Latex symbols list

Set construction

Symbol		Usage	LaTex
${\displaystyle \varnothing }$ ${\displaystyle \mathrm{\varnothing }}$	∅		\varnothing, \emptyset
${\displaystyle \{\}}$	{ }	${\displaystyle \{a,b,\dots \}}$	\{ \}
${\displaystyle \mid }$	|	${\displaystyle \{a\mid T(a)\}}$	\mid
${\displaystyle :}$	:	${\displaystyle \{a:T(a)\}}$	\colon

Set operations

Symbol		Usage	LaTex
${\displaystyle \cup }$	∪	${\displaystyle A\cup B}$	\cup
${\displaystyle \bigcup }$	⋃	${\displaystyle \bigcup }$	\bigcup
${\displaystyle \cap }$	∩	${\displaystyle A\cap B}$	\cap
${\displaystyle \bigcap }$	⋂	${\displaystyle \bigcap }$	\bigcap
${\displaystyle \setminus }$	∖	${\displaystyle A\setminus B}$	\setminus
${\displaystyle \mathrm{△}}$	∆	${\displaystyle A\mathrm{△}B}$	\triangle
${\displaystyle \times }$	⨯	${\displaystyle A\times B}$	\times
${\displaystyle \dot{\cup }}$	⊍	${\displaystyle A\dot{\cup }B}$	\dot\cup
${\displaystyle \uplus }$	⊎	${\displaystyle A\uplus B}$	\uplus
${\displaystyle \bigsqcup }$	⊔	${\displaystyle A\bigsqcup B}$	\sqcup
${\displaystyle \dot{\cap }}$	⩀	${\displaystyle A\dot{\cap }B}$	\dot\cap
${\displaystyle \sqcap }$	⊓	${\displaystyle A\sqcap B}$	\sqcap
${\displaystyle {}^{\mathrm{C}}}$	∁	${\displaystyle A^{\mathrm{C}}}$	\mathrm{C}
${\displaystyle \overline{}}$	◌̄	${\displaystyle \overline{z}}$	\bar
${\displaystyle \stackrel{―}{}}$	◌̅	${\displaystyle \bar{A}}$	\overline{A}
${\displaystyle \mathcal{P}}$	𝒫	${\displaystyle \mathcal{P}(A)}$	\mathcal{P}
${\displaystyle \mathfrak{P}}$	𝔓	${\displaystyle \mathfrak{P}(A)}$	\mathfrak{P}
${\displaystyle \mathrm{\wp }}$	℘	${\displaystyle \mathrm{\wp }(A)}$	\wp
${\displaystyle \bigwedge }$	⋀	${\displaystyle {\bigwedge }_{x\in A}}$	\bigwedge
${\displaystyle \bigvee }$	⋁	${\displaystyle {\bigvee }_{x\in A}}$	\bigvee

Set relations

Symbol		Usage	LaTex
${\displaystyle \subset }$	⊂	${\displaystyle A\subset B}$	\subset
${\displaystyle ⊊}$	⊊	${\displaystyle A⊊B}$	\subsetneq
${\displaystyle \subseteq }$	⊆	${\displaystyle A\subseteq B}$	\subseteq
${\displaystyle \supset }$	⊃	${\displaystyle A\supset B}$	\supset
${\displaystyle ⊋}$	⊋	${\displaystyle A⊋B}$	\supsetneq
${\displaystyle \supseteq }$	⊇	${\displaystyle A\supseteq B}$	\supseteq
${\displaystyle \not\subset }$	⊄	${\displaystyle A\not\subset B}$	\not\subset
${\displaystyle \not\supset }$	⊅	${\displaystyle A\not\supset B}$	\not\supset
${\displaystyle ⊈}$	⊈	${\displaystyle A⊈B}$	\not\subseteq
${\displaystyle ⊉}$	⊉	${\displaystyle A⊉B}$	\not\supseteq
${\displaystyle \in }$	∈	${\displaystyle a\in A}$	\in
${\displaystyle \ni }$	∋	${\displaystyle A\ni a}$	\ni, \owns
${\displaystyle \notin }$	∉	${\displaystyle a\notin A}$	\notin
${\displaystyle \not\ni }$	∌	${\displaystyle A\not\ni a}$	\not\ni
${\displaystyle ⊏}$	⊏	${\displaystyle A⊏B}$	\sqsubset
${\displaystyle ⊐}$	⊐	${\displaystyle A⊐B}$	\sqsupset
${\displaystyle ⊑}$	⊑	${\displaystyle A⊑B}$	\sqsubseteq
${\displaystyle ⊒}$	⊒	${\displaystyle A⊒B}$	\sqsupseteq

Arithmetic operators

Symbol		Usage	LaTex
${\displaystyle +}$	+	${\displaystyle a+b}$	+
${\displaystyle -}$	−	${\displaystyle a-b}$	-
${\displaystyle \cdot }$	⋅	${\displaystyle a\cdot b}$	\cdot
${\displaystyle \times }$	⨯	${\displaystyle a\times b}$	\times
${\displaystyle :}$	: or ∶	${\displaystyle a:b}$	:
${\displaystyle /}$	∕	${\displaystyle a/b}$	/
${\displaystyle ÷}$	÷	${\displaystyle a÷b}$	\div
	⁄	${\displaystyle \frac{a}{b}}$	\frac
${\displaystyle -}$	−	${\displaystyle -a}$	-
${\displaystyle \pm }$	±	${\displaystyle \pm a}$	\pm
${\displaystyle \mp }$	∓	${\displaystyle \mp a}$	\mp
${\displaystyle ()}$	( )	${\displaystyle (a)}$	( )
${\displaystyle []}$	[ ]	${\displaystyle [a]}$	[ ]

Equality signs

Symbol		Usage	LaTex
${\displaystyle =}$	=	${\displaystyle a=b}$	=
${\displaystyle \ne }$	≠	${\displaystyle a\ne b}$	\neq
${\displaystyle \equiv }$	≡	${\displaystyle a\equiv b}$	\equiv
${\displaystyle \approx }$	≈	${\displaystyle a\approx b}$	\approx
${\displaystyle \sim }$	∼	${\displaystyle a\sim b}$	\sim
${\displaystyle \propto }$	∝	${\displaystyle a\propto b}$	\propto
${\displaystyle \widehat{=}}$	≙	${\displaystyle a\widehat{=}b}$	\widehat{=}
${\displaystyle \stackrel{?}{=}}$	≟	${\displaystyle a\stackrel{?}{=}b}$	\overset{?}{=}
${\displaystyle \stackrel{\mathrm{def}}{=}}$	≝	${\displaystyle a\stackrel{\mathrm{def}}{=}b}$	\overset{\operatorname{def}}{=}
${\displaystyle \triangleq }$	≜	${\displaystyle a\triangleq b}$	\triangleq
${\displaystyle \doteq }$	≐	${\displaystyle x_n\doteq b}$	\doteq

Comparison

Symbol		Usage	LaTex
${\displaystyle <}$	<	${\displaystyle a<b}$	<
${\displaystyle >}$	>	${\displaystyle a>b}$	>
${\displaystyle \le }$	≤	${\displaystyle a\le b}$	\le, \leq
${\displaystyle \ge }$	≥	${\displaystyle a\ge b}$	\ge, \geq
${\displaystyle \leqq }$	≦	${\displaystyle a\leqq b}$	\leqq
${\displaystyle \geqq }$	≧	${\displaystyle a\geqq b}$	\geqq
${\displaystyle ⩽}$	⩽	${\displaystyle a⩽b}$	\leqslant
${\displaystyle ⩾}$	⩾	${\displaystyle a⩾b}$	\geqslant
${\displaystyle \ll }$	≪	${\displaystyle a\ll b}$	\ll
${\displaystyle \gg }$	≫	${\displaystyle a\gg b}$	\gg
${\displaystyle \lesssim }$	≲	${\displaystyle a\lesssim b}$	\lesssim
${\displaystyle \gtrsim }$	≳	${\displaystyle a\gtrsim b}$	\gtrsim
${\displaystyle ⪅}$	⪅	${\displaystyle a⪅b}$	\lessapprox
${\displaystyle ⪆}$	⪆	${\displaystyle a⪆b}$	\gtrapprox

Divisibility and modulo

Symbol		Usage	LaTex
${\displaystyle \mid }$	∣	${\displaystyle a\mid b}$	\mid
${\displaystyle \nmid }$	∤	${\displaystyle a\nmid b}$	\nmid
${\displaystyle \perp }$	⊥	${\displaystyle a\perp b}$	\perp
${\displaystyle \sqcap }$	⊓	${\displaystyle a\sqcap b}$	\sqcap
${\displaystyle \wedge }$	∧	${\displaystyle a\wedge b}$	\wedge
${\displaystyle \bigsqcup }$	⊔	${\displaystyle a\bigsqcup b}$	\sqcup
${\displaystyle \vee }$	∨	${\displaystyle a\vee b}$	\vee
${\displaystyle \equiv }$	≡	${\displaystyle a\equiv b}$	\equiv

Mathematical constants

Symbol		LaTex
${\displaystyle \pi }$	π	\pi
${\displaystyle e}$	e	e
${\displaystyle \varphi }$	ϕ	\phi
${\displaystyle \phi }$	φ	\varphi
${\displaystyle i}$	i	i
${\displaystyle \gamma }$	γ	\gamma
${\displaystyle ϵ}$	ε	\epsilon
${\displaystyle \epsilon }$	ϵ	\varepsilon
${\displaystyle \theta }$	θ	\theta
${\displaystyle \vartheta }$	ϑ	\vartheta
${\displaystyle \sigma }$	σ	\sigma
${\displaystyle \varsigma }$	ς	\varsigma
${\displaystyle \kappa }$	κ	\kappa
${\displaystyle \lambda }$	λ	\lambda
${\displaystyle \mu }$	μ	\mu
${\displaystyle \tau }$	τ	\tau

Calculus

Symbol		Usage	LaTex
${\displaystyle \sum }$	∑	${\displaystyle \sum _{i=1}^n,\sum _{i\in I}}$	\sum
${\displaystyle \prod }$	∏	${\displaystyle \prod _{i=1}^n,\prod _{i\in I}}$	\prod
${\displaystyle \coprod }$	∐	${\displaystyle \coprod _{i=1}^n,\coprod _{i\in I}}$	\coprod
${\displaystyle ()}$	( )	${\displaystyle (a_n)}$	( )
${\displaystyle \to }$	→	${\displaystyle a_n\to a}$	\to \rarr
${\displaystyle \mathrm{\infty }}$	∞	${\displaystyle n\to \mathrm{\infty }}$	\infty

Functions

Symbol		Usage	LaTex
${\displaystyle \to }$	→	${\displaystyle f:A\to B}$	\to
		${\displaystyle A\stackrel{f}{\to }B}$
${\displaystyle \mapsto }$	↦	${\displaystyle f:x\mapsto y}$	\mapsto
		${\displaystyle x\stackrel{f}{\mapsto }y}$
${\displaystyle ()}$	( )	${\displaystyle f(x)}$	( )
		${\displaystyle f(X)}$
${\displaystyle []}$	[ ]	${\displaystyle f[X]}$	[ ]
${\displaystyle |}$	|	${\displaystyle f{|}_X}$	\vert
${\displaystyle \cdot }$	⋅	${\displaystyle f(\cdot )}$	\cdot
${\displaystyle {}^{-1}}$	⁻	${\displaystyle f^{-1}}$	-1
${\displaystyle \circ }$	∘	${\displaystyle f\circ g}$	\circ
${\displaystyle \ast }$	∗	${\displaystyle f\ast g}$	\ast
${\displaystyle \hat{}}$	◌̂	${\displaystyle \hat{f}}$	\hat

Limits

Symbol		Usage	LaTex
${\displaystyle \to }$	→	${\displaystyle \underset{x\to a}{lim}f(x)}$	\to or \rightarrow
${\displaystyle ⟶}$	⟶	${\displaystyle x⟶a}$	\longrightarrow
${\displaystyle \uparrow }$	↑	${\displaystyle \underset{x\uparrow a}{lim}f(x)}$	\uparrow
${\displaystyle \nearrow }$	↗	${\displaystyle \underset{x\nearrow a}{lim}f(x)}$	\nearrow
${\displaystyle \searrow }$	↘	${\displaystyle \underset{x\searrow a}{lim}f(x)}$	\searrow
${\displaystyle \downarrow }$	↓	${\displaystyle \underset{x\downarrow a}{lim}f(x)}$	\downarrow
${\displaystyle \swarrow }$	↙	${\displaystyle a\swarrow x}$	\swarrow
${\displaystyle \leftarrow }$	←	${\displaystyle a\leftarrow x}$	\leftarrow
${\displaystyle ⟵}$	⟵	${\displaystyle a⟵x}$	\longleftarrow
${\displaystyle \nwarrow }$	↖	${\displaystyle a\nwarrow x}$	\nwarrow
${\displaystyle {}^{+}}$	⁺	${\displaystyle \underset{x\to a^{+}}{lim}f(x)}$	^+
${\displaystyle {}^{-}}$	⁻	${\displaystyle \underset{x\to a^{-}}{lim}f(x)}$	^-

Asymptotic behaviour

Symbol		Usage	LaTex
${\displaystyle \sim }$	∼	${\displaystyle f\sim }$	\sim
${\displaystyle o}$	o	${\displaystyle f\in o(g)}$	o
${\displaystyle \mathcal{O}}$	𝒪	${\displaystyle f\in \mathcal{O}(g)}$	\mathcal{O}
${\displaystyle \mathrm{\Theta }}$	Θ	${\displaystyle f\in \mathrm{\Theta }(g)}$	\Theta
${\displaystyle \mathrm{\Omega }}$	Ω	${\displaystyle f\in \mathrm{\Omega }(g)}$	\Omega
${\displaystyle \omega }$	ω	${\displaystyle f\in \omega (g)}$	\omega

Differential calculus

Symbol		Usage	LaTex
${\displaystyle {}^{\prime }}$ ${\displaystyle {}^{\prime }}$	′	${\displaystyle f^{\prime }}$ ${\displaystyle f^{\prime }}$	' ^\prime
${\displaystyle {}^{″}}$ ${\displaystyle {}^{\prime \prime }}$	″	${\displaystyle f^{″}}$ ${\displaystyle f^{\prime \prime }}$	'' ^{\prime\prime}
${\displaystyle {}^{‴}}$ ${\displaystyle {}^{\prime \prime \prime }}$	‴	${\displaystyle f^{‴}}$ ${\displaystyle f^{\prime \prime \prime }}$	''' ^{\prime\prime\prime}
${\displaystyle {}^{⁗}}$ ${\displaystyle {}^{\prime \prime \prime \prime }}$	⁗	${\displaystyle f^{⁗}}$ ${\displaystyle f^{\prime \prime \prime \prime }}$	'''' ^{\prime\prime\prime\prime}
${\displaystyle {}^{IV}{}^V{}^{VI}}$		${\displaystyle f^{IV},f^V,f^{VI}}$	^{IV} ^V ^{VI}
${\displaystyle {}^{iv}{}^v{}^{vi}}$		${\displaystyle f^{iv},f^v,f^{vi}}$	^{iv} ^v ^{vi}
${\displaystyle {}^{()}}$	⁽ ⁾	${\displaystyle f^{(4)},f^{(5)},f^{(n)}}$	^{( )}
${\displaystyle \dot{}}$	◌̇	${\displaystyle \dot{f}}$	\dot
${\displaystyle \ddot{}}$	◌̈	${\displaystyle \ddot{f}}$	\ddot
${\displaystyle d}$	d	${\displaystyle dx}$	d
		${\displaystyle \frac{df}{dx}}$
		${\displaystyle \frac{d}{dx}f}$
		${\displaystyle \frac{d^2}{d{x}^2}f}$
		${\displaystyle df}$
${\displaystyle \partial }$	∂	${\displaystyle \frac{\partial f}{\partial x}}$	\partial

Integral calulus

Symbol		Usage	LaTex
${\displaystyle \int }$	∫	${\displaystyle \int _{a}^{b}} , {\displaystyle \int _{G}}$	\int
${\displaystyle \iint }$	∬	${\displaystyle {\iint }_{\mathcal{F}}}$	\iint
${\displaystyle \iiint }$	∭	${\displaystyle {\iiint }_V}$	\iiint
${\displaystyle \oint }$	∮	${\displaystyle {\oint }_{\gamma }}$	\oint
${\displaystyle \text{oiint}}$	∯	${\displaystyle {\text{oiint}}_{\gamma }}$	\oiint

Vector calulus

Symbol		Usage	LaTex
${\displaystyle \mathrm{\nabla }}$	∇	${\displaystyle \mathrm{\nabla }f}$	\nabla
		${\displaystyle \mathrm{\nabla }\cdot F}$
		${\displaystyle \mathrm{\nabla }\times F}$
${\displaystyle \mathrm{\Delta }}$	∆	${\displaystyle \mathrm{\Delta }f}$	\Delta
${\displaystyle ◻}$	□	${\displaystyle ◻f}$	\square

Topology

Symbol		Usage	LaTex
${\displaystyle \partial }$	∂	${\displaystyle \partial U}$	\partial
${\displaystyle {}^{\circ }}$	˚	${\displaystyle U^{\circ }}$	\circ
${\displaystyle \overline{}}$	◌̄	${\displaystyle \overline{z}}$	\bar
${\displaystyle \stackrel{―}{}}$	◌̅	${\displaystyle \bar{z}}$	\overline
${\displaystyle \dot{}}$	◌̇	${\displaystyle \dot{U}(x)}$	\dot

Elementary geometry

Symbol		Usage	LaTex
${\displaystyle []}$	[ ]	${\displaystyle [AB]}$	[ ] \left[ \right]
${\displaystyle ||}$	| |	${\displaystyle |AB|}$	\vert
${\displaystyle \stackrel{―}{}}$	̅	${\displaystyle \overline{AB}}$	\overline
${\displaystyle \underset{―}{}}$	̲	${\displaystyle \underset{―}{AB}}$	\underline
${\displaystyle \overrightarrow{}}$	⃗	${\displaystyle \overrightarrow{AB}}$	\vec
${\displaystyle \mathrm{\angle }}$	∠	${\displaystyle \mathrm{\angle }ABC}$	\angle
${\displaystyle \mathrm{△}}$	△	${\displaystyle \mathrm{△}ABC}$	\triangle
${\displaystyle ◻}$	□	${\displaystyle ◻\mathit{ABCD}}$	\square
${\displaystyle \parallel }$	∥	${\displaystyle g\parallel h}$	\parallel
{\displaystyle \nparallel }	∦	{\displaystyle g\nparallel h}	\nparallel
{\displaystyle \perp }	⟂	{\displaystyle g\perp h}	\perp

Vectors and matrices

${\displaystyle \left(\begin{array}{c}{v}_1,\dots ,v_n\end{array}\right)}$	$$\left(\begin{array}{c}...\end{array}\right)$$ or \left( $$\begin{array}{}...\end{array}$$ \right)
${\displaystyle \left(\begin{array}{c}{v}_1\\ ⋮\\ v_m\end{array}\right)}$
${\displaystyle \left(\begin{array}{ccc}{a}_{11}& \dots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{m1}& \dots & a_{mn}\end{array}\right)}$

Vector calculus

Symbol		Usage	LaTex
${\displaystyle \cdot }$	⋅	${\displaystyle v\cdot w}$	\cdot
${\displaystyle ()}$	( )	${\displaystyle (v,w)}$	( )
${\displaystyle ⟨⟩}$	⟨ ⟩	${\displaystyle ⟨v,w⟩}$ ${\displaystyle ⟨v|w⟩}$	\langle \rangle
${\displaystyle \times }$	⨯	${\displaystyle v\times w}$	\times
${\displaystyle []}$	[ ]	${\displaystyle [v,w]}$	[ ]
${\displaystyle ()}$	( )	${\displaystyle (u,v,w)}$	( )
${\displaystyle \otimes }$	⊗	${\displaystyle v\otimes w}$	\otimes
${\displaystyle \wedge }$	∧	${\displaystyle v\wedge w}$	\wedge
${\displaystyle ||}$	| |	${\displaystyle |v|}$	\vert
${\displaystyle \Vert \Vert }$	‖	${\displaystyle \Vert v\Vert }$	\Vert, \|
${\displaystyle \hat{}}$	̂	${\displaystyle \hat{v}}$	\hat{}

Matrix calulus

Symbol		Usage	LaTex
${\displaystyle \cdot }$	⋅	${\displaystyle A\cdot B}$	\cdot
${\displaystyle \circ }$	∘	${\displaystyle A\circ B}$	\circ
${\displaystyle \oslash }$	⊘	${\displaystyle A\oslash B}$	\oslash
${\displaystyle \otimes }$	⊗	${\displaystyle A\otimes B}$	\otimes
${\displaystyle {}^{\mathrm{T}}}$	T	${\displaystyle A^{\mathrm{T}}}$	^T
${\displaystyle {}^{⊺}}$	⊺	${\displaystyle A^{⊺}}$	\intercal
${\displaystyle {}^{\mathrm{H}}}$	H	${\displaystyle A^{\mathrm{H}}}$	^H
${\displaystyle {}^{\ast }}$	*	${\displaystyle A^{\ast }}$	\ast
${\displaystyle {}^{†}}$	†	${\displaystyle A^{†}}$	\dagger
${\displaystyle {}^{-1}}$	⁻	${\displaystyle A^{-1}}$	-1
${\displaystyle {}^{+}}$	+	${\displaystyle A^{+}}$	+
${\displaystyle ||}$	| A |	${\displaystyle |A|}$	\vert
{\displaystyle \|~~\|}	‖	{\displaystyle \|A\|}	\Vert, \|

 

Symbol		Usage	LaTex
${\displaystyle \circ }$	∘	${\displaystyle R\circ S}$	\circ
		${\displaystyle a\circ b}$
${\displaystyle \bullet }$	•	${\displaystyle a\bullet b}$	\bullet
${\displaystyle \ast }$	∗	${\displaystyle a\ast b}$	\ast
${\displaystyle /}$	/	${\displaystyle M/\sim }$	/
${\displaystyle {}^{-1}}$	⁻	${\displaystyle R^{-1}}$	-1
${\displaystyle {}^{+}}$	+	${\displaystyle R^{+}}$	+
${\displaystyle {}^{\ast }}$	*	${\displaystyle R^{\ast }}$	\ast