math></td></tr><tr><th colspan="2">Sans Serif</th></tr><tr><td>\mathsf{ABCDEFGHI}</td><td style="position: relative"><math display="block"><mrow><mi>ð– </mi><mi>ð–¡</mi><mi>ð–¢</mi><mi>ð–£</mi><mi>ð–¤</mi><mi>ð–¥</mi><mi>ð–¦</mi><mi>ð–§</mi><mi>ð–¨</mi></mrow></math></td></tr><tr><td>\mathsf{JKLMNOPQR}</td><td style="position: relative"><math display="block"><mrow><mi>ð–©</mi><mi>ð–ª</mi><mi>ð–«</mi><mi>ð–¬</mi><mi>ð–</mi><mi>ð–®</mi><mi>ð–¯</mi><mi>ð–°</mi><mi>ð–±</mi></mrow></math></td></tr><tr><td>\mathsf{STUVWXYZ}</td><td style="position: relative"><math display="block"><mrow><mi>ð–²</mi><mi>ð–³</mi><mi>ð–´</mi><mi>ð–µ</mi><mi>ð–¶</mi><mi>ð–·</mi><mi>ð–¸</mi><mi>ð–¹</mi></mrow></math></td></tr><tr><td>\mathsf{abcdefghijklm}</td><td style="position: relative"><math display="block"><mrow><mi>ð–º</mi><mi>ð–»</mi><mi>ð–¼</mi><mi>ð–½</mi><mi>ð–¾</mi><mi>ð–¿</mi><mi>ð—€</mi><mi>ð—</mi><mi>ð—‚</mi><mi>ð—ƒ</mi><mi>ð—„</mi><mi>ð—…</mi><mi>ð—†</mi></mrow></math></td></tr><tr><td>\mathsf{nopqrstuvwxyz}</td><td style="position: relative"><math display="block"><mrow><mi>ð—‡</mi><mi>ð—ˆ</mi><mi>ð—‰</mi><mi>ð—Š</mi><mi>ð—‹</mi><mi>ð—Œ</mi><mi>ð—</mi><mi>ð—Ž</mi><mi>ð—</mi><mi>ð—</mi><mi>ð—‘</mi><mi>ð—’</mi><mi>ð—“</mi></mrow></math></td></tr><tr><td>\mathsf{0123456789}</td><td style="position: relative"><math display="block"><mrow><mn>ðŸ¢ðŸ£ðŸ¤ðŸ¥ðŸ¦ðŸ§ðŸ¨ðŸ©ðŸªðŸ«</mn></mrow></math></td></tr><tr><th colspan="2">Sans Serif Greek</th></tr><tr><td>\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}</td><td style="position: relative"><math display="block"><mrow><mi>Α</mi><mi>Î’</mi><mi>Γ</mi><mi>Δ</mi><mi>Ε</mi><mi>Ζ</mi><mi>Η</mi><mi>Θ</mi></mrow></math></td></tr><tr><td>\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}</td><td style="position: relative"><math display="block"><mrow><mi>Ι</mi><mi>Κ</mi><mi>Λ</mi><mi>Îœ</mi><mi>Î</mi><mi>Ξ</mi><mi>Ο</mi><mi>Î </mi></mrow></math></td></tr><tr><td>\mathsf{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}</td><td style="position: relative"><math display="block"><mrow><mi>Ρ</mi><mi>Σ</mi><mi>Τ</mi><mi>Î¥</mi><mi>Φ</mi><mi>Χ</mi><mi>Ψ</mi><mi>Ω</mi></mrow></math></td></tr><tr><th colspan="2">Sets</th></tr><tr><td>\{ \}, \emptyset, \varnothing</td><td style="position: relative"><math display="block"><mo symmetric="false" stretchy="false">{</mo><mo symmetric="false" stretchy="false">}</mo><mo>,</mo><mi>∅</mi><mo>,</mo><mi>⌀</mi></math></td></tr><tr><td>\in, \notin \not\in, \ni, \not\ni</td><td style="position: relative"><math display="block"><mo>∈</mo><mo>,</mo><mo>∉</mo><mo>∉</mo><mo>,</mo><mo>∋</mo><mo>,</mo><mo>∌</mo></math></td></tr><tr><td>\cap, \Cap, \sqcap, \bigcap</td><td style="position: relative"><math display="block"><mi>∩</mi><mo>,</mo><mi>â‹’</mi><mo>,</mo><mi>⊓</mi><mo>,</mo><mo movablelimits="false">â‹‚</mo></math></td></tr><tr><td>\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus</td><td style="position: relative"><math display="block"><mi>∪</mi><mo>,</mo><mi>â‹“</mi><mo>,</mo><mi>⊔</mi><mo>,</mo><mo movablelimits="false">⋃</mo><mo>,</mo><mo movablelimits="false">⨆</mo><mo>,</mo><mi>⊎</mi><mo>,</mo><mo movablelimits="false">⨄</mo></math></td></tr><tr><td>\setminus, \smallsetminus, \times</td><td style="position: relative"><math display="block"><mi>∖</mi><mo>,</mo><mi>∖</mi><mo>,</mo><mi>×</mi></math></td></tr><tr><td>\subset, \Subset, \sqsubset</td><td style="position: relative"><math display="block"><mo>⊂</mo><mo>,</mo><mo>â‹</mo><mo>,</mo><mo>âŠ</mo></math></td></tr><tr><td>\supset, \Supset, \sqsupset</td><td style="position: relative"><math display="block"><mo>⊃</mo><mo>,</mo><mo>â‹‘</mo><mo>,</mo><mo>âŠ</mo></math></td></tr><tr><td>\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq</td><td style="position: relative"><math display="block"><mo>⊆</mo><mo>,</mo><mo>⊈</mo><mo>,</mo><mo>⊊</mo><mo>,</mo><mo>⊊︀</mo><mo>,</mo><mo>⊑</mo></math></td></tr><tr><td>\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq</td><td style="position: relative"><math display="block"><mo>⊇</mo><mo>,</mo><mo>⊉</mo><mo>,</mo><mo>⊋</mo><mo>,</mo><mo>⊋︀</mo><mo>,</mo><mo>⊒</mo></math></td></tr><tr><td>\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq</td><td style="position: relative"><math display="block"><mo>â«…</mo><mo>,</mo><mo>⊈</mo><mo>,</mo><mo>â«‹</mo><mo>,</mo><mo>⫋︀</mo></math></td></tr><tr><td>\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq</td><td style="position: relative"><math display="block"><mo>⫆</mo><mo>,</mo><mo>⊉</mo><mo>,</mo><mo>â«Œ</mo><mo>,</mo><mo>⫌︀</mo></math></td></tr><tr><th colspan="2">Slashes And Backslashes</th></tr><tr><td>\left / \frac{a}{b} \right \backslash</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">/</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">\</mo></mrow></math></td></tr><tr><th colspan="2">Small Script</th></tr><tr><td>{\scriptstyle\text{abcdefghijklm}}</td><td style="position: relative"><math display="block"><mrow displaystyle="false" scriptlevel="1"><mtext>abcdefghijklm</mtext></mrow></math></td></tr><tr><th colspan="2">Special</th></tr><tr><td>\amalg \P \S \% \dagger \ddagger \ldots \cdots \vdots \ddots</td><td style="position: relative"><math display="block"><mi>⨿</mi><mi>¶</mi><mi>§</mi><mi>%</mi><mi>†</mi><mi>‡</mi><mi>…</mi><mi>⋯</mi><mi>â‹®</mi><mi>⋱</mi></math></td></tr><tr><td>\smile \frown \wr \triangleleft \triangleright</td><td style="position: relative"><math display="block"><mo>⌣</mo><mo>⌢</mo><mi>≀</mi><mi>â—ƒ</mi><mi>â–¹</mi></math></td></tr><tr><td>\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp</td><td style="position: relative"><math display="block"><mi>♢</mi><mo>,</mo><mi>♡</mi><mo>,</mo><mi>♣</mi><mo>,</mo><mi>â™ </mi><mo>,</mo><mi>â„·</mi><mo>,</mo><mi>â™</mi><mo>,</mo><mi>â™®</mi><mo>,</mo><mi>♯</mi></math></td></tr><tr><th colspan="2">Stacking</th></tr><tr><td>\overset{\alpha}{\omega}</td><td style="position: relative"><math display="block"><mover><mrow><mi>ω</mi></mrow><mrow><mi>α</mi></mrow></mover></math></td></tr><tr><td>\underset{\alpha}{\omega}</td><td style="position: relative"><math display="block"><munder><mrow><mi>ω</mi></mrow><mrow><mi>α</mi></mrow></munder></math></td></tr><tr><td>\overset{\alpha}{\underset{\gamma}{\omega}}</td><td style="position: relative"><math display="block"><mover><mrow><munder><mrow><mi>ω</mi></mrow><mrow><mi>γ</mi></mrow></munder></mrow><mrow><mi>α</mi></mrow></mover></math></td></tr><tr><td>\stackrel{\alpha}{\omega}</td><td style="position: relative"><math display="block"><mover><mrow><mi>ω</mi></mrow><mrow><mi>α</mi></mrow></mover></math></td></tr><tr><th colspan="2">Standard Numerical Functions</th></tr><tr><td>\exp_a b = a^b, \exp b = e^b, 10^m</td><td style="position: relative"><math display="block"><msub><mi>exp</mi><mi>a</mi></msub><mo>â¡</mo><mspace width="0.1667em" /><mi>b</mi><mo>=</mo><msup><mi>a</mi><mi>b</mi></msup><mo>,</mo><mi>exp</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>b</mi><mo>=</mo><msup><mi>e</mi><mi>b</mi></msup><mo>,</mo><msup><mn>10</mn><mi>m</mi></msup></math></td></tr><tr><td>\ln c = \log c, \lg d = \log_{10} d</td><td style="position: relative"><math display="block"><mi>ln</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>c</mi><mo>=</mo><mi>log</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>c</mi><mo>,</mo><mi>lg</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>d</mi><mo>=</mo><msub><mi>log</mi><mrow><mn>10</mn></mrow></msub><mo>â¡</mo><mspace width="0.1667em" /><mi>d</mi></math></td></tr><tr><td>\sin a, \cos b, \tan c, \cot d, \sec f, \csc g</td><td style="position: relative"><math display="block"><mi>sin</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>a</mi><mo>,</mo><mi>cos</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>b</mi><mo>,</mo><mi>tan</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>c</mi><mo>,</mo><mi>cot</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>d</mi><mo>,</mo><mi>sec</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>f</mi><mo>,</mo><mi>csc</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>g</mi></math></td></tr><tr><td>\arcsin h, \arccos i, \arctan j</td><td style="position: relative"><math display="block"><mi>arcsin</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>h</mi><mo>,</mo><mi>arccos</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>i</mi><mo>,</mo><mi>arctan</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>j</mi></math></td></tr><tr><td>\sinh k, \cosh l, \tanh m, \coth n</td><td style="position: relative"><math display="block"><mi>sinh</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>k</mi><mo>,</mo><mi>cosh</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>l</mi><mo>,</mo><mi>tanh</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>m</mi><mo>,</mo><mi>coth</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>n</mi></math></td></tr><tr><td>\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n</td><td style="position: relative"><math display="block"><mi>sh</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>k</mi><mo>,</mo><mi>ch</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>l</mi><mo>,</mo><mi>th</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>m</mi><mo>,</mo><mi>coth</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>n</mi></math></td></tr><tr><td>\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q</td><td style="position: relative"><math display="block"><mi>argsh</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>o</mi><mo>,</mo><mi>argch</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>p</mi><mo>,</mo><mi>argth</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>q</mi></math></td></tr><tr><td>\sgn r, \left\vert s \right\vert</td><td style="position: relative"><math display="block"><mi>sgn</mi><mo>â¡</mo><mspace width="0.1667em" /><mi>r</mi><mo>,</mo><mrow><mo stretchy="true">|</mo><mi>s</mi><mo stretchy="true">|</mo></mrow></math></td></tr><tr><td>\min(x,y), \max(x,y)</td><td style="position: relative"><math display="block"><mi>min</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo><mo>,</mo><mi>max</mi><mo>â¡</mo><mo symmetric="false" stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo symmetric="false" stretchy="false">)</mo></math></td></tr><tr><th colspan="2">Subscript</th></tr><tr><td>a_2</td><td style="position: relative"><math display="block"><msub><mi>a</mi><mn>2</mn></msub></math></td></tr><tr><th colspan="2">Sum</th></tr><tr><td>\sum_{k=1}^N k^2</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msup><mi>k</mi><mn>2</mn></msup></math></td></tr><tr><td>\textstyle \sum_{k=1}^N k^2</td><td style="position: relative"><math display="block"><msubsup displaystyle="false" scriptlevel="0"><mo displaystyle="false" scriptlevel="0" movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><msup displaystyle="false" scriptlevel="0"><mi displaystyle="false" scriptlevel="0">k</mi><mn>2</mn></msup></math></td></tr><tr><th colspan="2">Sum In Fraction</th></tr><tr><td>\frac{\sum_{k=1}^N k^2}{a}</td><td style="position: relative"><math display="block"><mfrac><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msup><mi>k</mi><mn>2</mn></msup></mrow><mrow><mi>a</mi></mrow></mfrac></math></td></tr><tr><td>\frac{\displaystyle \sum_{k=1}^N k^2}{a}</td><td style="position: relative"><math display="block"><mfrac><mrow displaystyle="true" scriptlevel="0"><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msup><mi>k</mi><mn>2</mn></msup></mrow><mrow><mi>a</mi></mrow></mfrac></math></td></tr><tr><td>\frac{\sum\limits^{N}_{k=1} k^2}{a}</td><td style="position: relative"><math display="block"><mfrac><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><msup><mi>k</mi><mn>2</mn></msup></mrow><mrow><mi>a</mi></mrow></mfrac></math></td></tr><tr><th colspan="2">Summation</th></tr><tr><td>\sum_{i=0}^{n-1} i</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></munderover><mi>i</mi></math></td></tr><tr><td>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2 n}{3^m\left(m 3^n + n 3^m\right)}</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><munderover><mo movablelimits="false">∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>∞</mi></munderover><mfrac><mrow><msup><mi>m</mi><mn>2</mn></msup><mi>n</mi></mrow><mrow><msup><mn>3</mn><mi>m</mi></msup><mrow><mo stretchy="true">(</mo><mi>m</mi><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mi>n</mi><msup><mn>3</mn><mi>m</mi></msup><mo stretchy="true">)</mo></mrow></mrow></mfrac></math></td></tr><tr><th colspan="2">Super Super</th></tr><tr><td>10^{10^{8}}</td><td style="position: relative"><math display="block"><msup><mn>10</mn><mrow><msup><mn>10</mn><mrow><mn>8</mn></mrow></msup></mrow></msup></math></td></tr><tr><th colspan="2">Superscript</th></tr><tr><td>a^2, a^{x+3}</td><td style="position: relative"><math display="block"><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><msup><mi>a</mi><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></msup></math></td></tr><tr><th colspan="2">Tall Parentheses And Fractions</th></tr><tr><td>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</td><td style="position: relative"><math display="block"><mn>2</mn><mo>=</mo><mrow><mo stretchy="true">(</mo><mfrac><mrow><mrow><mo stretchy="true">(</mo><mn>3</mn><mo>−</mo><mi>x</mi><mo stretchy="true">)</mo></mrow><mo>×</mo><mn>2</mn></mrow><mrow><mn>3</mn><mo>−</mo><mi>x</mi></mrow></mfrac><mo stretchy="true">)</mo></mrow></math></td></tr><tr><td>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</td><td style="position: relative"><math display="block"><msub><mi>S</mi><mrow><mtext>new</mtext></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mtext>old</mtext></mrow></msub><mo>−</mo><mfrac><mrow><msup><mrow><mo stretchy="true">(</mo><mn>5</mn><mo>−</mo><mi>T</mi><mo stretchy="true">)</mo></mrow><mn>2</mn></msup></mrow><mrow><mn>2</mn></mrow></mfrac></math></td></tr><tr><td>\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</td><td style="position: relative"><math display="block"><msub><mi>Ï•</mi><mi>n</mi></msub><mo symmetric="false" stretchy="false">(</mo><mi>κ</mi><mo symmetric="false" stretchy="false">)</mo><mo>=</mo><mn>0.033</mn><msubsup><mi>C</mi><mi>n</mi><mn>2</mn></msubsup><msup><mi>κ</mi><mrow><mi>−</mi><mn>11</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>,</mo><mspace width="1em" /><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mi>L</mi><mn>0</mn></msub></mrow></mfrac><mo>≪</mo><mi>κ</mi><mo>≪</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mi>l</mi><mn>0</mn></msub></mrow></mfrac></math></td></tr><tr><th colspan="2">Triple Integral</th></tr><tr><td>\iiint\limits_{D} dx\,dy\,dz</td><td style="position: relative"><math display="block"><munder><mo movablelimits="false">âˆ</mo><mrow><mi>D</mi></mrow></munder><mi>d</mi><mi>x</mi><mspace width="0.16666667em" /><mi>d</mi><mi>y</mi><mspace width="0.16666667em" /><mi>d</mi><mi>z</mi></math></td></tr><tr><th colspan="2">Underline Overline Vectors</th></tr><tr><td>\hat a \ \bar b \ \vec c</td><td style="position: relative"><math display="block"><mover><mi>a</mi><mi>^</mi></mover><mtext> </mtext><mover><mi>b</mi><mi>‾</mi></mover><mtext> </mtext><mover><mi>c</mi><mi>→</mi></mover></math></td></tr><tr><td>\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}</td><td style="position: relative"><math display="block"><mover><mrow><mi>a</mi><mi>b</mi></mrow><mo stretchy="true">→</mo></mover><mtext> </mtext><mover><mrow><mi>c</mi><mi>d</mi></mrow><mo stretchy="true">â†</mo></mover><mtext> </mtext><mover><mrow><mi>d</mi><mi>e</mi><mi>f</mi></mrow><mo stretchy="true">^</mo></mover></math></td></tr><tr><td>\overline{g h i} \ \underline{j k l}</td><td style="position: relative"><math display="block"><mover><mrow><mi>g</mi><mi>h</mi><mi>i</mi></mrow><mi>‾</mi></mover><mtext> </mtext><munder><mrow><mi>j</mi><mi>k</mi><mi>l</mi></mrow><mo stretchy="true">_</mo></munder></math></td></tr><tr><th colspan="2">Unions</th></tr><tr><td>\bigcup_{i=1}^n E_i</td><td style="position: relative"><math display="block"><munderover><mo movablelimits="false">⋃</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>E</mi><mi>i</mi></msub></math></td></tr><tr><th colspan="2">Unsorted</th></tr><tr><td>\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes</td><td style="position: relative"><math display="block"><mi>╱</mi><mi>╲</mi><mo>·</mo><mi>⋉</mi><mo>â‹Š</mo><mi>â‹‹</mi><mi>â‹Œ</mi></math></td></tr><tr><td>\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq</td><td style="position: relative"><math display="block"><mo>≖</mo><mo>≗</mo><mo>≜</mo><mo>â‰</mo><mo>≎</mo><mo>≑</mo><mo>≓</mo><mo>≒</mo></math></td></tr><tr><td>\intercal \barwedge \veebar \doublebarwedge \between \pitchfork</td><td style="position: relative"><math display="block"><mi>⊺</mi><mo>⌅</mo><mi>⊻</mi><mi>â©ž</mi><mo>≬</mo><mo>â‹”</mo></math></td></tr><tr><td>\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright</td><td style="position: relative"><math display="block"><mo>⊲</mo><mo>⋪</mo><mo>⊳</mo><mo>â‹«</mo></math></td></tr><tr><td>\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq</td><td style="position: relative"><math display="block"><mo>⊴</mo><mo>⋬</mo><mo>⊵</mo><mo>â‹</mo></math></td></tr><tr><th colspan="2">Up Down Updown Arrows</th></tr><tr><td>\left \uparrow \frac{a}{b} \right \downarrow</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">↑</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">↓</mo></mrow></math></td></tr><tr><td>\left \Uparrow \frac{a}{b} \right \Downarrow</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">⇑</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">⇓</mo></mrow></math></td></tr><tr><td>\left \updownarrow \frac{a}{b} \right \Updownarrow</td><td style="position: relative"><math display="block"><mrow><mo stretchy="true">↕</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo stretchy="true">⇕</mo></mrow></math></td></tr><tr><th colspan="2">Volume Of Sphere Stand</th></tr><tr><td>V = \frac{1}{6} \pi h \left [ 3 \left ( r_1^2 + r_2^2 \right ) + h^2 \right ]</td><td style="position: relative"><math display="block"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mi>Ï€</mi><mi>h</mi><mrow><mo stretchy="true">[</mo><mn>3</mn><mrow><mo stretchy="true">(</mo><msubsup><mi>r</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>r</mi><mn>2</mn><mn>2</mn></msubsup><mo stretchy="true">)</mo></mrow><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup><mo stretchy="true">]</mo></mrow></math></td></tr></table></body>
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