# Help:Math

 Shortcut:A:MATH

Math can be written in the wiki in the form of LaTeX, a typesetting language used primarily to type mathematical expressions in an elegant fashion. For example, without LaTeX, $\frac{35}{137}$ would have to be written as 35/137. To use LaTeX in the forums, enclose your LaTeX code with dollar signs: <dollar/>your codes here<dollar/>. You can also use double dollar signs or other normal $\LaTeX$ indicators: <dollar/><dollar/>your codes here<dollar/><dollar/> or $your codes here$. (There are also deprecated [tex] tags, but let's not get into that) To use LaTeX on AoPSWiki, you can enclose the code with dollar signs as in the forum, or you can also enclose your code with math tags, like so: $your codes here$.

## Useful Codes

\frac{a}{b} produces a fraction with numerator $a$ and denominator $b$. $\frac{a}{b}$

^\circ produces the degrees symbol. $a^{\circ}$

\text{Your Text Here} produces text within LaTeX. $\mbox{Your Text Here}$.

\sqrt{x} produces the square root of $x$. $\sqrt{x}$

\sqrt[n]{x} produces the $n$th root of $x$. $\sqrt[n]{x}$

a\equiv b \pmod{c} produces $a$ is equivalent to $b$ mod $c$. $a\equiv b \pmod{c}$ See Modular Arithmetic

\binom{9}{3} produces 9 choose 3.

x^{y} produces x to the power of y. $x^y$

x_{y} produces x with y in subscript. $x_y$

\rightarrow produces an arrow to the right. $\rightarrow$

\leftarrow produces an arrow to the left. $\leftarrow$

\uparrow produces an arrow pointing upwards. $\uparrow$

\downarrow produces an arrow pointing downwards. $\downarrow$

\updownarrow produces an arrow pointing up and down. $\updownarrow$

\ge produces a greater than or equal to sign. $\ge$

\le produces a less than or equal to sign. $\le$

\not> produces a not greater than sign. $\not>$

\not< produces a not less than sign. $\not<$

\not\ge produces a not greater than or equal to sign. $\not\ge$

\not\le produces a not less than or equal to sign. $\not\le$

\neq produces a not equal to sign. $\neq$

\inf produces an infinity sign.

\perp produces a perpendicular sign. $\perp$

\angle produces an angle sign. $\angle$

\triangle produces a triangle. $\triangle$

\ldots produces three dots at the bottom of a line (ellipsis). $\ldots$

\cdots produces three dots in the middle of a line (as in a series sum or product). $\cdots$

\times produces an $\times$ as used in multiplication

\otimes produces a $\otimes$

$\LaTeX$ is in math mode by default, so there's no difference between \frac{}{} and \dfrac{}{}, for example. Also note that you do not have to use braces, "{" and "}", when you only want one character in the operation.

### Examples

• x^y is the same as x^{y}. $x^y$
• x_y is the same as x_{y}. $x_y$
• BUT x^10 is not the same as x^{10}. $x^10$ instead of $x^{10}$.

## Fonts

### Font families

• Roman (default): \textrm{...}
• Sans-serif:

### Font sizes

To activate a font size, write '{\tiny{This text is tiny}}', for example.

• \tiny (5 pt.)
• \scriptsize (7 pt.)
• \footnotesize (8 pt.)
• \small (9 pt.)
• \normalsize (10 pt.)
• \large (12 pt.)
• \Large (14 pt.)
• \LARGE (18 pt.)
• \huge (20 pt.)
• \Huge (24 pt.)

### Font styles

• Bold \textbf{...}
• Italics \textit{...}
• Slanted \textsl{...}
• Small capitals \textsc{...}
• Sans-serif \textsf{...}
• Monospace \texttt{...}
• Emphasis \emph{...}