Latex symbols list

Set construction

Symbol		Usage	LaTex
${\displaystyle \varnothing }$ ${\displaystyle \emptyset }$	∅		\varnothing, \emptyset
${\displaystyle \{~\}}$	{ }	${\displaystyle \{a,b,\ldots \}}$	\{ \}
${\displaystyle \mid }$	|	${\displaystyle \{a\mid T(a)\}}$	\mid
${\displaystyle \colon }$	:	${\displaystyle \{a\,\colon T(a)\}}$	\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
${\displaystyle \triangle }$	∆	${\displaystyle A\,\triangle \,B}$	\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
${\displaystyle \sqcup }$	⊔	${\displaystyle A\sqcup B}$	\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}
${\displaystyle {\bar {~}}}$	◌̄	${\displaystyle {\bar {z}}}$	\bar
${\displaystyle {\overline {~~}}}$	◌̅	${\displaystyle {\overline {A}}}$	\overline{A}
${\displaystyle {\mathcal {P}}}$	𝒫	${\displaystyle {\mathcal {P}}(A)}$	\mathcal{P}
${\displaystyle {\mathfrak {P}}}$	𝔓	${\displaystyle {\mathfrak {P}}(A)}$	\mathfrak{P}
${\displaystyle \wp }$	℘	${\displaystyle \wp (A)}$	\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
${\displaystyle \subsetneq }$	⊊	${\displaystyle A\subsetneq B}$	\subsetneq
${\displaystyle \subseteq }$	⊆	${\displaystyle A\subseteq B}$	\subseteq
${\displaystyle \supset }$	⊃	${\displaystyle A\supset B}$	\supset
${\displaystyle \supsetneq }$	⊋	${\displaystyle A\supsetneq B}$	\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
${\displaystyle \not \subseteq }$	⊈	${\displaystyle A\not \subseteq B}$	\not\subseteq
${\displaystyle \not \supseteq }$	⊉	${\displaystyle A\not \supseteq B}$	\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
${\displaystyle \sqsubset }$	⊏	${\displaystyle A\sqsubset B}$	\sqsubset
${\displaystyle \sqsupset }$	⊐	${\displaystyle A\sqsupset B}$	\sqsupset
${\displaystyle \sqsubseteq }$	⊑	${\displaystyle A\sqsubseteq B}$	\sqsubseteq
${\displaystyle \sqsupseteq }$	⊒	${\displaystyle A\sqsupseteq B}$	\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 ∶	${\displaystyle a:b}$	:
${\displaystyle /}$	∕	${\displaystyle a/b}$	/
${\displaystyle \div }$	÷	${\displaystyle a\div b}$	\div
${\displaystyle {\frac {~~}{~~}}}$	⁄	${\displaystyle {\tfrac {a}{b}}}$	\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
${\displaystyle =}$	=	${\displaystyle a=b}$	=
${\displaystyle \neq }$	≠	${\displaystyle a\neq b}$	\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{=}
${\displaystyle {\overset {?}{=}}}$	≟	${\displaystyle a\,{\overset {?}{=}}\,b}$	\overset{?}{=}
${\displaystyle {\overset {\operatorname {def} }{=}}}$	≝	${\displaystyle a\,{\overset {\operatorname {def} }{=}}\,b}$	\overset{\operatorname{def}}{=}
${\displaystyle \triangleq }$	≜	${\displaystyle a\,\triangleq \,b}$	\triangleq
${\displaystyle \doteq }$	≐	${\displaystyle x_{n}\,\doteq \,b}$	\doteq

Comparison

Symbol		Usage	LaTex
${\displaystyle <}$	<	${\displaystyle a<b}$	<
${\displaystyle >}$	>	${\displaystyle a>b}$	>
${\displaystyle \leq }$	≤	${\displaystyle a\leq b}$	\le, \leq
${\displaystyle \geq }$	≥	${\displaystyle a\geq b}$	\ge, \geq
${\displaystyle \leqq }$	≦	${\displaystyle a\leqq b}$	\leqq
${\displaystyle \geqq }$	≧	${\displaystyle a\geqq b}$	\geqq
${\displaystyle \leqslant }$	⩽	${\displaystyle a\leqslant b}$	\leqslant
${\displaystyle \geqslant }$	⩾	${\displaystyle a\geqslant b}$	\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
${\displaystyle \lessapprox }$	⪅	${\displaystyle a\lessapprox b}$	\lessapprox
${\displaystyle \gtrapprox }$	⪆	${\displaystyle a\gtrapprox b}$	\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
${\displaystyle \sqcup }$	⊔	${\displaystyle a\sqcup b}$	\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
${\displaystyle \phi }$	ϕ	\phi
${\displaystyle \varphi }$	φ	\varphi
${\displaystyle i}$	i	i
${\displaystyle \gamma }$	γ	\gamma
${\displaystyle \epsilon }$	ε	\epsilon
${\displaystyle \varepsilon }$	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
${\displaystyle \infty }$	∞	${\displaystyle n\to \infty }$	\infty

Functions

Symbol		Usage	LaTex
${\displaystyle \to }$	→	${\displaystyle f\colon A\to B}$	\to
		${\displaystyle A\,{\stackrel {f}{\to }}\,B}$
${\displaystyle \mapsto }$	↦	${\displaystyle f\colon x\mapsto y}$	\mapsto
		${\displaystyle x\,{\stackrel {f}{\mapsto }}\,y}$
${\displaystyle (~~)}$	( )	${\displaystyle f(x)}$	( )
		${\displaystyle f(X)}$
${\displaystyle [~~]}$	[ ]	${\displaystyle f[X]}$	[ ]
${\displaystyle \vert }$	|	${\displaystyle f\vert _{X}}$	\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
${\displaystyle \to }$	→	${\displaystyle \lim _{x\to a}f(x)}$	\to or \rightarrow
${\displaystyle \longrightarrow }$	⟶	${\displaystyle x\longrightarrow a}$	\longrightarrow
${\displaystyle \uparrow }$	↑	${\displaystyle \lim _{x\uparrow a}f(x)}$	\uparrow
${\displaystyle \nearrow }$	↗	${\displaystyle \lim _{x\nearrow a}f(x)}$	\nearrow
${\displaystyle \searrow }$	↘	${\displaystyle \lim _{x\searrow a}f(x)}$	\searrow
${\displaystyle \downarrow }$	↓	${\displaystyle \lim _{x\downarrow a}f(x)}$	\downarrow
${\displaystyle \swarrow }$	↙	${\displaystyle a\swarrow x}$	\swarrow
${\displaystyle \leftarrow }$	←	${\displaystyle a\leftarrow x}$	\leftarrow
${\displaystyle \longleftarrow }$	⟵	${\displaystyle a\longleftarrow x}$	\longleftarrow
${\displaystyle \nwarrow }$	↖	${\displaystyle a\nwarrow x}$	\nwarrow
${\displaystyle ^{+}}$	⁺	${\displaystyle \lim _{x\to a^{+}}f(x)}$	^+
${\displaystyle ^{-}}$	⁻	${\displaystyle \lim _{x\to a^{-}}f(x)}$	^-

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}
${\displaystyle \Theta }$	Θ	${\displaystyle f\in \Theta (g)}$	\Theta
${\displaystyle \Omega }$	Ω	${\displaystyle f\in \Omega (g)}$	\Omega
${\displaystyle \omega }$	ω	${\displaystyle f\in \omega (g)}$	\omega

Differential calculus

Symbol		Usage	LaTex
${\displaystyle {}'}$ ${\displaystyle {}^{\prime }}$	′	${\displaystyle f'}$ ${\displaystyle f^{\prime }}$	' ^\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
		${\displaystyle {\frac {df}{dx}}}$
		${\displaystyle {\frac {d}{dx}}f}$
		${\displaystyle {\frac {d^{2}}{dx^{2}}}f}$
		${\displaystyle df}$
${\displaystyle \partial }$	∂	${\displaystyle {\frac {\partial f}{\partial x}}}$	\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
${\displaystyle \oiint }$	∯	${\displaystyle \oiint _{\gamma }}$	\oiint

Vector calulus

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

Topology

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

Elementary geometry

Symbol		Usage	LaTex
${\displaystyle [~~]}$	[ ]	${\displaystyle [AB]}$	[ ] \left[ \right]
${\displaystyle |~~|}$	| |	${\displaystyle |AB|}$	\vert
${\displaystyle {\overline {~~}}}$	̅	${\displaystyle {\overline {AB}}}$	\overline
${\displaystyle {\underline {~~}}}$	̲	${\displaystyle {\underline {AB}}}$	\underline
${\displaystyle {\overrightarrow {~~}}}$	⃗	${\displaystyle {\overrightarrow {AB}}}$	\vec
${\displaystyle \angle }$	∠	${\displaystyle \angle ABC}$	\angle
${\displaystyle \triangle }$	△	${\displaystyle \triangle ABC}$	\triangle
${\displaystyle \square }$	□	${\displaystyle \square {\mathit {ABCD}}}$	\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

${\displaystyle {\begin{pmatrix}v_{1},\ldots ,v_{n}\end{pmatrix}}}$	\begin{pmatrix} ... \end{pmatrix} or \left( \begin{array}{...} ... \end{array} \right)
${\displaystyle {\begin{pmatrix}v_{1}\\\vdots \\v_{m}\end{pmatrix}}}$
${\displaystyle {\begin{pmatrix}a_{11}&\!\ldots \!&a_{1n}\\\vdots &\!\ddots \!&\vdots \\a_{m1}&\!\ldots \!&a_{mn}\end{pmatrix}}}$

Vector calculus

Symbol		Usage	LaTex
${\displaystyle \cdot }$	⋅	${\displaystyle v\cdot w}$	\cdot
${\displaystyle (~~)}$	( )	${\displaystyle (v,w)}$	( )
${\displaystyle \langle ~~\rangle }$	⟨ ⟩	${\displaystyle \langle v,w\rangle }$ ${\displaystyle \langle v\,|\,w\rangle }$	\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
${\displaystyle \|~~\|}$	‖	${\displaystyle \|v\|}$	\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
${\displaystyle {}^{\intercal }}$	⊺	${\displaystyle A^{\intercal }}$	\intercal
${\displaystyle {}^{\mathrm {H} }}$	H	${\displaystyle A^{\mathrm {H} }}$	^H
${\displaystyle {}^{\ast }}$	*	${\displaystyle A^{\ast }}$	\ast
${\displaystyle {}^{\dagger }}$	†	${\displaystyle A^{\dagger }}$	\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