# KaTeX: Supported functions | Toshiki's Note
Supported functions within KaTeX syntaxes.
Author: Anda Toshiki
Keywords: Toshiki, Anda Toshiki, andatoshiki, GitHub, GitHub action, Vitepress, Vite, Notebook, Knowledge base, Programming, Programming Notes, Academic, Personal, Notebook, Productivity, Journal, Note-taking, Markdown, Notepad, Organization, Tutorial

Skip to content

####

# KaTeX: Supported function ​

Author:Anda Toshiki
Updated:a minute ago
Words:3.9k
Reading:24 min

note

This is an direct shameful copy of the documentation pulled from KaTeX documentation, I do not own any of the content below on behalf of this part of the documentation, the table might be outdated as versions migrates, please also refer to KaTeX's official documentation.

This following is a list of TeX functions supported by KaTeX. It is sorted into logical groups.

There is a similar Support Table on the next page, sorted alphabetically in am more intuitive way with the lists both supported and un-supported functions, viewing both tables are suggested comprehensibly and interchangeably is highly suggested.

## 1: Accents ​

a′a'a′ `a'` | a~\tilde{a}a~ `\tilde{a}` | g˚\mathring{g}g˚​ `\mathring{g}`
a′′a''a′′ `a''` | ac~\widetilde{ac}ac `\widetilde{ac}` | AB⏠\overgroup{AB}AB `\overgroup{AB}`
a′a^{\prime}a′ `a^{\prime}` | AB~\utilde{AB} AB​ `\utilde{AB}` | AB⏡\undergroup{AB} AB​ `\undergroup{AB}`
a ˊ\acute{a}aˊ `\acute{a}` | F⃗\vec{F}F `\vec{F}` | AB⇒\Overrightarrow{AB}AB `\Overrightarrow{AB}`
y ˉ\bar{y}yˉ​ `\bar{y}` | AB←\overleftarrow{AB}AB `\overleftarrow{AB}` | AB→\overrightarrow{AB}AB `\overrightarrow{AB}`
a˘\breve{a}a˘ `\breve{a}` | AB←\underleftarrow{AB} AB​ `\underleftarrow{AB}` | AB→\underrightarrow{AB} AB​ `\underrightarrow{AB}`
a ˇ\check{a}aˇ `\check{a}` | ac↼\overleftharpoon{ac}ac `\overleftharpoon{ac}` | ac⇀\overrightharpoon{ac}ac `\overrightharpoon{ac}`
a˙\dot{a}a˙ `\dot{a}` | AB↔\overleftrightarrow{AB}AB `\overleftrightarrow{AB}` | AB⏞\overbrace{AB}AB `\overbrace{AB}`
a¨\ddot{a}a¨ `\ddot{a}` | AB↔\underleftrightarrow{AB} AB​ `\underleftrightarrow{AB}` | AB⏟\underbrace{AB} AB​ `\underbrace{AB}`
a ˋ\grave{a}aˋ `\grave{a}` | AB‾\overline{AB}AB `\overline{AB}` | AB undefined\overlinesegment{AB}AB `\overlinesegment{AB}`
θ^\hat{\theta}θ^ `\hat{\theta}` | AB‾\underline{AB}AB​ `\underline{AB}` | AB undefined\underlinesegment{AB} AB​ `\underlinesegment{AB}`
ac^\widehat{ac}ac `\widehat{ac}` | ac ˇ\widecheck{ac}ac `\widecheck{ac}` |

Accent functions inside \text{…}

a ˊ\text{\'{a}}aˊ `\'{a}` | a˜\text{\~{a}}a˜ `\~{a}` | a˙\text{\.{a}}a˙ `\.{a}` | a˝\text{\H{a}}a˝ `\H{a}`
a ˋ\text{\`{a}}aˋ `\`{a}` | a ˉ\text{\={a}}aˉ `\={a}` | a¨\text{\"{a}}a¨ `\"{a}` | a ˇ\text{\v{a}}aˇ `\v{a}`
a ˆ\text{\^{a}}aˆ `\^{a}` | a˘\text{\u{a}}a˘ `\u{a}` | a˚\text{\r{a}}a˚ `\r{a}` |

See also letters.

## 2: Delimiters ​

( )(~)( ) `( )` | ( )\lparen~\rparen( ) `\lparen` ~~~~ `\rparen` | ⌈ ⌉⌈~⌉⌈ ⌉ `⌈ ⌉` | ⌈ ⌉\lceil~\rceil⌈ ⌉ `\lceil` ~~~~~ `\rceil` | ↑\uparrow↑ `\uparrow`
[ ][~][ ] `[ ]` | [ ]\lbrack~\rbrack[ ] `\lbrack` ~~~~ `\rbrack` | ⌊ ⌋⌊~⌋⌊ ⌋ `⌊ ⌋` | ⌊ ⌋\lfloor~\rfloor⌊ ⌋ `\lfloor` ~~~~~ `\rfloor` | ↓\downarrow↓ `\downarrow`
{}\{ \}{} `\{ \}` | {}\lbrace \rbrace{} `\lbrace` ~~~~ `\rbrace` | ⎰⎱⎰⎱⎰⎱ `⎰⎱` | ⎰⎱\lmoustache \rmoustache⎰⎱ `\lmoustache` ~~~~ `\rmoustache` | ↕\updownarrow↕ `\updownarrow`
⟨ ⟩⟨~⟩⟨ ⟩ `⟨ ⟩` | ⟨ ⟩\langle~\rangle⟨ ⟩ `\langle` ~~~~ `\rangle` | ⟮ ⟯⟮~⟯⟮ ⟯ `⟮ ⟯` | ⟮ ⟯\lgroup~\rgroup⟮ ⟯ `\lgroup` ~~~~~ `\rgroup` | ⇑\Uparrow⇑ `\Uparrow`
∣\vert∣ `|` | ∣\vert∣ `\vert` | ┌┐┌ ┐┌┐ `┌ ┐` | ⌜⌝\ulcorner \urcorner┌┐ `\ulcorner` ~~~~ `\urcorner` | ⇓\Downarrow⇓ `\Downarrow`
∥\Vert∥ `\|` | ∥\Vert∥ `\Vert` | └┘└ ┘└┘ `└ ┘` | ⌞⌟\llcorner \lrcorner└┘ `\llcorner` ~~~~ `\lrcorner` | ⇕\Updownarrow⇕ `\Updownarrow`
∣ ∣\lvert~\rvert∣ ∣ `\lvert` ~~~~ `\rvert` | ∥ ∥\lVert~\rVert∥ ∥ `\lVert` ~~~~~ `\rVert` | `\left.` | `\right.` | \\backslash\ `\backslash`
⟨ ⟩\lang~\rang⟨ ⟩ `\lang` ~~~~ `\rang` | < >\lt~\gt< > `\lt \gt` |  |  |

Delimiter Sizing

(AB)\left(\LARGE{AB}\right)(AB) `\left(\LARGE{AB}\right)`

(((((( \big( \Big( \bigg( \Bigg(((((( `( \big( \Big( \bigg( \Bigg(`

`\left` | `\big` | `\bigl` | `\bigm` | `\bigr`
`\middle` | `\Big` | `\Bigl` | `\Bigm` | `\Bigr`
`\right` | `\bigg` | `\biggl` | `\biggm` | `\biggr`
| `\Bigg` | `\Biggl` | `\Biggm` | `\Biggr`

## 3: Environments ​

abcd\begin{matrix} a & b \\ c & d \end{matrix}ac​bd​ | `\begin{matrix}` `a & b \\` `c & d` `\end{matrix}` | abcd\begin{array}{cc}a & b\\c & d\end{array}ac​bd​ | `\begin{array}{cc}` `a & b \\` `c & d` `\end{array}`
(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}(ac​bd​) | `\begin{pmatrix}` `a & b \\` `c & d` `\end{pmatrix}` | [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}[ac​bd​] | `\begin{bmatrix}` `a & b \\` `c & d` `\end{bmatrix}`
∣abcd∣\begin{vmatrix} a & b \\ c & d \end{vmatrix} ​ac​bd​ ​ | `\begin{vmatrix}` `a & b \\` `c & d` `\end{vmatrix}` | ∥abcd∥\begin{Vmatrix} a & b \\ c & d \end{Vmatrix} ​ac​bd​ ​ | `\begin{Vmatrix}` `a & b \\` `c & d` `\end{Vmatrix}`
{abcd}\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}{ac​bd​} | `\begin{Bmatrix}` `a & b \\` `c & d` `\end{Bmatrix}` | abcdefghi\def\arraystretch{1.5}\begin{array}{c:c:c} a & b & c \\ \hline d & e & f \\ \hdashline g & h & i \end{array}adg​beh​cfi​​ | `\def\arraystretch{1.5}` `\begin{array}{c:c:c}` `a & b & c \\ \hline` `d & e & f \\` `\hdashline` `g & h & i` `\end{array}`
a=b+cd+e=f\begin{aligned} a&=b+c \\ d+e&=f \end{aligned}ad+e​=b+c=f​ | `\begin{aligned}` `a&=b+c \\` `d+e&=f` `\end{aligned}` | 10 x+3 y=23 x+13 y=4\begin{alignedat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignedat}103​x+x+​313​y=2y=4​ | `\begin{alignedat}{2}` `10&x+ &3&y = 2 \\` `3&x+&13&y = 4` `\end{alignedat}`
a=be=b+c\begin{gathered} a=b \\ e=b+c \end{gathered}a=be=b+c​ | `\begin{gathered}` `a=b \\` `e=b+c` `\end{gathered}` | x={aif bcif d x = \begin{cases} a &\text{if } b \\ c &\text{if } d \end{cases}x={ac​if bif d​ | `x = \begin{cases}` `a &\text{if } b \\` `c &\text{if } d` `\end{cases}`

KaTeX also supports `darray` and `dcases`.

Acceptable line separators include: `\\`, `\cr`, `\\[distance]`, and `\cr[distance]`. Distance can be written with any of the KaTeX units.

The `{array}` environment supports `|` and `:` vertical separators.

The `{array}` environment does not yet support `\cline` or `\multicolumn`.

## 4: HTML ​

\href\href{https://katex.org/}{\KaTeX}\href | `\href{https://katex.org/}{\KaTeX}`
\url\url{https://katex.org/}\url | `\url{https://katex.org/}`

## 5: Letters and Unicode ​

Greek Letters

Direct Input: ABΓΔEZHΘI KΛMNΞOΠPΣTΥΦXΨΩ Α Β Γ Δ Ε Ζ Η Θ Ι \allowbreak Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ ΩABΓΔEZHΘIKΛMNΞOΠPΣTΥΦXΨΩ αβγδϵζηθικλμνξoπ ρστυϕχψωεϑϖϱςφ\allowbreak α β γ δ ϵ ζ η θ ι κ λ μ ν ξ o π \allowbreak ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φαβγδϵζηθικλμνξoπρστυϕχψωεϑϖϱςφ

A\AlphaA `\Alpha` | B\BetaB `\Beta` | Γ\GammaΓ `\Gamma` | Δ\DeltaΔ `\Delta`
E\EpsilonE `\Epsilon` | Z\ZetaZ `\Zeta` | H\EtaH `\Eta` | Θ\ThetaΘ `\Theta`
I\IotaI `\Iota` | K\KappaK `\Kappa` | Λ\LambdaΛ `\Lambda` | M\MuM `\Mu`
N\NuN `\Nu` | Ξ\XiΞ `\Xi` | O\OmicronO `\Omicron` | Π\PiΠ `\Pi`
Σ\SigmaΣ `\Sigma` | T\TauT `\Tau` | Υ\UpsilonΥ `\Upsilon` | Φ\PhiΦ `\Phi`
X\ChiX `\Chi` | Ψ\PsiΨ `\Psi` | Ω\OmegaΩ `\Omega` |
Γ\varGammaΓ `\varGamma` | Δ\varDeltaΔ `\varDelta` | Θ\varThetaΘ `\varTheta` | Λ\varLambdaΛ `\varLambda`
Ξ\varXiΞ `\varXi` | Π\varPiΠ `\varPi` | Σ\varSigmaΣ `\varSigma` | Υ\varUpsilonΥ `\varUpsilon`
Φ\varPhiΦ `\varPhi` | Ψ\varPsiΨ `\varPsi` | Ω\varOmegaΩ `\varOmega` |
α\alphaα `\alpha` | β\betaβ `\beta` | γ\gammaγ `\gamma` | δ\deltaδ `\delta`
ϵ\epsilonϵ `\epsilon` | ζ\zetaζ `\zeta` | η\etaη `\eta` | θ\thetaθ `\theta`
ι\iotaι `\iota` | κ\kappaκ `\kappa` | λ\lambdaλ `\lambda` | μ\muμ `\mu`
ν\nuν `\nu` | ξ\xiξ `\xi` | ο\omicronο `\omicron` | π\piπ `\pi`
ρ\rhoρ `\rho` | σ\sigmaσ `\sigma` | τ\tauτ `\tau` | υ\upsilonυ `\upsilon`
ϕ\phiϕ `\phi` | χ\chiχ `\chi` | ψ\psiψ `\psi` | ω\omegaω `\omega`
ε\varepsilonε `\varepsilon` | ϰ\varkappaϰ `\varkappa` | ϑ\varthetaϑ `\vartheta` | ϑ\thetasymϑ `\thetasym`
ϖ\varpiϖ `\varpi` | ϱ\varrhoϱ `\varrho` | ς\varsigmaς `\varsigma` | φ\varphiφ `\varphi`

| ϝ\digammaϝ `\digamma`

Other Letters

ı\imath `\imath` | ∇\nabla∇ `\nabla` | ℑ\Imℑ `\Im` | R\RealsR `\Reals` | Œ\text{\OE}Œ `\text{\OE}`
ȷ\jmath `\jmath` | ∂\partial∂ `\partial` | ℑ\imageℑ `\image` | ℘\wp℘ `\wp` | ø\text{\o}ø `\text{\o}`
ℵ\alephℵ `\aleph` | ⅁\Game⅁ `\Game` | k\Bbbkk `\Bbbk` | ℘\weierp℘ `\weierp` | Ø\text{\O}Ø `\text{\O}`
ℵ\alefℵ `\alef` | Ⅎ\FinvℲ `\Finv` | N\NN `\N` | Z\ZZ `\Z` | ß\text{\ss}ß `\text{\ss}`
ℵ\alefsymℵ `\alefsym` | C\cnumsC `\cnums` | N\natnumsN `\natnums` | a˚\text{\aa}a˚ `\text{\aa}` | ı\text{\i}ı `\text{\i}`
ℶ\bethℶ `\beth` | C\ComplexC `\Complex` | R\RR `\R` | A˚\text{\AA}A˚ `\text{\AA}` | ȷ\text{\j}ȷ `\text{\j}`
ℷ\gimelℷ `\gimel` | ℓ\ellℓ `\ell` | ℜ\Reℜ `\Re` | æ\text{\ae}æ `\text{\ae}` |
ℸ\dalethℸ `\daleth` | ℏ\hbarℏ `\hbar` | ℜ\realℜ `\real` | Æ\text{\AE}Æ `\text{\AE}` |
ð\ethð `\eth` | ℏ\hslashℏ `\hslash` | R\realsR `\reals` | œ\text{\oe}œ `\text{\oe}` |

Direct Input: ∂∇ℑℲℵℶℷℸ⅁ℏð∂ ∇ ℑ Ⅎ ℵ ℶ ℷ ℸ ⅁ ℏ ð∂∇ℑℲℵℶℷℸ⅁ℏð ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖÙÚÛÜÝÞßàáâãäåçèéêëìíîïðñòóôöùúûüýþÿ

Unicode Mathematical Alphanumeric Symbols

Item | Range | Item | Range
--- | --- | --- | ---
Bold | 𝐀-𝐙 𝐚-𝐳 𝟎-𝟗\text{𝐀-𝐙 𝐚-𝐳 𝟎-𝟗}A-Z a-z 0-9 | Double-struck | 𝔸-Z 𝕜\text{𝔸-}ℤ\ 𝕜A-Z k
Italic | 𝐴-𝑍 𝑎-𝑧\text{𝐴-𝑍 𝑎-𝑧}A-Z a-z | Sans serif | 𝖠-𝖹 𝖺-𝗓 𝟢-𝟫\text{𝖠-𝖹 𝖺-𝗓 𝟢-𝟫}A-Z a-z 0-9
Bold Italic | 𝑨-𝒁 𝒂-𝒛\text{𝑨-𝒁 𝒂-𝒛}A-Z a-z | Sans serif bold | 𝗔-𝗭 𝗮-𝘇 𝟬-𝟵\text{𝗔-𝗭 𝗮-𝘇 𝟬-𝟵}A-Z a-z 0-9
Script | 𝒜-𝒵\text{𝒜-𝒵}A-Z | Sans serif italic | 𝘈-𝘡 𝘢-𝘻\text{𝘈-𝘡 𝘢-𝘻}A-Z a-z
Fractur | 𝔄-Z 𝔞-𝔷\text{𝔄-}ℨ\text{ 𝔞-𝔷}A-Z a-z | Monospace | 𝙰-𝚉 𝚊-𝚣 𝟶-𝟿\text{𝙰-𝚉 𝚊-𝚣 𝟶-𝟿}A-Z a-z 0-9

Unicode

The letters listed above will render in any KaTeX rendering mode.

If the KaTeX rendering mode is set to `strict: false` or `strict:"warn"` (default), then KaTeX will accept all Unicode letters. The letters not listed above will be rendered from system fonts, not KaTeX-supplied fonts, so their typography may clash. They may also cause small vertical alignment issues. KaTeX has detailed metrics for glyphs in Latin, Greek, and Cyrillic, but other glyphs are treated as if they are each as tall as the letter M.

For Persian composite characters, a user-supplied plug-in is under development.

## 6: Layout ​

### 6.1: Annotation ​

5\cancel{5}5 ​ `\cancel{5}` | a+b+c⏞note\overbrace{a+b+c}^{\text{note}}a+b+c ​note​ `\overbrace{a+b+c}^{\text{note}}`
5\bcancel{5}5 ​ `\bcancel{5}` | a+b+c⏟note\underbrace{a+b+c}_{\text{note}}note a+b+c​​ `\underbrace{a+b+c}_{\text{note}}`
ABC\xcancel{ABC}ABC `\xcancel{ABC}` | ≠\not == `\not =`
abc\sout{abc}abc `\sout{abc}` | π=cd\boxed{\pi=\frac c d}π=dc​​ `\boxed{\pi=\frac c d}`

`\tag{hi} x+y^{2x}`

x+y 2 x(hi)\tag{hi} x+y^{2x} x+y2x(hi)

`\tag*{hi} x+y^{2x}`

x+y 2 xhi\tag*{hi} x+y^{2x} x+y2xhi

### 6.2: Line Breaks ​

KaTeX 0.10.0+ will insert automatic line breaks in inline math after relations or binary operators such as “=” or “+”. These can be suppressed by `\nobreak` or by placing math inside a pair of braces, as in `{F=ma}`. `\allowbreak` will allow automatic line breaks at locations other than relations or operators.

Hard line breaks are `\\` and `\newline`.

In display math, KaTeX does not insert automatic line breaks. It ignores display math hard line breaks when rendering option `strict: true`.

### 6.3: Vertical Layout ​

xn x_nxn​ `x_n` | =!\stackrel{!}{=}=! `\stackrel{!}{=}` | ab a \atop bba​ `a \atop b`
ex e^xex `e^x` | =!\overset{!}{=}=! `\overset{!}{=}` | a b c a\raisebox{0.25em}{b}cabc `a\raisebox{0.25em}{b}c`
$_u^o $ `_u^o` | =!\underset{!}{=}!=​ `\underset{!}{=}` |

The second argument of `\raisebox` can contain math if it is nested within `$…$` delimiters, as in `\raisebox{0.25em}{$\frac a b$}`

### 6.4: Overlap and Spacing ​

=/ {=}\mathllap{/\,}=/ `{=}\mathllap{/\,}` | (x 2)\left(x^{\smash{2}}\right)(x2) `\left(x^{\smash{2}}\right)`
/=\mathrlap{\,/}{=}/= `\mathrlap{\,/}{=}` | y\sqrt{\smash[b]{y}}y ​ `\sqrt{\smash[b]{y}}`

∑1≤i≤j≤n x ij\displaystyle\sum_{\mathclap{1\le i\le j\le n}} x_{ij}1≤i≤j≤n∑​xij​ `\sum_{\mathclap{1\le i\le j\le n}} x_{ij}`

KaTeX also supports `\llap`, `\rlap`, and `\clap`, but they will take only text, not math, as arguments.

Spacing

Function | Produces | Function | Produces
--- | --- | --- | ---
`\,` | ³∕₁₈ em space | `\kern{distance}` | space, width = distance
`\thinspace` | ³∕₁₈ em space | `\mkern{distance}` | space, width = distance
`\:` | ⁴∕₁₈ em space | `\mskip{distance}` | space, width = distance
`\medspace` | ⁴∕₁₈ em space | `\hskip{distance}` | space, width = distance
`\;` | ⁵∕₁₈ em space | `\hspace{distance}` | space, width = distance
`\thickspace` | ⁵∕₁₈ em space | `\hspace*{distance}` | space, width = distance
`\enspace` | ½ em space | `\phantom{content}` | space the width and height of content
`\quad` | 1 em space | `\hphantom{content}` | space the width of content
`\qquad` | 2 em space | `\vphantom{content}` | a strut the height of content
`~` | non-breaking space | `\!` | – ³∕₁₈ em space
`\<space>` | space | `\negthinspace` | – ³∕₁₈ em space
`\nobreakspace` | non-breaking space | `\negmedspace` | – ⁴∕₁₈ em space
`\space` | space | `\negthickspace` | – ⁵∕₁₈ em space

Notes:

`distance` will accept any of the KaTeX units.

`\kern`, `\mkern`, `\mskip`, and `\hspace` accept unbraced distances, as in: `\kern1em`.

`\mkern` and `\mskip` will not work in text mode and both will write a console warning for any unit except `mu`.

## 7: Logic and Set Theory ​

∀\forall∀ `\forall` | ∁\complement∁ `\complement` | ∴\therefore∴ `\therefore` | ∅\emptyset∅ `\emptyset`
∃\exists∃ `\exists` | ⊂\subset⊂ `\subset` | ∵\because∵ `\because` | ∅\empty∅ `\empty`
∃\exist∃ `\exist` | ⊃\supset⊃ `\supset` | ↦\mapsto↦ `\mapsto` | ∅\varnothing∅ `\varnothing`
∄\nexists∄ `\nexists` | ∣\mid∣ `\mid` | →\to→ `\to` | ⟹ \implies⟹ `\implies`
∈\in∈ `\in` | ∧\land∧ `\land` | ←\gets← `\gets` | ⟸ \impliedby⟸ `\impliedby`
∈\isin∈ `\isin` | ∨\lor∨ `\lor` | ↔\leftrightarrow↔ `\leftrightarrow` | ⟺ \iff⟺ `\iff`
∉\notin∈/ `\notin` | ∋\ni∋ `\ni` | ∌\notni∋ `\notni` | ¬\neg¬ `\neg` or `\lnot`

Direct Input: ∀∴∁∵∃∣∈∉∋⊂⊃∧∨↦→←↔¬∀ ∴ ∁ ∵ ∃ ∣ ∈ ∉ ∋ ⊂ ⊃ ∧ ∨ ↦ → ← ↔ ¬∀∴∁∵∃∣∈∈/∋⊂⊃∧∨↦→←↔¬ ℂ ℍ ℕ ℙ ℚ ℝ

## 8: Macros ​

x 2+x 2\def\foo{x^2} \foo + \foox2+x2 | `\def\foo{x^2} \foo + \foo`
y 2+y 2\gdef\bar#1{#1^2} \bar{y} + \bar{y}y2+y2 | `\gdef\bar#1{#1^2} \bar{y} + \bar{y}`
| `\global\def\macroname#1#2…{definition}`
| `\newcommand\macroname[numargs]{definition}`
| `\renewcommand\macroname[numargs]{definition}`
| `\providecommand\macroname[numargs]{definition}`

Macros can also be defined in the KaTeX rendering options.

Macros accept up to nine arguments: #1, #2, etc.

`\gdef` and `\global\def` macros will persist between math expressions.

Available functions include:

`\char` `\mathchoice` `\TextOrMath` `\@ifstar` `\@ifnextchar` `\@firstoftwo` `\@secondoftwo` `\relax`

@ is a valid character for commands, as if `\makeatletter` were in effect.

## 9: Operators ​

### 9.1: Big Operators ​

∑\sum∑ `\sum` | ∏\prod∏ `\prod` | ⨂\bigotimes⨂ `\bigotimes` | ⋁\bigvee⋁ `\bigvee`
∫\int∫ `\int` | ∐\coprod∐ `\coprod` | ⨁\bigoplus⨁ `\bigoplus` | ⋀\bigwedge⋀ `\bigwedge`
∬\iint∬ `\iint` | ∫\intop∫ `\intop` | ⨀\bigodot⨀ `\bigodot` | ⋂\bigcap⋂ `\bigcap`
∭\iiint∭ `\iiint` | ∫\smallint∫ `\smallint` | ⨄\biguplus⨄ `\biguplus` | ⋃\bigcup⋃ `\bigcup`
∮\oint∮ `\oint` | ∯\oiint∬ ​ `\oiint` | ∰\oiiint∭ ​ `\oiiint` | ⨆\bigsqcup⨆ `\bigsqcup`

Direct Input: ∫∬∭∮∏∐∑⋀⋁⋂⋃⨀⨁⨂⨄⨆∫ ∬ ∭ ∮ ∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ ⨄ ⨆∫∬∭∮∏∐∑⋀⋁⋂⋃⨀⨁⨂⨄⨆

### 9.2: Binary Operators ​

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

Direct Input: +−/∗⋅±×÷∓∔∧∨∩∪≀⊎⊓⊔⊕⊖⊗⊘⊙⊚⊛⊝+ - / * ⋅ ± × ÷ ∓ ∔ ∧ ∨ ∩ ∪ ≀ ⊎ ⊓ ⊔ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊝+−/∗⋅±×÷∓∔∧∨∩∪≀⊎⊓⊔⊕⊖⊗⊘⊙⊚⊛⊝

### 9.3: Fractions and Binomials ​

ab\frac{a}{b}ba​ `\frac{a}{b}` | ab\tfrac{a}{b}ba​ `\tfrac{a}{b}` | (a a+1]\genfrac ( ] {2pt}{1}a{a+1}(a+1a​] `\genfrac ( ] {2pt}{1}a{a+1}`
ab{a \over b}ba​ `{a \over b}` | ab\dfrac{a}{b}ba​ `\dfrac{a}{b}` | a b+1{a \above{2pt} b+1}b+1a​ `{a \above{2pt} b+1}`
a/b a/ba/b `a/b` |  | a 1+1 b\cfrac{a}{1 + \cfrac{1}{b}}1+b1​a​ `\cfrac{a}{1 + \cfrac{1}{b}}`

(nk)\binom{n}{k}(kn​) `\binom{n}{k}` | (nk)\dbinom{n}{k}(kn​) `\dbinom{n}{k}` | {nk}{n\brace k}{kn​} `{n\brace k}`
(nk){n \choose k}(kn​) `{n \choose k}` | (nk)\tbinom{n}{k}(kn​) `\tbinom{n}{k}` | [nk]{n\brack k}[kn​] `{n\brack k}`

### 9.4: Math Operators ​

arcsin⁡\arcsinarcsin `\arcsin` | cotg⁡\cotgcotg `\cotg` | ln⁡\lnln `\ln` | det⁡\detdet `\det`
arccos⁡\arccosarccos `\arccos` | coth⁡\cothcoth `\coth` | log⁡\loglog `\log` | gcd⁡\gcdgcd `\gcd`
arctan⁡\arctanarctan `\arctan` | csc⁡\csccsc `\csc` | sec⁡\secsec `\sec` | inf⁡\infinf `\inf`
arctg⁡\arctgarctg `\arctg` | ctg⁡\ctgctg `\ctg` | sin⁡\sinsin `\sin` | lim⁡\limlim `\lim`
arcctg⁡\arcctgarcctg `\arcctg` | cth⁡\cthcth `\cth` | sinh⁡\sinhsinh `\sinh` | lim inf⁡\liminfliminf `\liminf`
arg⁡\argarg `\arg` | deg⁡\degdeg `\deg` | sh⁡\shsh `\sh` | lim sup⁡\limsuplimsup `\limsup`
ch⁡\chch `\ch` | dim⁡\dimdim `\dim` | tan⁡\tantan `\tan` | max⁡\maxmax `\max`
cos⁡\coscos `\cos` | exp⁡\expexp `\exp` | tanh⁡\tanhtanh `\tanh` | min⁡\minmin `\min`
cosec⁡\coseccosec `\cosec` | hom⁡\homhom `\hom` | tg⁡\tgtg `\tg` | Pr⁡\PrPr `\Pr`
cosh⁡\coshcosh `\cosh` | ker⁡\kerker `\ker` | th⁡\thth `\th` | sup⁡\supsup `\sup`
cot⁡\cotcot `\cot` | lg⁡\lglg `\lg` | f⁡\operatorname{f}f `\operatorname{f}` |

Functions on the right column of this table can take `\limits`.

### 9.5: `\sqrt` ​

x\sqrt{x}x
​ `\sqrt{x}`

x 3\sqrt[3]{x}3x
​ `\sqrt[3]{x}`

## 10: Relations ​

=!\stackrel{!}{=}=! `\stackrel{!}{=}`

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

Direct Input: =<>:∈∋∝∼∽≂≃≅≈≊≍≎≏≐≑≒≓≖≗≜≡≤≥≦≧≫≬≳≷≺≻≼≽≾≿⊂⊃⊆⊇⊏⊐⊑⊒⊢⊣⊩⊪⊸⋈⋍⋐⋑⋔⋙⋛⋞⋟⌢⌣⩾⪆⪌⪕⪖⪯⪰⪷⪸⫅⫆≲⩽⪅≶⋚⪋⊥⊨= < > : ∈ ∋ ∝ ∼ ∽ ≂ ≃ ≅ ≈ ≊ ≍ ≎ ≏ ≐ ≑ ≒ ≓ ≖ ≗ ≜ ≡ ≤ ≥ ≦ ≧ ≫ ≬ ≳ ≷ ≺ ≻ ≼ ≽ ≾ ≿ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ⊩ ⊪ ⊸ ⋈ ⋍ ⋐ ⋑ ⋔ ⋙ ⋛ ⋞ ⋟ ⌢ ⌣ ⩾ ⪆ ⪌ ⪕ ⪖ ⪯ ⪰ ⪷ ⪸ ⫅ ⫆ ≲ ⩽ ⪅ ≶ ⋚ ⪋ ⟂ ⊨=<>:∈∋∝∼∽≂≃≅≈≊≍≎≏≐≑≒≓≖≗≜≡≤≥≦≧≫≬≳≷≺≻≼≽≾≿⊂⊃⊆⊇⊏⊐⊑⊒⊢⊣⊩⊪⊸⋈⋍⋐⋑⋔⋙⋛⋞⋟⌢⌣⩾⪆⪌⪕⪖⪯⪰⪷⪸⫅⫆≲⩽⪅≶⋚⪋⊥⊨ `≔ ≕ ⩴`

### 10.1: Negated Relations ​

≠\not == `\not =`

⪊\gnapprox⪊ `\gnapprox` | ≱\ngeqslant `\ngeqslant` | ⊈\nsubseteq⊈ `\nsubseteq` | ⪵\precneqq⪵ `\precneqq`
⪈\gneq⪈ `\gneq` | ≯\ngtr≯ `\ngtr` | ⊈\nsubseteqq `\nsubseteqq` | ⋨\precnsim⋨ `\precnsim`
≩\gneqq≩ `\gneqq` | ≰\nleq≰ `\nleq` | ⊁\nsucc⊁ `\nsucc` | ⊊\subsetneq⊊ `\subsetneq`
⋧\gnsim⋧ `\gnsim` | ≰\nleqq `\nleqq` | ⋡\nsucceq⋡ `\nsucceq` | ⫋\subsetneqq⫋ `\subsetneqq`
≩\gvertneqq `\gvertneqq` | ≰\nleqslant `\nleqslant` | ⊉\nsupseteq⊉ `\nsupseteq` | ⪺\succnapprox⪺ `\succnapprox`
⪉\lnapprox⪉ `\lnapprox` | ≮\nless≮ `\nless` | ⊉\nsupseteqq `\nsupseteqq` | ⪶\succneqq⪶ `\succneqq`
⪇\lneq⪇ `\lneq` | ∤\nmid∤ `\nmid` | ⋪\ntriangleleft⋪ `\ntriangleleft` | ⋩\succnsim⋩ `\succnsim`
≨\lneqq≨ `\lneqq` | ∉\notin∈/ `\notin` | ⋬\ntrianglelefteq⋬ `\ntrianglelefteq` | ⊋\supsetneq⊋ `\supsetneq`
⋦\lnsim⋦ `\lnsim` | ∌\notni∋ `\notni` | ⋫\ntriangleright⋫ `\ntriangleright` | ⫌\supsetneqq⫌ `\supsetneqq`
≨\lvertneqq `\lvertneqq` | ∦\nparallel∦ `\nparallel` | ⋭\ntrianglerighteq⋭ `\ntrianglerighteq` | ⊊\varsubsetneq `\varsubsetneq`
≆\ncong≆ `\ncong` | ⊀\nprec⊀ `\nprec` | ⊬\nvdash⊬ `\nvdash` | ⫋\varsubsetneqq `\varsubsetneqq`
≠\ne= `\ne` | ⋠\npreceq⋠ `\npreceq` | ⊭\nvDash⊭ `\nvDash` | ⊋\varsupsetneq `\varsupsetneq`
≠\neq= `\neq` | ∤\nshortmid `\nshortmid` | ⊯\nVDash⊯ `\nVDash` | ⫌\varsupsetneqq `\varsupsetneqq`
≱\ngeq≱ `\ngeq` | ∦\nshortparallel `\nshortparallel` | ⊮\nVdash⊮ `\nVdash` |
≱\ngeqq `\ngeqq` | ≁\nsim≁ `\nsim` | ⪹\precnapprox⪹ `\precnapprox` |

Direct Input:

∉∌∤∦≁≆≠≨≩≮≯≰≱⊀⊁⊈⊉⊊⊋⊬⊭⊮⊯⋠⋡⋦⋧⋨⋩⋬⋭⪇⪈⪉⪊⪵⪶⪹⪺⫋⫌∉ ∌ ∤ ∦ ≁ ≆ ≠ ≨ ≩ ≮ ≯ ≰ ≱ ⊀ ⊁ ⊈ ⊉ ⊊ ⊋ ⊬ ⊭ ⊮ ⊯ ⋠ ⋡ ⋦ ⋧ ⋨ ⋩ ⋬ ⋭ ⪇ ⪈ ⪉ ⪊ ⪵ ⪶ ⪹ ⪺ ⫋ ⫌ ∈/∋∤∦≁≆=≨≩≮≯≰≱⊀⊁⊈⊉⊊⊋⊬⊭⊮⊯⋠⋡⋦⋧⋨⋩⋬⋭⪇⪈⪉⪊⪵⪶⪹⪺⫋⫌

### 10.2: Arrows ​

↺\circlearrowleft↺ `\circlearrowleft` | ↼\leftharpoonup↼ `\leftharpoonup` | ⇒\rArr⇒ `\rArr`
↻\circlearrowright↻ `\circlearrowright` | ⇇\leftleftarrows⇇ `\leftleftarrows` | →\rarr→ `\rarr`
↶\curvearrowleft↶ `\curvearrowleft` | ↔\leftrightarrow↔ `\leftrightarrow` | ↾\restriction↾ `\restriction`
↷\curvearrowright↷ `\curvearrowright` | ⇔\Leftrightarrow⇔ `\Leftrightarrow` | →\rightarrow→ `\rightarrow`
⇓\Darr⇓ `\Darr` | ⇆\leftrightarrows⇆ `\leftrightarrows` | ⇒\Rightarrow⇒ `\Rightarrow`
⇓\dArr⇓ `\dArr` | ⇋\leftrightharpoons⇋ `\leftrightharpoons` | ↣\rightarrowtail↣ `\rightarrowtail`
↓\darr↓ `\darr` | ↭\leftrightsquigarrow↭ `\leftrightsquigarrow` | ⇁\rightharpoondown⇁ `\rightharpoondown`
⇠\dashleftarrow⇠ `\dashleftarrow` | ⇚\Lleftarrow⇚ `\Lleftarrow` | ⇀\rightharpoonup⇀ `\rightharpoonup`
⇢\dashrightarrow⇢ `\dashrightarrow` | ⟵\longleftarrow⟵ `\longleftarrow` | ⇄\rightleftarrows⇄ `\rightleftarrows`
↓\downarrow↓ `\downarrow` | ⟸\Longleftarrow⟸ `\Longleftarrow` | ⇌\rightleftharpoons⇌ `\rightleftharpoons`
⇓\Downarrow⇓ `\Downarrow` | ⟷\longleftrightarrow⟷ `\longleftrightarrow` | ⇉\rightrightarrows⇉ `\rightrightarrows`
⇊\downdownarrows⇊ `\downdownarrows` | ⟺\Longleftrightarrow⟺ `\Longleftrightarrow` | ⇝\rightsquigarrow⇝ `\rightsquigarrow`
⇃\downharpoonleft⇃ `\downharpoonleft` | ⟼\longmapsto⟼ `\longmapsto` | ⇛\Rrightarrow⇛ `\Rrightarrow`
⇂\downharpoonright⇂ `\downharpoonright` | ⟶\longrightarrow⟶ `\longrightarrow` | ↱\Rsh↱ `\Rsh`
←\gets← `\gets` | ⟹\Longrightarrow⟹ `\Longrightarrow` | ↘\searrow↘ `\searrow`
⇔\Harr⇔ `\Harr` | ↫\looparrowleft↫ `\looparrowleft` | ↙\swarrow↙ `\swarrow`
⇔\hArr⇔ `\hArr` | ↬\looparrowright↬ `\looparrowright` | →\to→ `\to`
↔\harr↔ `\harr` | ⇔\Lrarr⇔ `\Lrarr` | ↞\twoheadleftarrow↞ `\twoheadleftarrow`
↩\hookleftarrow↩ `\hookleftarrow` | ⇔\lrArr⇔ `\lrArr` | ↠\twoheadrightarrow↠ `\twoheadrightarrow`
↪\hookrightarrow↪ `\hookrightarrow` | ↔\lrarr↔ `\lrarr` | ⇑\Uarr⇑ `\Uarr`
⟺ \iff⟺ `\iff` | ↰\Lsh↰ `\Lsh` | ⇑\uArr⇑ `\uArr`
⟸ \impliedby⟸ `\impliedby` | ↦\mapsto↦ `\mapsto` | ↑\uarr↑ `\uarr`
⟹ \implies⟹ `\implies` | ↗\nearrow↗ `\nearrow` | ↑\uparrow↑ `\uparrow`
⇐\Larr⇐ `\Larr` | ↚\nleftarrow↚ `\nleftarrow` | ⇑\Uparrow⇑ `\Uparrow`
⇐\lArr⇐ `\lArr` | ⇍\nLeftarrow⇍ `\nLeftarrow` | ↕\updownarrow↕ `\updownarrow`
←\larr← `\larr` | ↮\nleftrightarrow↮ `\nleftrightarrow` | ⇕\Updownarrow⇕ `\Updownarrow`
⇝\leadsto⇝ `\leadsto` | ⇎\nLeftrightarrow⇎ `\nLeftrightarrow` | ↿\upharpoonleft↿ `\upharpoonleft`
←\leftarrow← `\leftarrow` | ↛\nrightarrow↛ `\nrightarrow` | ↾\upharpoonright↾ `\upharpoonright`
⇐\Leftarrow⇐ `\Leftarrow` | ⇏\nRightarrow⇏ `\nRightarrow` | ⇈\upuparrows⇈ `\upuparrows`
↢\leftarrowtail↢ `\leftarrowtail` | ↖\nwarrow↖ `\nwarrow` |
↽\leftharpoondown↽ `\leftharpoondown` | ⇒\Rarr⇒ `\Rarr` |

Direct Input: ←↑→↓↔↕↖↗↘↙↚↛↞↠↢↣↦↩↪↫↬↭↮↰↱↶↷↺↻↼↽↾↾↿⇀⇁⇂⇃⇄⇆⇇⇈⇉⇊⇋⇌⇍⇎⇏⇐⇑⇒⇓⇔⇕⇚⇛⇝⇠⇢⟵⟶⟷⟸⟹⟺⟼← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↞ ↠ ↢ ↣ ↦ ↩ ↪ ↫ ↬ ↭ ↮ ↰ ↱↶ ↷ ↺ ↻ ↼ ↽ ↾ ↾ ↿ ⇀ ⇁ ⇂ ⇃ ⇄ ⇆ ⇇ ⇈ ⇉ ⇊ ⇋ ⇌⇍ ⇎ ⇏ ⇐ ⇑ ⇒ ⇓ ⇔ ⇕ ⇚ ⇛ ⇝ ⇠ ⇢ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟼←↑→↓↔↕↖↗↘↙↚↛↞↠↢↣↦↩↪↫↬↭↮↰↱↶↷↺↻↼↽↾↾↿⇀⇁⇂⇃⇄⇆⇇⇈⇉⇊⇋⇌⇍⇎⇏⇐⇑⇒⇓⇔⇕⇚⇛⇝⇠⇢⟵⟶⟷⟸⟹⟺⟼ ↽

Extensible Arrows

←abc\xleftarrow{abc}abc ​ `\xleftarrow{abc}` | →underover\xrightarrow[under]{over}over under​ `\xrightarrow[under]{over}`
⇐abc\xLeftarrow{abc}abc ​ `\xLeftarrow{abc}` | ⇒abc\xRightarrow{abc}abc ​ `\xRightarrow{abc}`
↔abc\xleftrightarrow{abc}abc ​ `\xleftrightarrow{abc}` | ⇔abc\xLeftrightarrow{abc}abc ​ `\xLeftrightarrow{abc}`
↩abc\xhookleftarrow{abc}abc ​ `\xhookleftarrow{abc}` | ↪abc\xhookrightarrow{abc}abc ​ `\xhookrightarrow{abc}`
↞abc\xtwoheadleftarrow{abc}abc `\xtwoheadleftarrow{abc}` | ↠abc\xtwoheadrightarrow{abc}abc `\xtwoheadrightarrow{abc}`
↼abc\xleftharpoonup{abc}abc ​ `\xleftharpoonup{abc}` | ⇀abc\xrightharpoonup{abc}abc ​ `\xrightharpoonup{abc}`
↽abc\xleftharpoondown{abc}abc ​ `\xleftharpoondown{abc}` | ⇁abc\xrightharpoondown{abc}abc ​ `\xrightharpoondown{abc}`
⇋abc\xleftrightharpoons{abc}abc ​ `\xleftrightharpoons{abc}` | ⇌abc\xrightleftharpoons{abc}abc ​ `\xrightleftharpoons{abc}`
⇄abc\xtofrom{abc}abc ​ `\xtofrom{abc}` | ↦abc\xmapsto{abc}abc ​ `\xmapsto{abc}`

|=abc\xlongequal{abc}abc
`\xlongequal{abc}`

Extensible arrows all can take an optional argument in the same manner, as `\xrightarrow[under]{over}`.

## 11: Style, Color, Size, and Font ​

Class Assignment

- `\mathbin` `\mathclose` `\mathinner` `\mathop`

- `\mathopen` `\mathord` `\mathpunct` `\mathrel`

Color

F=ma\color{blue} F=maF=ma `\color{blue} F=ma`

Note that KaTeX `\color` acts like a switch. This aligns with LaTeX and differs from MathJax. Other KaTeX color functions expect the content to be a function argument:

- F=ma\textcolor{blue}{F=ma}F=ma `\textcolor{blue}{F=ma}`
- F=ma\textcolor{#228B22}{F=ma}F=ma `\textcolor{#228B22}{F=ma}`
- A\colorbox{aqua}{A}A​ `\colorbox{aqua}{A}`
- A\fcolorbox{red}{aqua}{A}A​ `\fcolorbox{red}{aqua}{A}`

For color definition, KaTeX color functions will accept the standard HTML predefined color names. They will also accept an RGB argument in CSS hexadecimal style. The "#" is optional before a six-digit specification.

Font

Ab 0\mathrm{Ab0}Ab0 `\mathrm{Ab0}` | Ab 0\mathbf{Ab0}Ab0 `\mathbf{Ab0}` | Ab\mathit{Ab}Ab `\mathit{Ab}`
Ab 0\mathnormal{Ab0}Ab0 `\mathnormal{Ab0}` | Ab0\textbf{Ab0}Ab0 `\textbf{Ab0}` | Ab\textit{Ab}Ab `\textit{Ab}`
Ab0\textrm{Ab0}Ab0 `\textrm{Ab0}` | Ab 0\bf Ab0Ab0 `\bf Ab0` | Ab\it AbAb `\it Ab`
Ab 0\rm Ab0Ab0 `\rm Ab0` | Ab 0\bold{Ab0}Ab0 `\bold{Ab0}` | AB\Bbb{AB}AB `\Bbb{AB}`
Ab0\textnormal{Ab0}Ab0 `\textnormal{Ab0}` | Ab\boldsymbol{Ab}Ab `\boldsymbol{Ab}` | AB\mathbb{AB}AB `\mathbb{AB}`
Ab0\text{Ab0}Ab0 `\text{Ab0}` | Ab\bm{Ab}Ab `\bm{Ab}` | Ab 0\frak{Ab0}Ab0 `\frak{Ab0}`
Ab 0\mathsf{Ab0}Ab0 `\mathsf{Ab0}` | Ab 0\mathtt{Ab0}Ab0 `\mathtt{Ab0}` | Ab 0\mathfrak{Ab0}Ab0 `\mathfrak{Ab0}`
Ab0\textsf{Ab0}Ab0 `\textsf{Ab0}` | Ab0\texttt{Ab0}Ab0 `\texttt{Ab0}` | AB 0\mathcal{AB0}AB0 `\mathcal{AB0}`
Ab 0\sf Ab0Ab0 `\sf Ab0` | Ab 0\tt Ab0Ab0 `\tt Ab0` | AB\mathscr{AB}AB `\mathscr{AB}`

One can stack font family, font weight, and font shape by using the `\textXX` versions of the font functions. So `\textsf{\textbf{H}}` will produce H\textsf{\textbf{H}}H. The other versions do not stack, e.g., `\mathsf{\mathbf{H}}` will produce H\mathsf{\mathbf{H}}H.

In cases where KaTeX fonts do not have a bold glyph, `\pmb` can simulate one. For example, `\pmb{\mu}` renders as : μ\pmb{\mu}μ

Size

AB\Huge ABAB `\Huge AB` | AB\normalsize ABAB `\normalsize AB`
AB\huge ABAB `\huge AB` | AB\small ABAB `\small AB`
AB\LARGE ABAB `\LARGE AB` | AB\footnotesize ABAB `\footnotesize AB`
AB\Large ABAB `\Large AB` | AB\scriptsize ABAB `\scriptsize AB`
AB\large ABAB `\large AB` | AB\tiny ABAB `\tiny AB`

Style

|∑i=1 n\displaystyle\sum_{i=1}^ni=1∑n​ `\displaystyle\sum_{i=1}^n` |∑i=1 n\textstyle\sum_{i=1}^n∑i=1n​ `\textstyle\sum_{i=1}^n` |x\scriptstyle xx `\scriptstyle x` (The size of a first sub/superscript) |x\scriptscriptstyle xx `\scriptscriptstyle x` (The size of subsequent sub/superscripts) |lim⁡x\lim\limits_xxlim​ `\lim\limits_x` |lim⁡x\lim\nolimits_xlimx​ `\lim\nolimits_x` |x^2\verb!x^2!x^2 `\verb!x^2!`

`\text{…}` will accept nested `$…$` fragments and render them in math mode.

## 12: Symbols and Punctuation ​

`% comment` | …\dots… `\dots` | KaTeX\KaTeXKATE​X `\KaTeX`
%\%% `\%` | ⋯\cdots⋯ `\cdots` | LaTeX\LaTeXLATE​X `\LaTeX`
#\## `\#` | ⋱\ddots⋱ `\ddots` | TeX\TeXTE​X `\TeX`
&\&& `\&` | …\ldots… `\ldots` | ∇\nabla∇ `\nabla`
_\__ `\_` | ⋮\vdots⋮ `\vdots` | ∞\infty∞ `\infty`
_\text{\textunderscore}_ `\text{\textunderscore}` | ⋯\dotsb⋯ `\dotsb` | ∞\infin∞ `\infin`
–\text{--}– `\text{--}` | …\dotsc… `\dotsc` | ✓\checkmark✓ `\checkmark`
–\text{\textendash}– `\text{\textendash}` | ⁣⋯\dotsi⋯ `\dotsi` | †\dag† `\dag`
—\text{---}— `\text{---}` | ⋯\dotsm⋯ `\dotsm` | †\dagger† `\dagger`
—\text{\textemdash}— `\text{\textemdash}` | …\dotso… `\dotso` | †\text{\textdagger}† `\text{\textdagger}`
~\text{\textasciitilde}~ `\text{\textasciitilde}` | ⋅\sdot⋅ `\sdot` | ‡\ddag‡ `\ddag`
‘`‘ ``` | …\mathellipsis… `\mathellipsis` | ‡\ddagger‡ `\ddagger`
‘\text{\textquoteleft}‘ `text{\textquoteleft}` | …\text{\textellipsis}… `\text{\textellipsis}` | ‡\text{\textdaggerdbl}‡ `\text{\textdaggerdbl}`
‘\lq‘ `\lq` | □\Box□ `\Box` | ‡\Dagger‡ `\Dagger`
’\text{\textquoteright}’ `\text{\textquoteright}` | □\square□ `\square` | ∠\angle∠ `\angle`
′\rq′ `\rq` | ■\blacksquare■ `\blacksquare` | ∡\measuredangle∡ `\measuredangle`
“\text{\textquotedblleft}“ `\text{\textquotedblleft}` | △\triangle△ `\triangle` | ∢\sphericalangle∢ `\sphericalangle`
""" `"` | ▽\triangledown▽ `\triangledown` | ⊤\top⊤ `\top`
”\text{\textquotedblright}” `\text{\textquotedblright}` | ◃\triangleleft◃ `\triangleleft` | ⊥\bot⊥ `\bot`
⁣:\colon: `\colon` | ▹\triangleright▹ `\triangleright` | $\$$ `\$`
‵\backprime‵ `\backprime` | ▽\bigtriangledown▽ `\bigtriangledown` | $\text{\textdollar}$ `\text{\textdollar}`
′\prime′ `\prime` | △\bigtriangleup△ `\bigtriangleup` | £\pounds£ `\pounds`
<\text{\textless}< `\text{\textless}` | ▲\blacktriangle▲ `\blacktriangle` | £\mathsterling£ `\mathsterling`
>\text{\textgreater}> `\text{\textgreater}` | ▼\blacktriangledown▼ `\blacktriangledown` | £\text{\textsterling}£ `\text{\textsterling}`
|\text{\textbar}| `\text{\textbar}` | ◀\blacktriangleleft◀ `\blacktriangleleft` | ¥\yen¥ `\yen`
∥\text{\textbardbl}∥ `\text{\textbardbl}` | ▶\blacktriangleright▶ `\blacktriangleright` | √\surd√ `\surd`
{\text{\textbraceleft}{ `\text{\textbraceleft}` | ⋄\diamond⋄ `\diamond` | °\degree° `\degree`
}\text{\textbraceright}} `\text{\textbraceright}` | ◊\Diamond◊ `\Diamond` | °\text{\textdegree}° `\text{\textdegree}`
¶\text{\P}¶ `\text{\P}` | ◊\lozenge◊ `\lozenge` | ℧\mho℧ `\mho`
§\text{\S}§ `\text{\S}` | ⧫\blacklozenge⧫ `\blacklozenge` | ╲\diagdown╲ `\diagdown`
§\text{\sect}§ `\text{\sect}` | ⋆\star⋆ `\star` | ╱\diagup╱ `\diagup`
©\copyrightc◯ `\copyright` | ★\bigstar★ `\bigstar` | ♭\flat♭ `\flat`
®\circledR® `\circledR` | ♣\clubsuit♣ `\clubsuit` | ♮\natural♮ `\natural`
®\text{\textregistered}R◯ `\text{\textregistered}` | ♣\clubs♣ `\clubs` | ♯\sharp♯ `\sharp`
Ⓢ\circledSⓈ `\circledS` | ♢\diamondsuit♢ `\diamondsuit` | ♡\heartsuit♡ `\heartsuit`
a◯\text{\textcircled a}a◯ `\text{\textcircled a}` | ♢\diamonds♢ `\diamonds` | ♡\hearts♡ `\hearts`
✠\maltese✠ `\maltese` | ♠\spadesuit♠ `\spadesuit` | ♠\spades♠ `\spades`

Direct Input: £¥∇∞⋅∠∡∢♠♡♢♣♭♮♯✓…⋮⋯⋱!£ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ … ⋮ ⋯ ⋱ !£¥∇∞⋅∠∡∢♠♡♢♣♭♮♯✓…⋮⋯⋱! ‼

## 13: Units ​

In KaTeX, units are proportioned as they are in TeX. KaTeX units are different than CSS units.

KaTeX Unit | Value | KaTeX Unit | Value
--- | --- | --- | ---
em | CSS em | bp | 1/72​ inch × F × G
ex | CSS ex | pc | 12 KaTeX pt
mu | 1/18 CSS em | dd | 1238/1157​ KaTeX pt
pt | 1/72.27 inch × F × G | cc | 14856/1157 KaTeX pt
mm | 1 mm × F × G | nd | 685/642 KaTeX pt
cm | 1 cm × F × G | nc | 1370/107​ KaTeX pt
in | 1 inch × F × G | sp | 1/65536 KaTeX pt

where:

- F = (font size of surrounding HTML text)/(10 pt)

- G = 1.21 by default, because KaTeX font-size is normally 1.21 × the surrounding font size. This value can be overridden by the CSS of an HTML page.

The effect of style and size:

Unit | textstyle | scriptscript | huge
--- | --- | --- | ---
em or ex | \rule{1em}{1em} | \scriptscriptstyle\rule{1em}{1em} | \huge\rule{1em}{1em}
mu | \rule{18mu}{18mu} | \scriptscriptstyle\rule{18mu}{18mu} | \huge\rule{18mu}{18mu}
others | \rule{10pt}{10pt} | \scriptscriptstyle\rule{10pt}{10pt} | \huge\rule{10pt}{10pt}