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TeX sample extracted from math.SE tutorial
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<p>Licensed under <a href="https://creativecommons.org/licenses/by-sa/3.0/" rel="license">cc by-sa 3.0</a>. Original source: <a href="http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference">meta.math.stackexchange</a> (cc by-sa 3.0), with <a href="http://blog.stackoverflow.com/2009/06/attribution-required/" rel="license">attribution required</a>.</p>
<div>\(\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\)</div>
<div>\[\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\]</div>
<div>\(\alpha, \beta, … \omega\)</div>
<div>\(\Gamma, \Delta, …, \Omega\)</div>
<div>\(x_i^2\)</div>
<div>\(\log_2 x\)</div>
<div>\(10^10\)</div>
<div>\(10^{10}\)</div>
<div>\({x^y}^z\)</div>
<div>\(x^{y^z}\)</div>
<div>\(x_i^2\)</div>
<div>\(x_{i^2}\)</div>
<div>\((2+3)[4+4]\)</div>
<div>\(\{\}\)</div>
<div>\((\frac{\sqrt x}{y^3})\)</div>
<div>\(\left(\frac{\sqrt x}{y^3}\right)\)</div>
<div>\((x)\)</div>
<div>\([x]\)</div>
<div>\(\{ x \}\)</div>
<div>\(|x|\)</div>
<div>\(\vert x \vert\)</div>
<div>\(\Vert x \Vert\)</div>
<div>\(\langle x \rangle\)</div>
<div>\(\lceil x \rceil\)</div>
<div>\(\lfloor x \rfloor\)</div>
<div>\(\left.\frac12\right\rbrace\)</div>
<div>\(\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)\)</div>
<div>\(\sum_1^n\)</div>
<div>\(\sum_{i=0}^\infty i^2\)</div>
<div>\(\prod\)</div>
<div>\(\int\)</div>
<div>\(\bigcup\)</div>
<div>\(\bigcap\)</div>
<div>\(\iint\)</div>
<div>\(\iiint\)</div>
<div>\(\frac ab\)</div>
<div>\(\frac{a+1}{b+1}\)</div>
<div>\({a+1\over b+1}\)</div>
<div>\(\cfrac{a}{b}\)</div>
<div>\(\mathbb{CHNQRZ}\)</div>
<div>\(\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathbf{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathtt{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathrm{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathsf{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\sqrt{x^3}\)</div>
<div>\(\sqrt[3]{\frac xy}\)</div>
<div>\(\sin x\)</div>
<div>\(sin x\)</div>
<div>\[\lim_{x\to 0}\]</div>
<div>\(\lt\, \gt\, \le\, \leq\, \leqq\, \leqslant\, \ge\, \geq\, \geqq\, \geqslant\, \neq\)</div>
<div>\(\not\lt\)</div>
<div>\(\times\, \div\, \pm\, \mp\)</div>
<div>\(x\cdot y\)</div>
<div>\(\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing\)</div>
<div>\({n+1 \choose 2k}\)</div>
<div>\(\to\, \rightarrow\, \leftarrow\, \Rightarrow\, \Leftarrow\, \mapsto\)</div>
<div>\(\land\, \lor\, \lnot\, \forall\, \exists\, \top\, \bot\, \vdash\, \vDash\)</div>
<div>\(\star\, \ast\, \oplus\, \circ\, \bullet\)</div>
<div>\(\approx\, \sim \, \simeq\, \cong\, \equiv\, \prec, \lhd\)</div>
<div>\(\infty\, \aleph_0\)</div>
<div>\(\nabla\, \partial\)</div>
<div>\(\Im\, \Re\)</div>
<div>\(a\equiv b\pmod n\)</div>
<div>\(a_1, a_2, \ldots ,a_n\)</div>
<div>\(a_1+a_2+\cdots+a_n\)</div>
<div>\(\epsilon\, \varepsilon\)</div>
<div>\(\phi\, \varphi\)</div>
<div>\(\ell\)</div>
<div>\(\TeX\)</div>
<div>\(\LaTeX\)</div>
<div>\(\TeX\)</div>
<div>\(a b\)</div>
<div>\(a\,b\)</div>
<div>\(a\;b\)</div>
<div>\(a\quad b\)</div>
<div>\(a\qquad b\)</div>
<div>\(\{x\in s\mid x\text{ is extra large}\}\)</div>
<div>\(\hat x\)</div>
<div>\(\widehat{xy}\)</div>
<div>\(\bar x\)</div>
<div>\(\overline{xyz}\)</div>
<div>\(\vec x\)</div>
<div>\(\overrightarrow{xy}\)</div>
<div>\(\overleftrightarrow{xy}\)</div>
<div>\(\frac d{dx}x\dot x = \dot x^2 + x\ddot x\)</div>
<div>\(\$\)</div>
<div>\(\{\)</div>
<div>\(\_\)</div>
<div>\(\backslash\)</div>
<div>\(\LaTeX\)</div>
<div>\(\mathrm{B}\)</div>
<div>\(\sin\)</div>
<div>\(\operatorname{Spec} A\)</div>
<div>\(_5C_3\)</div>
<div>\(\TeX\)</div>
<div>\(\TeX\)</div>
<div>\(\LaTeX\)</div>
<div>\(\mathrm{d}x\)</div>
<div>\[
\begin{matrix}
1 &amp; x &amp; x^2 \\
1 &amp; y &amp; y^2 \\
1 &amp; z &amp; z^2 \\
\end{matrix}
\]
</div>
<div>\(\begin{pmatrix}1&amp;2\\3&amp;4\\ \end{pmatrix}\)</div>
<div>\(\begin{bmatrix}1&amp;2\\3&amp;4\\ \end{bmatrix}\)</div>
<div>\(\begin{Bmatrix}1&amp;2\\3&amp;4\\ \end{Bmatrix}\)</div>
<div>\(\begin{vmatrix}1&amp;2\\3&amp;4\\ \end{vmatrix}\)</div>
<div>\(\begin{Vmatrix}1&amp;2\\3&amp;4\\ \end{Vmatrix}\)</div>
<div>\(\cdots\)</div>
<div>\(\ddots\)</div>
<div>\(\vdots\)</div>
<div>\begin{pmatrix}
1 &amp; a_1 &amp; a_1^2 &amp; \cdots &amp; a_1^n \\
1 &amp; a_2 &amp; a_2^2 &amp; \cdots &amp; a_2^n \\
\vdots &amp; \vdots&amp; \vdots &amp; \ddots &amp; \vdots \\
1 &amp; a_m &amp; a_m^2 &amp; \cdots &amp; a_m^n
\end{pmatrix}</div>
<div>\[
\left[\begin{array}{cc|c}
1&amp;2&amp;3\\
4&amp;5&amp;6
\end{array}\right]
\]
</div>
<div>\[
\begin{pmatrix}
a &amp; b \\
c &amp; d\\
\hline
1 &amp; 0\\
0 &amp; 1
\end{pmatrix}
\]
</div>
<div>\(\bigl( \begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix} \bigr)\)</div>
<div>\begin{align}
\sqrt{37} &amp; = \sqrt{\frac{73^2-1}{12^2}} \\
&amp; = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
&amp; = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
&amp; = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
&amp; \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}</div>
<div>\[
\begin{align} f(x)&amp;=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\ f'(x)&amp;=\left(\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\right)\\ f''(x)&amp;=\left(6x+2\right)\\ \end{align}
\]</div>
<div>\({}{}{}{}{}{}{}{}\)</div>
<div>\(\Psi\)</div>
<div>\(\delta\)</div>
<div>\(\zeta\)</div>
<div>\(\ge\)</div>
<div>\(\subseteq\)</div>
<div>\(\LaTeX\)</div>
<div>\(\LaTeX\)</div>
<div>f(n) =
\begin{cases}
n/2, &amp; \text{if $n$ is even} \\
3n+1, &amp; \text{if $n$ is odd}
\end{cases}</div>
<div>\[
\left.
\begin{array}{l}
\text{if $n$ is even:}&amp;n/2\\
\text{if $n$ is odd:}&amp;3n+1
\end{array}
\right\}
=f(n)
\]
</div>
<div>f(n) =
\begin{cases}
\frac{n}{2}, &amp; \text{if $n$ is even} \\[2ex]
3n+1, &amp; \text{if $n$ is odd}
\end{cases}</div>
<div>\begin{array}{c|lcr}
n &amp; \text{Left} &amp; \text{Center} &amp; \text{Right} \\
\hline
1 &amp; 0.24 &amp; 1 &amp; 125 \\
2 &amp; -1 &amp; 189 &amp; -8 \\
3 &amp; -20 &amp; 2000 &amp; 1+10i
\end{array}
</div>
<div>\[
% outer vertical array of arrays
\begin{array}{c}
% inner horizontal array of arrays
\begin{array}{cc}
% inner array of minimum values
\begin{array}{c|cccc}
\text{min} &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
\hline
0 &amp; 0 &amp; 0 &amp; 0 &amp; 0\\
1 &amp; 0 &amp; 1 &amp; 1 &amp; 1\\
2 &amp; 0 &amp; 1 &amp; 2 &amp; 2\\
3 &amp; 0 &amp; 1 &amp; 2 &amp; 3
\end{array}
&amp;
% inner array of maximum values
\begin{array}{c|cccc}
\text{max}&amp;0&amp;1&amp;2&amp;3\\
\hline
0 &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
1 &amp; 1 &amp; 1 &amp; 2 &amp; 3\\
2 &amp; 2 &amp; 2 &amp; 2 &amp; 3\\
3 &amp; 3 &amp; 3 &amp; 3 &amp; 3
\end{array}
\end{array}
\\
% inner array of delta values
\begin{array}{c|cccc}
\Delta&amp;0&amp;1&amp;2&amp;3\\
\hline
0 &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
1 &amp; 1 &amp; 0 &amp; 1 &amp; 2\\
2 &amp; 2 &amp; 1 &amp; 0 &amp; 1\\
3 &amp; 3 &amp; 2 &amp; 1 &amp; 0
\end{array}
\end{array}
\]
</div>
<div>\(\mathsf{Show\ Math\ As\ }\blacktriangleright\mathsf{\ TeX\ Commands}\)</div>
<div>\(all italics, weird-looking spacing, an' odd apostrophes\)</div>
<div>\(\LaTeX\)</div>
<div>\[
\begin{array}{ll} \hfill\mathrm{Bad}\hfill &amp; \hfill\mathrm{Better}\hfill \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}&amp; e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx &amp; \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}
\]</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}&amp; e^{i\pi/2} \\
\int_{-\frac\pi2}^\frac\pi2 \sin x\,dx &amp; \int_{-\pi/2}^{\pi/2}\sin x\,dx \\
\end{array}</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\{x|x^2\in\Bbb Z\} &amp; \{x\mid x^2\in\Bbb Z\} \\
\end{array}</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\int\int_S f(x)\,dy\,dx &amp; \iint_S f(x)\,dy\,dx \\
\int\int\int_V f(x)\,dz\,dy\,dx &amp; \iiint_V f(x)\,dz\,dy\,dx
\end{array}</div>
<div>\(\TeX\)</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\iiint_V f(x)dz dy dx &amp; \iiint_V f(x)\,dz\,dy\,dx
\end{array}</div>
<div>\(\left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}\)</div>
<div>\[
\require{cancel}\begin{array}{rl}
\verb|y+\cancel{x}| &amp; y+\cancel{x}\\
\verb|\cancel{y+x}| &amp; \cancel{y+x}\\
\verb|y+\bcancel{x}| &amp; y+\bcancel{x}\\
\verb|y+\xcancel{x}| &amp; y+\xcancel{x}\\
\verb|y+\cancelto{0}{x}| &amp; y+\cancelto{0}{x}\\
\verb+\frac{1\cancel9}{\cancel95} = \frac15+&amp; \frac{1\cancel9}{\cancel95} = \frac15 \\
\end{array}
\]
</div>
<div>\[
\require{enclose}\begin{array}{rl}
\verb|\enclose{horizontalstrike}{x+y}| &amp; \enclose{horizontalstrike}{x+y}\\
\verb|\enclose{verticalstrike}{\frac xy}| &amp; \enclose{verticalstrike}{\frac xy}\\
\verb|\enclose{updiagonalstrike}{x+y}| &amp; \enclose{updiagonalstrike}{x+y}\\
\verb|\enclose{downdiagonalstrike}{x+y}| &amp; \enclose{downdiagonalstrike}{x+y}\\
\verb|\enclose{horizontalstrike,updiagonalstrike}{x+y}| &amp; \enclose{horizontalstrike,updiagonalstrike}{x+y}\\
\end{array}
\]
</div>
<div>\(19/95 = 1/5\)</div>
<div>\(\cancelto{\cancelto{\cancelto{x^{2+x}}{\cancelto{x^2}{x}+4}}4}0\)</div>
<div>\(\LaTeX\)</div>
<div>
\[
\left\{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{array}
\right.
\]
</div>
<div>
\[
\begin{cases}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{cases}
\]
</div>
<div>\[\left\{\begin{aligned} a_1x+b_1y+c_1z&amp;=d_1+e_1 \\
a_2x+b_2y&amp;=d_2 \\
a_3x+b_3y+c_3z&amp;=d_3 \end{aligned} \right. \]</div>
<div>\[
\left\{\begin{array}{ll}a_1x+b_1y+c_1z &amp;=d_1+e_1 \\ a_2x+b_2y &amp;=d_2 \\ a_3x+b_3y+c_3z &amp;=d_3 \end{array} \right.
\]</div>
<div>
\[\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex]
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex]
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
\]
</div>
<div>
\[
\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
\]
</div>
<div>\[
\left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.
\]
</div>
<div>\(\longrightarrow\)</div>
<div>
\[
\begin{array}{|rc|}
\hline
\verb+\color{black}{text}+ &amp; \color{black}{text} \\
\verb+\color{gray}{text}+ &amp; \color{gray}{text} \\
\verb+\color{silver}{text}+ &amp; \color{silver}{text} \\
\verb+\color{white}{text}+ &amp; \color{white}{text} \\
\hline
\verb+\color{maroon}{text}+ &amp; \color{maroon}{text} \\
\verb+\color{red}{text}+ &amp; \color{red}{text} \\
\verb+\color{yellow}{text}+ &amp; \color{yellow}{text} \\
\verb+\color{lime}{text}+ &amp; \color{lime}{text} \\
\verb+\color{olive}{text}+ &amp; \color{olive}{text} \\
\verb+\color{green}{text}+ &amp; \color{green}{text} \\
\verb+\color{teal}{text}+ &amp; \color{teal}{text} \\
\verb+\color{aqua}{text}+ &amp; \color{aqua}{text} \\
\verb+\color{blue}{text}+ &amp; \color{blue}{text} \\
\verb+\color{navy}{text}+ &amp; \color{navy}{text} \\
\verb+\color{purple}{text}+ &amp; \color{purple}{text} \\
\verb+\color{fuchsia}{text}+ &amp; \color{magenta}{text} \\
\hline
\end{array}
\]</div>
<div>\(r, g, b\)</div>
<div>\(0–15\)</div>
<div>
\[
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ &amp; \color{#000}{text} &amp; &amp; &amp;
\verb+#00F+ &amp; \color{#00F}{text} &amp; &amp; \\
&amp; &amp; \verb+#0F0+ &amp; \color{#0F0}{text} &amp;
&amp; &amp; \verb+#0FF+ &amp; \color{#0FF}{text}\\
\verb+#F00+ &amp; \color{#F00}{text} &amp; &amp; &amp;
\verb+#F0F+ &amp; \color{#F0F}{text} &amp; &amp; \\
&amp; &amp; \verb+#FF0+ &amp; \color{#FF0}{text} &amp;
&amp; &amp; \verb+#FFF+ &amp; \color{#FFF}{text}\\
\hline
\end{array}
\]
</div>
<div>\begin{array}{|rrrrrrrr|}
\hline
\verb+#000+ &amp; \color{#000}{text} &amp; \verb+#005+ &amp; \color{#005}{text} &amp; \verb+#00A+ &amp; \color{#00A}{text} &amp; \verb+#00F+ &amp; \color{#00F}{text} \\
\verb+#500+ &amp; \color{#500}{text} &amp; \verb+#505+ &amp; \color{#505}{text} &amp; \verb+#50A+ &amp; \color{#50A}{text} &amp; \verb+#50F+ &amp; \color{#50F}{text} \\
\verb+#A00+ &amp; \color{#A00}{text} &amp; \verb+#A05+ &amp; \color{#A05}{text} &amp; \verb+#A0A+ &amp; \color{#A0A}{text} &amp; \verb+#A0F+ &amp; \color{#A0F}{text} \\
\verb+#F00+ &amp; \color{#F00}{text} &amp; \verb+#F05+ &amp; \color{#F05}{text} &amp; \verb+#F0A+ &amp; \color{#F0A}{text} &amp; \verb+#F0F+ &amp; \color{#F0F}{text} \\
\hline
\verb+#080+ &amp; \color{#080}{text} &amp; \verb+#085+ &amp; \color{#085}{text} &amp; \verb+#08A+ &amp; \color{#08A}{text} &amp; \verb+#08F+ &amp; \color{#08F}{text} \\
\verb+#580+ &amp; \color{#580}{text} &amp; \verb+#585+ &amp; \color{#585}{text} &amp; \verb+#58A+ &amp; \color{#58A}{text} &amp; \verb+#58F+ &amp; \color{#58F}{text} \\
\verb+#A80+ &amp; \color{#A80}{text} &amp; \verb+#A85+ &amp; \color{#A85}{text} &amp; \verb+#A8A+ &amp; \color{#A8A}{text} &amp; \verb+#A8F+ &amp; \color{#A8F}{text} \\
\verb+#F80+ &amp; \color{#F80}{text} &amp; \verb+#F85+ &amp; \color{#F85}{text} &amp; \verb+#F8A+ &amp; \color{#F8A}{text} &amp; \verb+#F8F+ &amp; \color{#F8F}{text} \\
\hline
\verb+#0F0+ &amp; \color{#0F0}{text} &amp; \verb+#0F5+ &amp; \color{#0F5}{text} &amp; \verb+#0FA+ &amp; \color{#0FA}{text} &amp; \verb+#0FF+ &amp; \color{#0FF}{text} \\
\verb+#5F0+ &amp; \color{#5F0}{text} &amp; \verb+#5F5+ &amp; \color{#5F5}{text} &amp; \verb+#5FA+ &amp; \color{#5FA}{text} &amp; \verb+#5FF+ &amp; \color{#5FF}{text} \\
\verb+#AF0+ &amp; \color{#AF0}{text} &amp; \verb+#AF5+ &amp; \color{#AF5}{text} &amp; \verb+#AFA+ &amp; \color{#AFA}{text} &amp; \verb+#AFF+ &amp; \color{#AFF}{text} \\
\verb+#FF0+ &amp; \color{#FF0}{text} &amp; \verb+#FF5+ &amp; \color{#FF5}{text} &amp; \verb+#FFA+ &amp; \color{#FFA}{text} &amp; \verb+#FFF+ &amp; \color{#FFF}{text} \\
\hline
\end{array}</div>
<div>\(\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}\)</div>
<div>\(\demo\overline A\)</div>
<div>\(\demo\underline B\)</div>
<div>\(\demo\widetilde C\)</div>
<div>\(\demo\widehat D\)</div>
<div>\(\demo\fbox {$E$}\)</div>
<div>\(\demo\underleftarrow{F}\qquad\)</div>
<div>\(\xleftarrow{abc}\)</div>
<div>\(\demo\underrightarrow{G}\qquad\)</div>
<div>\(\xrightarrow{abc}\)</div>
<div>\(\demo\underleftrightarrow{H}\)</div>
<div>\(\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}\)</div>
<div>\((n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)\)</div>
<div>\[\underbrace{a\cdot a\cdots a}_{b\text{ times}}\]</div>
<div>\(\varliminf\)</div>
<div>\(\varlimsup\)</div>
<div>\(\check{I}\)</div>
<div>\(\acute{J}\)</div>
<div>\(\grave{K}\)</div>
<div>\(\vec u\ \vec{AB}\)</div>
<div>\(\bar z\)</div>
<div>\(\hat x\)</div>
<div>\(\tilde x\)</div>
<div>\(\dot x,\ddot x,\dddot x\)</div>
<div>\(\mathring A\)</div>
<div>\(\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}\)</div>
<div> \[
x = a_0 + \cfrac{1^2}{a_1
+ \cfrac{2^2}{a_2
+ \cfrac{3^2}{a_3 + \cfrac{4^4}{a_4 + \cdots}}}}
\]
</div>
<div> \[
x = a_0 + \frac{1^2}{a_1
+ \frac{2^2}{a_2
+ \frac{3^2}{a_3 + \frac{4^4}{a_4 + \cdots}}}}
\]
</div>
<div> \[
x = a_0 + \frac{1^2}{a_1+}
\frac{2^2}{a_2+}
\frac{3^2}{a_3 +} \frac{4^4}{a_4 +} \cdots
\]
</div>
<div>\([a_0; a_1, a_2, a_3, \ldots]\)</div>
<div>\[ \cfrac{a_{1}}{b_{1}+\cfrac{a_{2}}{b_{2}+\cfrac{a_{3}}{b_{3}+\ddots }}}= {\genfrac{}{}{}{}{a_1}{b_1}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_2}{b_2}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_3}{b_3}} {\genfrac{}{}{0pt}{}{}{+\dots}} \]</div>
<div>\(\LaTeX\)</div>
<div>\[\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}.\]</div>
<div>\[\mathop{\LARGE\mathrm K}_{i=1}^\infty \frac{a_i}{b_i}\]</div>
<div>
\[
\require{AMScd}
\begin{CD}
A @&gt;a&gt;&gt; B\\
@V b V V= @VV c V\\
C @&gt;&gt;d&gt; D
\end{CD}
\]
</div>
<div>
\[
\begin{CD}
A @&gt;&gt;&gt; B @&gt;{\text{very long label}}&gt;&gt; C \\
@. @AAA @| \\
D @= E @&lt;&lt;&lt; F
\end{CD}
\]
</div>
<div>
\[
\require{AMScd}
\begin{CD}
RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}&gt;&gt; (RCOR')+NaCl+SO_2+ H_2O
\end{CD}
\]
</div>
<div>\( \newcommand{\SES}[3]{ 0 \to #1 \to #2 \to #3 \to 0 }\)</div>
<div>\[ \SES{A}{B}{C} \]</div>
<div>\(\implies\)</div>
<div>\(\Rightarrow\)</div>
<div>\(\iff\)</div>
<div>\(\impliedby\)</div>
<div>\(\to\)</div>
<div>\(f\colon A \to B\)</div>
<div>\(\gets\)</div>
<div>\(T:\mathbb R\to \mathbb R,\; x\mapsto x+1\)</div>
<div>\(p\land((q\lor r)\to s)\)</div>
<div>\[x+2=4-x\implies x=1.\]</div>
<div>\[ a := x^2-y^3 \tag{*}\label{*} \]</div>
<div>\[ a+y^3 \stackrel{\eqref{*}}= x^2 \]</div>
<div>\(\eqref{*}\)</div>
<div>\(\ref{*}\)</div>
<div>\(\eqref{*}\)</div>
<div>\[(1)\qquad\qquad\sum\limits_{j}k\tag*{}\]</div>
<div>\((1)\)</div>
<div>
\[
f\left(\left[ \frac{1+\left\{x,y\right\}}{\left(\frac{x}{y}+\frac{y}{x}\right)\left(u+1\right)}+a\right]^{3/2}\right).
\]
</div>
<div>
\[
\begin{aligned}
a=&amp;\left(1+2+3+ \cdots \right. \\
&amp; \cdots+ \left. \infty-2+\infty-1+\infty\right).
\end{aligned}
\]
</div>
<div>
\[
\left\langle q\middle\|\frac{\frac{x}{y}}{\frac{u}{v}} \middle| p \right\rangle.
\]
</div>
<div>\(\Big(\dots\Big)\)</div>
<div>\[\operatorname{arsinh}(x)\]</div>
<div>\(arsinh(x)\)</div>
<div>
\[
\operatorname*{Res}_{z=1}\left(\frac1{z^2-z}\right)=1
\]
</div>
<div>\(\verb*{\rm ...}*\)</div>
<div>\(\verb*{\rm arsinh}*\)</div>
<div>\({\rm arsinh}\)</div>
<div>\(\operatorname{arsinh}x\)</div>
<div>\({\rm arsinh}x\)</div>
<div>\({\tt operatorname}\)</div>
<div>\(\text{arsinh }x\)</div>
<div>\(\operatorname{arsinh}x\)</div>
<div>\(\lim \limits_{x \to 1} \frac{x^2-1}{x-1}\)</div>
<div>\(\lim\)</div>
<div>\(lim\)</div>
<div>\(\lim \limits_{x \to 1}\)</div>
<div>\(\to\)</div>
<div>\(x \to 1\)</div>
<div>\(\lim\)</div>
<div>\(x \to 1\)</div>
<div>\(\lim \limits_{x \to 1} \frac{x^2-1}{x-1}\)</div>
<div>\[\lim_{x\to 1}?\]</div>
<div>\[\mathop{+}\limits_{i=1}^k\text{ instead of }+_{i=1}^k\]</div>
<div>\(\lim\limits_{x\to 1}\)</div>
<div>\(\lim_{x\to 1}\)</div>
<div>\(\lim_{x\to 1}\)</div>
<div>\(\lim\limits_{x\to 1}\)</div>
<div>\(x\to 1\)</div>
<div>\(\lim \limits_{x \to 1}\)</div>
<div>\(\lim\limits_{x\mapsto 1}\dfrac1x\)</div>
<div>\(\TeX\)</div>
<div>\(\lim_{x\mapsto 1}\frac1x\)</div>
<div>\(\TeX\)</div>
<div>\(\lvert x\rvert\)</div>
<div>\(\lVert v\rVert\)</div>
<div>\[|x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert\]</div>
<div>\(\|x\|\)</div>
<div>\(\lVert x \rVert\)</div>
<div>
\[
\bbox[yellow]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
\]
</div>
<div>
\[
\bbox[yellow,5px]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
\]
</div>
<div>
\[
\bbox[5px,border:2px solid red]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (2)
}
\]
</div>
<div>
\[
\bbox[yellow,5px,border:2px solid red]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
\]
</div>
<div>\begin{align}
v + w &amp; = 0 &amp;&amp;\text{Given} \tag 1\\
-w &amp; = -w + 0 &amp;&amp; \text{additive identity} \tag 2\\
-w + 0 &amp; = -w + (v + w) &amp;&amp; \text{equations $(1)$ and $(2)$}
\end{align}</div>
<div>\[\spadesuit\quad\heartsuit\quad\diamondsuit\quad\clubsuit\]</div>
<div>\[\color{red}{\heartsuit}\quad\color{red}{\diamondsuit}\]</div>
<div>\[♠\quad♡\quad♢\quad♣\\
♤\quad♥\quad♦\quad♧\]
</div>
<div>\(\Rightarrow\)</div>
<div>\(\Leftarrow\)</div>
<div>\(\Leftrightarrow\)</div>
<div>\(\implies\)</div>
<div>\(\impliedby\)</div>
<div>\(\iff\)</div>
<div>
\[
\require{enclose}
\begin{array}{r}
13 \\[-3pt]
4 \enclose{longdiv}{52} \\[-3pt]
\underline{4}\phantom{2} \\[-3pt]
12 \\[-3pt]
\underline{12}
\end{array}
\]
</div>
<div>\[x^3−6x^2+11x−6=(x−{\color{red}1})(x^2−5x+6)+{\color{blue}0}\]</div>
<div>\[\begin{array}{c|rrrr}&amp; x^3 &amp; x^2 &amp; x^1 &amp; x^0\\ &amp; 1 &amp; -6 &amp; 11 &amp; -6\\ {\color{red}1} &amp; \downarrow &amp; 1 &amp; -5 &amp; 6\\ \hline &amp; 1 &amp; -5 &amp; 6 &amp; |\phantom{-} {\color{blue}0} \end{array}\]</div>
<div>\(90°\)</div>
<div>\(90^\circ\)</div>
<div>\[\sum_{n=1}^\infty \frac{1}{n^2} \to
\textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to
\displaystyle \sum_{n=1}^\infty \frac{1}{n^2}\]</div>
<div>\(\displaystyle \lim_{t \to 0} \int_t^1 f(t)\, dt\)</div>
<div>\(\lim_{t \to 0} \int_t^1 f(t)\, dt\)</div>
<div>\(\overline a+\overline b=\overline {a\cdot b}\)</div>
<div>\(\sqrt{a}-\sqrt{b}\)</div>
<div>\(\sqrt{\mathstrut a} - \sqrt{\mathstrut b}\)</div>
<div>\(\sqrt{\vphantom{b} a} - \sqrt{b}\)</div>
<div>\(\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}\)</div>
<div>\(\smash{\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}}\)</div>
<div>\(n\)</div>
<div>\(T_1,\ldots,T_n\)</div>
<div>\(T_1\gets 1\)</div>
<div>\(k\)</div>
<div>\(2\)</div>
<div>\(n\)</div>
<div>\(T_k\gets (k−1)T_{k−1}\)</div>
<div>\(k\)</div>
<div>\(2\)</div>
<div>\(n\)</div>
<div>\(j\)</div>
<div>\(k\)</div>
<div>\(n\)</div>
<div>\(T_j\gets (j −k)T_{j−1} + (j −k+2)T_j\)</div>
<div>\(\;T_1,T_2,\ldots,T_n\)</div>
<div>\(n\)</div>
<div>\(T_1,\ldots,T_n\)</div>
<div>\(T_1\gets 1\)</div>
<div>\(\;k\;\)</div>
<div>\(2\;\)</div>
<div>\(\;n\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(T_k\gets (k−1)T_{k−1}\)</div>
<div>\(\;k\;\)</div>
<div>\(2\;\)</div>
<div>\(\;n\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(\;j\;\)</div>
<div>\(\;k\;\)</div>
<div>\(\;n\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(T_j\gets (j −k)T_{j−1} + (j −k+2)T_j\)</div>
<div>\(\;T_1,T_2,\ldots,T_n\)</div>
<div>\(\LaTeX\)</div>
<div>\[e=mc^2 \tag{1}\label{eq1}\]</div>
<div>\(\eqref{eq1}\)</div>
<div>\(\eqref{eq1}\)</div>
<div>
\[
\begin{equation}\begin{aligned}
a &amp;= b + c \\
&amp;= d + e + f + g \\
&amp;= h + i
\end{aligned}\end{equation}\tag{2}\label{eq2}
\]
</div>
<div>\(\eqref{eq2}\)</div>
<div>\(\eqref{eq2}\)</div>
<div>\begin{align}
a &amp;= b + c \tag{3}\label{eq3} \\
x &amp;= yz \tag{4}\label{eq4}\\
l &amp;= m - n \tag{5}\label{eq5}
\end{align}</div>
<div>\(\eqref{eq3}\)</div>
<div>\(\eqref{eq4}\)</div>
<div>\(\eqref{eq5}\)</div>
<div>\begin{array}{ll}
\text{maximize} &amp; c^T x \\
\text{subject to}&amp; d^T x = \alpha \\
&amp;0 \le x \le 1.
\end{array}</div>
<div>\begin{alignat}{5}
\max \quad &amp; z = &amp; x_1 &amp; + &amp; 12 x_2 &amp; &amp; &amp; &amp;&amp; \\
\mbox{s.t.} \quad &amp; &amp; 13 x_1 &amp; + &amp; x_2 &amp; + &amp; 12x_3 &amp; \geq 5 &amp;&amp; \tag{constraint 1} \\
&amp; &amp; x_1 &amp; &amp; &amp; + &amp; x_3 &amp; \leq 16 &amp;&amp; \tag{constraint 2} \\
&amp; &amp; 15 x_1 &amp; + &amp; 201 x_2 &amp; &amp; &amp; = 14 &amp;&amp; \tag{constraint 3} \\
&amp; &amp; \rlap{x_i \ge 0, i = 1, 2, 3}
\end{alignat}</div>
<div>\(\max\)</div>
<div>\(z\)</div>
<div>\(\pm\)</div>
<div>\(\rm\LaTeX\)</div>
<div>\(\rm\LaTeX\)</div>
<div>
\[
\begin{bmatrix}
1 &amp; 2 &amp; 2 \\
2 &amp; 3 &amp; 4 \\
4 &amp; 4 &amp; 2
\end{bmatrix}.
\]
</div>
<div>\(z\)</div>
<div>\(z\)</div>
<div>\begin{array}{rrrrrr|r}
&amp; x_1 &amp; x_2 &amp; s_1 &amp; s_2 &amp; s_3 &amp; \\ \hline
s_1 &amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 8 \\
s_2 &amp; 1 &amp; -1 &amp; 0 &amp; 1 &amp; 0 &amp; 4 \\
s_3 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 12 \\ \hline
&amp; -1 &amp; -1 &amp; 0 &amp; 0 &amp; 0 &amp; 0
\end{array}</div>
<div>\begin{array}{rrrrrrr|rr}
&amp; x_1 &amp; x_2 &amp; s_1 &amp; s_2 &amp; s_3 &amp; w &amp; &amp; \text{ratio} \\ \hline
s_1 &amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 8 &amp; - \\
w &amp; 1^* &amp; -1 &amp; 0 &amp; -1 &amp; 0 &amp; 1 &amp; 4 &amp; 4 \\
s_3 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 12 &amp; 12 \\ \hdashline
&amp; 1 &amp; -1 &amp; 0 &amp; -1 &amp; 0 &amp; 0 &amp; 4 &amp; \\ \hline
s_1 &amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 8 &amp; \\
x_1 &amp; 1 &amp; -1 &amp; 0 &amp; -1 &amp; 0 &amp; 1 &amp; 4 &amp; \\
s_3 &amp; 0 &amp; 2 &amp; 0 &amp; 2 &amp; 1 &amp; -1 &amp; 8 &amp; \\ \hdashline
&amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -1 &amp; 0 &amp;
\end{array}</div>
<div>\begin{array}{rrrrrrrr|r}
&amp; x_1 &amp; x_2 &amp; x_3 &amp; x_4 &amp; x_5 &amp; x_6 &amp; x_7 &amp; \\ \hline
x_4 &amp; 0 &amp; -3 &amp; 7 &amp; 1 &amp; 0 &amp; 0 &amp; 2 &amp; 2M -4 \\
x_5 &amp; 0 &amp; -9 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; -1 &amp; -M -3 \\
x_6 &amp; 0 &amp; 6 &amp; -1 &amp; 0 &amp; 0 &amp; 1 &amp; -4^* &amp; -4M +8 \\
x_1 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; M \\ \hline
&amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 2 &amp; 2M \\
\text{ratio} &amp; &amp; &amp; 1 &amp; &amp; &amp; &amp; 1/2 &amp;
\end{array}</div>
<div>\begin{array}{rrrrrrr|r}
&amp; x_1 &amp; x_2 &amp; x_3 &amp; s_1 &amp; s_2 &amp; s_3 &amp; \\ \hline
s_1 &amp; -2 &amp; 0 &amp; -2 &amp; 1 &amp; 0 &amp; 0 &amp; -60 \\
s_2 &amp; -2 &amp; -4^* &amp; -5 &amp; 0 &amp; 1 &amp; 0 &amp; -70 \\
s_3 &amp; 0 &amp; -3 &amp; -1 &amp; 0 &amp; 0 &amp; 1 &amp; -27 \\ \hdashline
&amp; 8 &amp; 10 &amp; 25 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
\text{ratio} &amp; -4 &amp; -5/2 &amp; -5 &amp; &amp; &amp; &amp; \\ \hline
s_1 &amp; -2^* &amp; 0 &amp; -2 &amp; 1 &amp; 0 &amp; 0 &amp; -60 \\
x_2 &amp; 1/2 &amp; 1 &amp; 5/4 &amp; 0 &amp; -1/4 &amp; 0 &amp; 35/2 \\
s_3 &amp; 3/2 &amp; 0 &amp; 11/4 &amp; 0 &amp; -3/4 &amp; 1 &amp; 51/2 \\ \hdashline
&amp; 3 &amp; 0 &amp; 25/2 &amp; 0 &amp; 5/2 &amp; 0 &amp; -175 \\
\text{ratio} &amp; -3/2 &amp; &amp; 25/4 &amp; &amp; &amp; &amp; \\ \hline
x_1 &amp; 1 &amp; 0 &amp; 1 &amp; -1/2 &amp; 0 &amp; 0 &amp; 30 \\
x_2 &amp; 0 &amp; 1 &amp; 3/4 &amp; 1/4 &amp; -1/4 &amp; 0 &amp; 5/2 \\
s_3 &amp; 0 &amp; 0 &amp; 5/4 &amp; 3/4 &amp; -3/4^* &amp; 1 &amp; -39/2 \\ \hdashline
&amp; 0 &amp; 0 &amp; 19/2 &amp; 3/2 &amp; 5/2 &amp; 0 &amp; -265 \\
\text{ratio} &amp; &amp; &amp; &amp; &amp; \dots &amp; &amp; \\ \hline
x_1 &amp; 1 &amp; 0 &amp; 1 &amp; -1/2 &amp; 0 &amp; 0 &amp; 30 \\
x_2 &amp; 0 &amp; 1 &amp; 1/3 &amp; 0 &amp; 0 &amp; -1/3 &amp; 9 \\
s_2 &amp; 0 &amp; 0 &amp; -5/3 &amp; -1 &amp; 1 &amp; -4/3 &amp; 26 \\ \hdashline
&amp; 0 &amp; 0 &amp; 41/3 &amp; 4 &amp; 0 &amp; 10/3 &amp; -330
\end{array}</div>
<div>\[
\require{extpfeil} % produce extensible horizontal arrows
\begin{array}{ccc} % arrange LPPs
% first row
% first LPP
\begin{array}{ll}
\max &amp; z = c^T x \\
\text{s.t.} &amp; A x \le b \\
&amp; x \ge 0
\end{array}
&amp; \xtofrom{\text{duality}} &amp;
% second LPP
\begin{array}{ll}
\min &amp; v = b^T y \\
\text{s.t.} &amp; A^T y \ge c \\
&amp; y \ge 0
\end{array} \\
({\cal PC}) &amp; &amp; ({\cal DC}) \\
\text{add } {\Large \downharpoonleft} \text{slack var} &amp; &amp; \text{minus } {\Large \downharpoonright} \text{surplus var}\\ % Change to your favorite arrow style
%
% second row
% third LPP
\begin{array}{ll}
\max &amp; z = c^T x \\
\text{s.t.} &amp; A x + s = b \\
&amp; x,s \ge 0
\end{array}
&amp; \xtofrom[\text{some steps skipped}]{\text{duality}} &amp;
% fourth LPP
\begin{array}{ll}
\min &amp; v = b^T y \\
\text{s.t.} &amp; A^T y - t = c \\
&amp; y,t \ge 0
\end{array} \\
({\cal PS}) &amp; &amp; ({\cal DS})
%
\end{array}
\]
</div>
<div>\(\sum_{i=n}^\mathbb{N}\)</div>
<div>\(\sum\)</div>
</body>
</html>
<!DOCTYPE html><html><head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Math.SE extracted Samples</title>
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<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 4.646em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 6.57em; top: -1.87em;"><span class="mjx-mrow" style=""><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 6.57em; bottom: -0.687em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 4.646em;" class="mjx-line"></span></span><span style="height: 1.808em; vertical-align: -0.486em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.721em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.74em; padding-bottom: 0.74em;"></span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.21em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 7.39em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 7.39em; top: -1.667em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-denominator" style="width: 7.39em; bottom: -0.778em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 7.39em;" class="mjx-line"></span></span><span style="height: 2.445em; vertical-align: -0.778em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\alpha, \beta, … \omega"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">α</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.446em; padding-right: 0.007em;">β</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">ω</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Gamma, \Delta, …, \Omega"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Γ</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Δ</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;"></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Ω</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x_i^2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-stack" style="vertical-align: -0.311em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\log_2 x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">log</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.377em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="10^10"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="10^{10}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{x^y}^z"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.594em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x^{y^z}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0.069em; padding-right: 0.06em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x_i^2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-stack" style="vertical-align: -0.311em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x_{i^2}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.365em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(2+3)[4+4]"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">[</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">]</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\{\}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(\frac{\sqrt x}{y^3})"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.135em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.605em; top: -1.766em;"><span class="mjx-msqrt" style=""><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span><span class="mjx-box" style="padding-top: 0.236em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.605em; bottom: -1.043em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0.069em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.135em;" class="mjx-line"></span></span><span style="height: 1.987em; vertical-align: -0.738em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\left(\frac{\sqrt x}{y^3}\right)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.135em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.605em; top: -1.766em;"><span class="mjx-msqrt" style=""><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span><span class="mjx-box" style="padding-top: 0.236em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.605em; bottom: -1.043em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0.069em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.135em;" class="mjx-line"></span></span><span style="height: 1.987em; vertical-align: -0.738em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(x)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="[x]"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">[</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">]</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\{ x \}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="|x|"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\vert x \vert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Vert x \Vert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\langle x \rangle"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lceil x \rceil"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lfloor x \rfloor"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\left.\frac12\right\rbrace"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="width: 0.12em;"></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.495em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.7em; top: -1.372em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.7em; bottom: -0.665em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.495em;" class="mjx-line"></span></span><span style="height: 1.441em; vertical-align: -0.47em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">}</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">(</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">(</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">)</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">)</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sum_1^n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sum_{i=0}^\infty i^2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;"></span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\prod"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\int"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bigcup"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bigcap"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\iint"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\iiint"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\frac ab"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.515em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.729em; top: -1.157em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.729em; bottom: -0.704em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.515em;" class="mjx-line"></span></span><span style="height: 1.316em; vertical-align: -0.498em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\frac{a+1}{b+1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.419em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 2.007em; top: -1.454em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 2.007em; bottom: -0.775em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.419em;" class="mjx-line"></span></span><span style="height: 1.577em; vertical-align: -0.548em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{a+1\over b+1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.419em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 2.007em; top: -1.454em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 2.007em; bottom: -0.775em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.419em;" class="mjx-line"></span></span><span style="height: 1.577em; vertical-align: -0.548em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\cfrac{a}{b}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.67em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.948em; top: -1.816em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.948em; bottom: -1.266em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.67em;" class="mjx-line"></span></span><span style="height: 2.18em; vertical-align: -0.895em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathbb{CHNQRZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.593em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathbf{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em; padding-right: 0.101em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.593em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em; padding-right: 0.002em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.225em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em; padding-right: 0.003em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathtt{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.225em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em; padding-right: 0.011em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.02em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.066em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em; padding-right: 0.007em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathsf{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.041em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.446em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.021em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.007em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.006em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.036em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.11em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.004em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.097em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.161em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.519em; padding-bottom: 0.372em; padding-right: 0.159em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.037em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.036em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.288em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.061em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.045em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.046em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.094em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.046em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.042em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.213em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.02em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.153em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.081em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.156em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.095em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.128em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.272em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.137em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.081em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.29em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.161em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.136em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.306em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.067em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.018em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.002em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.037em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.148em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.249em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.16em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.228em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.221em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.187em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.249em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.211em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.001em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.014em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.007em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.019em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.008em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.519em; padding-bottom: 0.446em;">Z</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.015em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.446em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt{x^3}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;"></span></span><span class="mjx-box" style="padding-top: 0.081em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt[3]{\frac xy}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mroot"><span class="mjx-root" style="font-size: 58.9%; vertical-align: 0.477em; width: 0px;"><span class="mjx-mn" style="padding-left: 0.561em;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;"></span></span><span class="mjx-box" style="padding-top: 0.224em; border-top: 1px solid;"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.718em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.327em; vertical-align: -0.507em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sin x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="sin x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\lim_{x\to 0}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lt\, \gt\, \le\, \leq\, \leqq\, \leqslant\, \ge\, \geq\, \geqq\, \geqslant\, \neq"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">&lt;</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">&gt;</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.519em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.519em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\not\lt"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.519em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\times\, \div\, \pm\, \mp"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">×</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">÷</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">±</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.519em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x\cdot y"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;"></span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.519em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.298em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{n+1 \choose 2k}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-TeXmathchoice"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span></span></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.328em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.878em; top: -1.319em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.878em; bottom: -0.524em;"><span class="mjx-mrow" style=""><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span></span><span style="height: 1.303em; vertical-align: -0.37em;" class="mjx-vsize"></span></span><span class="mjx-TeXmathchoice"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\to\, \rightarrow\, \leftarrow\, \Rightarrow\, \Leftarrow\, \mapsto"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\land\, \lor\, \lnot\, \forall\, \exists\, \top\, \bot\, \vdash\, \vDash"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">¬</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\star\, \ast\, \oplus\, \circ\, \bullet"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\approx\, \sim \, \simeq\, \cong\, \equiv\, \prec, \lhd"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;"></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;">