LaTeX Symbols - Lookup mathematical symbols, operations, relations, and arrows

Relations

Symbol and Macro	Negated Variant
$=$ =	$\ne$ \ne, \neq
$\approx$ \approx	$\not\approx$ \not\approx
$<$ <	$\nless$ \nless
$>$ >	$\ngtr$ \ngtr
$\le$ \le, \leq	$\nleqq$ \nleq
$\ge$ \ge, \geq	$\ngeqq$ \ngeq
$\triangleq$ \triangleq $:=$ \coloneqq
$\equiv$ \equiv	$\not\equiv$ \not\equiv
$\in$ \in	$\notin$ \notin
$\ni$ \ni	$\not\ni$ \not\ni1
$\subset$ \subset	$\not\subset$ \not\subset
$\supset$ \supset	$\not\supset$ \not\supset
$\subseteq$ \subseteq	$⊈$ \nsubseteq
$\supseteq$ \supseteq	$⊉$ \nsupseteq
$\sim$ \sim	$\nsim$ \nsim
$\ll$ \ll	$/\ll$ \not\ll
$\gg$ \gg	$/\gg$ \not\gg

Logical/Extensible Arrow

Arrow and Macro	Negated Variant
$⟹$ \implies $\stackrel{xxx}{\Rightarrow }$ \;\xRightarrow{xxx}\;	$=\nRightarrow$ \;=\!\nRightarrow\; $/⟹$ \mathrlap{\quad\not}\implies
$⟸$ \impliedby $\stackrel{xxx}{\Leftarrow }$ \;\xLeftarrow{xxx}\;	$\nLeftarrow =$ \;\nLeftarrow\!=\; $/⟸$ \mathrlap{\quad\not}\impliedby
$⟺$ \iff $\stackrel{xxx}{\iff }$ \;\xLeftrightarrow{xxx}\;	$\Leftarrow \nRightarrow$ \;\Leftarrow\!\nRightarrow\; $/⟺$ \mathrlap{\quad\not}\iff
$\to$ \to $\underset{yyy}{\overset{xxx}{\to }}$ \xrightarrow[yyy]{xxx}	$\nrightarrow$ \nrightarrow
$\leftarrow$ \gets $\stackrel{xxx}{\leftarrow }$ \xleftarrow{xxx}	$\nleftarrow$ \nleftarrow
$\leftrightarrow$ \leftrightarrow $\stackrel{xxx}{\leftrightarrow }$ \xleftrightarrow{xxx}	$\nleftrightarrow$ \nleftrightarrow
$\stackrel{xxx}{=}$ \xlongequal{xxx}
$\stackrel{xxx}{\mapsto }$ \xmapsto{xxx}

Regular Arrow

Arrow and Macro	Mirrored Version
$\circlearrowright$ \circlearrowright	$\circlearrowleft$ \circlearrowleft
$\curvearrowright$ \curvearrowright	$\curvearrowleft$ \curvearrowleft
$\Rsh$ \Rsh	$\Lsh$ \Lsh
$\to$ \to $⟶$ \longrightarrow $⇢$ \dashrightarrow	$\leftarrow$ \gets $⟵$ \longleftarrow $⇠$ \dashleftarrow
$\leftrightarrow$ \leftrightarrow $⟷$ \longleftrightarrow	$\updownarrow$ \updownarrow
$\nearrow$ \nearrow	$\searrow$ \searrow
$\downarrow$ \downarrow	$\uparrow$ \uparrow
$\nwarrow$ \nwarrow	$\swarrow$ \swarrow
$\Rightarrow$ \Rightarrow $⟹$ \Longrightarrow $⟹$ \implies	$\Leftarrow$ \Leftarrow $⟸$ \Longleftarrow $⟸$ \impliedby
$\Downarrow$ \Downarrow	$\Uparrow$ \Uparrow
$\iff$ \Leftrightarrow $⟺$ \Longleftrightarrow $⟺$ \iff	$\Updownarrow$ \Updownarrow

See more relations and arrows in external resources

• Relation Symbols from LaTeX math symbols
• Packages for Relations p. 67 or Arrows p. 94 from Comprehensive LaTeX Symbol List
• Arrows from KaTeX docs; Arrows from LaTeX math symbols

Generically negate/comment any relation

• negate $\not\equiv$ \not\equiv
• comment $\stackrel{\text{def}}{=}$ \overset{\text{def}}{=}, and see Comment equation operators

Operators

Operator and Macro	Similar Operator
$+$ +	$-$ -
$\cdot$ \cdot $\times$ \times	$/$ / $÷$ \div
$:$ :	${}^{\circ }$ ^\circ
$\mid$ \mid	$\parallel$ \parallel
$\cup$ \cup	$\cap$ \cap
$\setminus$ \setminus	$\neg$ \neq, lnot
$\wedge$ \land, \wedge	$\vee$ \lor, \vee
$\pm$ \pm $\mp$ \mp	$\bowtie$ \Join 2
$\Im$ \Im imaginary	$\Re$ \Re real
$\sum$ sum	$\prod$ \prod
$\int$ \int $\oint$ \oint	$\iint$ \iint $\iiint$ \iiint
$\bigcup$ \bigcup $⨄$ \biguplus	$\bigcap$ \bigcap
$\bigwedge$ \bigwedge	$\bigvee$ \bigvee

$$\begin{array}{c}\min \max \log \ln \det \lim \\ \sin \cos \tan \arcsin \arccos \arctan \\ x\sin \alpha ,x\sin (\alpha ),{\sin }^2\alpha ,\cancel{x\sin x,xsin()x}\\ \underset{a\to \infty }{\lim }{\lim }_{a\to \infty };{\sum }_0^{\infty }\sum _0^{\infty };pre-norm(){{\mathbb{P}}_0}_a^b()\end{array}\text{\hspace{1em}(1a)(1b)(1c)(1d)}$$

See more operators in external resources

• Operators or Big operators from KaTeX docs
• Packages for Operators p. 37 from Comprehensive LaTeX Symbol List
• Operator names ch. 2.12 p. 66 or create custom big operator mathchar ch. 3.2.7 p. 79 from Mathematical Typsetting with LaTeX by H. Voß

Operators with function name

• Use predefined operators \min - \sin - etc., see $(1a\text{-}\mathrm{b})$
• [p] Proper operators get correct right and left spacing compared to last two examples, see $(1c)$
• Create custom operator with text name \operatorname{pre-norm}() or math name \mathop{\mathbb{P}_0}_a^b(), see end of $(1d)$

Use limits, or exponents and indices $(1d)$

• Display mode defaults to limits; to force exponents and indices \lim\nolimits_0^1
• Text mode defaults to exponents and indices; to force limits \sum\limits_0^1
• See Follow varying typographic conventions with the same input syntax

Greek Letters

Lower Case	Upper Case
$\alpha$ \alpha	$\mathrm{A}$ A
$\beta$ \beta	$\mathrm{B}$ B
$\gamma$ \gamma	$\Gamma$ \Gamma $\Gamma$ \varGamma
$\delta$ \delta	$\Delta$ \Delta $\Delta$ \varDelta
$\epsilon$ \varepsilon $ϵ$ \epsilon	$\mathrm{E}$ E
$\zeta$ \zeta	$\mathrm{Z}$ Z
$\eta$ \eta	$\mathrm{H}$ H
$\theta$ \theta $\vartheta$ \vartheta	$\Theta$ \Theta $\Theta$ \varTheta
$\iota$ \iota	$\mathrm{I}$ I
$\kappa$ \kappa ${\varkappa }^1$ \varkappa	$\mathrm{K}$ K
$\lambda$ \lambda	$\Lambda$ \Lambda $\Lambda$ \varLambda
$\mu$ \mu	$\mathrm{M}$ M
$\nu$ \nu	$\mathrm{N}$ N
$\xi$ \xi	$\Xi$ \Xi $\Xi$ \varXi
$o$ o	$\mathrm{O}$ O
$\pi$ \pi $\varpi$ \varpi	$\Pi$ \Pi $\Pi$ \varPi
$\rho$ \rho $\varrho$ \varrho	$\mathrm{P}$ P
$\sigma$ \sigma $\varsigma$ \varsigma	$\Sigma$ \Sigma $\Sigma$ \varSigma
$\tau$ \tau	$\mathrm{T}$ T
$\upsilon$ \upsilon	${\rm Y}$ \Upsilon ${\rm Y}$ \varUpsilon
$\phi$ \varphi $\varphi$ \phi	$\Phi$ \Phi $\Phi$ \varPhi
$\chi$ \chi	$\mathrm{X}$ X
$\psi$ \psi	$\Psi$ \Psi $\Psi$ \varPsi
$\omega$ \omega	$\Omega$ \Omega $\Omega$ \varOmega
$ϝ$ \digamma 3

Delimiters

$$\begin{array}{ccc}(x)\left(\sqrt{2}\right)& e^{x^2}\uparrow & \left\{x|x>\frac{1}{2}\right\}\\ ((\left(\right((& \left[\begin{array}{cc}a& b\\ c& d\end{array}\right]& \left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\end{array}\text{\hspace{1em}(2a,2b,2c)(2d,2e,2f)}$$

• Use default size (…) or auto scale to enclosed content \left(…\right), see $(2a)$
• Enclose with a blank delimiter \left.…\right\uparrow, see $(2b)$
• Enclose with a middle delimiter \left\{…\;\middle\vert\;…\right\}, see $(2c)$
• Manually set size \big( - \Big( - \bigg( - \Bigg(, see $(2d)$
• Use matrix with auto scaled delimiters: \begin{matrix} a&b\\c&d \end{matrix}, see $(2e)$
  $()$ pmatrix - $[]$ bmatrix - $\{\}$ Bmatrix - $||$ vmatrix - $\Vert \Vert$ Vmatrix
• Use smaller matrix variant, see $(2f)$:

\left[ \begin{smallmatrix} a&b\\c&d \end{smallmatrix} \right]

$$()⟮⟯[]\{\}||\Vert \Vert \lfloor \rfloor \lceil \rceil ⟨⟩┌┐└┘\uparrow \downarrow \updownarrow \Updownarrow \Uparrow \Downarrow$$

Math	Markup
$(x),\left(\genfrac{}{}{0ex}{}{n}{k}\right),\left(\genfrac{}{}{0ex}{}{n}{k}\right)$	(…) ; \binom{n}{k} ; {n \choose k}
$⟮x⟯$	\lgroup…\rgroup
$[x],\left[\genfrac{}{}{0ex}{}{n}{k}\right]$	[…] ; {n \brack k}
$\{x\},\left\{\genfrac{}{}{0ex}{}{n}{k}\right\}$	\{…\} ; {n \brace k}
$|x|$	\vert…\vert
$x\mid x\in \mathbb{N}$	…\mid…
$\left\{x|x>\frac{1}{2}\right\}$	\left\{…\;\middle\vert\;…\right\}
$\Vert \vec{x}\Vert$	\Vert…\Vert
$AB\parallel CD$	…\parallel…
$\lfloor x\rfloor$	\lfloor…\rfloor
$\lceil x\rceil$	\lceil…\rceil
$⟨x⟩$	\langle…\rangle
${}_1^2,\genfrac{}{}{0ex}{}{2}{1}$	{_1^2} ; {2 \atop 1}

See more delimiters in external resources

• Delimiters from KaTeX docs

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Sources:

• 2022-06-10: The Not So Short Introduction to LaTeX2e
• 2022-06-10: LaTeX Math Symbols Cheat Sheet - Kapeli
• 2022-06-10: LaTeX Math for Undergrads
• 2022-06-10: List of mathematical symbols by subject - Wikipedia

Related:
Vary the style of mathematical symbols - ϖ vs π
Other LaTeX symbols

Tags:
Values - Standardize math, numbers, symbols, quantities, money
Graphical elements - Standardize tables, images, plots
LaTeX

Footnotes

1. the macros \notni isn’t supported by MathJax ↩

2. improved by latexsym ↩

3. requires amssymb ↩