List of mathematical symbols by subject

For interpretations of these symbols, see Glossary of mathematical symbols.

The following list of mathematical symbols by subject features a selection of the most common symbols used in modern mathematical notation within formulas, grouped by mathematical topic. As it is impossible to know if a complete list existing today of all symbols used in history is a representation of all ever used in history, as this would necessitate knowing if extant records are of all usages, only those symbols which occur often in mathematics or mathematics education are included. Many of the characters are standardized, for example in DIN 1302 General mathematical symbols or DIN EN ISO 80000-2 Quantities and units – Part 2: Mathematical signs for science and technology.

The following list is largely limited to non-alphanumeric characters. It is divided by areas of mathematics and grouped within sub-regions. Some symbols have a different meaning depending on the context and appear accordingly several times in the list. Further information on the symbols and their meaning can also be found in the respective linked articles.

Guide

The following information is provided for each mathematical symbol:

Symbol

The symbol as it is represented by LaTeX. If there are several typographic variants, only one of the variants is shown.

Usage

An exemplary use of the symbol in a formula. Letters here stand as a placeholder for numbers, variables or complex expressions. Different possible applications are listed separately.

Articles with usage

Examples of Wikipedia articles in which the symbol is used.

LaTeX

The LaTeX command that creates the icon. Characters from the ASCII character set can be used directly, with a few exceptions (e.g., pound sign #, backslash \, braces {}, and percent sign %). High-and low-position is indicated via the ^ and _ characters, and is not explicitly specified.

HTML

The icon in HTML, if it is defined as a named mark. Non-named characters can be indicated in the form &#xnnnn by specifying the Unicode code point of the next column. High and low position can be indicated via and . The character × whose HTML code is Time can be displayed by typing ×.

Unicode

The code point of the corresponding Unicode character. Some characters are combining and require the entry of additional characters. For brackets, the code points of opening and closing forms are specified. The Unicode character ⨯ whose hexadecimal value is U+2A2F can be displayed by typing ⨯ where #x indicates that the value in hexadecimal.

Numbers

Number sets

Symbol	Unicode character	Articles with usage	LaTeX	HTML	Unicode Hex
$\mathbb {A}$	𝔸	Algebraic number	\mathbb{A}	𝔸	U+1D538
$\mathbb {C}$	ℂ	Complex number	\mathbb{C}, \Complex	ℂ	U+2102
$\mathbb {H}$	ℍ	Quaternion	\mathbb{H}	ℍ	U+210D
$\mathbb {N}$	ℕ	Natural number	\mathbb{N}, \N	ℕ	U+2115
$\mathbb {O}$	𝕆	Octonion	\mathbb{O}	𝕆	U+1D546
$\mathbb {Q}$	ℚ	Rational number	\mathbb{Q}, \Q	ℚ	U+211A
$\mathbb {R}$	ℝ	Real number	\mathbb{R}, \R, \Reals	ℝ	U+211D
$\mathbb {S}$	𝕊	Sedenion	\mathbb{S}	𝕊	U+1D54A
$\mathbb {Z}$	ℤ	Integer	\mathbb{Z}, \Z	ℤ	U+2124

Intervals

Symbol	Usage	LaTeX	HTML	Unicode Hex
$[~~]$	$[a,b]$	( ) [ ]	( ) [ ]	U+0028/9 U+005B/D
$]~~[$	$]a,b[$
$(~~)$	$(a,b)$
$[~~[$	$[a,b[$
$[~~)$	$[a,b)$
$]~~]$	$]a,b]$
$(~~]$	$(a,b]$

Mathematical constants

For symbols of additional mathematical constants, see Mathematical constant.

Symbol	Unicode character	Articles with usage	LaTeX	HTML	Template	Unicode Hex	Note
$\pi$	π	Pi	\pi	π	{{pi}}	U+03C0
$e$ or $\mathrm {e}$	e	e (mathematics)	e or \mathrm{e}	e		U+0065	Recommend {{mvar|e}} or {{math|e}} over e
$\phi$	ϕ	Golden ratio	\phi	φ	{{phi}}	U+03C6
$\varphi$	φ		\varphi	ϕ	{{varphi}}	U+03D5
$i$ or $\mathrm {i}$	i	Imaginary unit	i or \mathrm{i}	i		U+0069	Recommend {{mvar|i}} or {{math|i}} over i
$\gamma$	γ	Euler–Mascheroni constant	\gamma	γ	{{gamma}}	U+03B3
$\epsilon$	ε	Vacuum permittivity	\epsilon	ε	{{epsilon}}	U+03B5
$\varepsilon$	ϵ	Dual number	\varepsilon	ϵ	{{varepsilon}}	U+03F5
$\theta$	θ	Mills' constant	\theta	θ	{{theta}}	U+03B8
$\vartheta$	ϑ		\vartheta	ϑ	{{vartheta}}	U+03D1
$\sigma$	σ	Somos' quadratic recurrence constant	\sigma	σ	{{sigma}}	U+03C3
$\varsigma$	ς		\varsigma	ς	{{varsigma}}	U+03C2
$\kappa$	κ	Einstein gravitational constant	\kappa	κ	{{kappa}}	U+03BA
$\lambda$	λ	Prouhet–Thue–Morse constant	\lambda	λ	{{lambda}}	U+03BB
$\mu$	μ	Ramanujan–Soldner constant	\mu	μ	{{mu}}	U+03BC
$\tau$	τ	Prouhet–Thue–Morse constant	\tau	τ	{{tau}}	U+03C4

Complex numbers

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\Im$	ℑ	$\Im (2+i)=1$	Complex number	\Im	ℑ	U+2111
$\operatorname {Im}$	Im	$\operatorname {Im} (2+i)=1$		\operatorname{Im}	Im
$\Re$	ℜ	$\Re (2+i)=2$		\Re	ℜ	U+211C
$\operatorname {Re}$	Re	$\operatorname {Re} (2+i)=2$		\operatorname{Re}	Re
${\bar {~}}$	◌̄	${\bar {z}}$	Complex conjugate	\bar	̄	U+0304
${\bar {\bar {~}}}$	◌̄̄	${\bar {\bar {z}}}$		\bar{\bar{}}	̄̄
${\overline {~~}}$	◌̅	${\overline {z}}$		\overline	̅	U+0305
${\overline {\overline {~~}}}$	◌̅̅	${\overline {\overline {z}}}$		\overline{\overline{}}	̅̅
${}^{\ast }$	*	$z^{\ast }$		{}^\ast	*	U+002A
$|~~|$	|	$|z|$	Absolute value	\vert	|	U+007C
$\arg {}$		$\arg(z)$	Polar coordinate system	\arg

Remark: real and imaginary parts of a complex number are often also denoted by $\operatorname {Re}$ and $\operatorname {Im}$.

Elementary arithmetic operations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex	Notes
$+$	+	$a+b$	Addition	+	+	U+002B
$-$	−	$a-b$	Subtraction	-	−	U+2212
$\cdot$	⋅	$a\cdot b$	Multiplication	\cdot	⋅	U+22C5
$\times$	⨯	$a\times b$		\times	×	U+2A2F
$:$	∶  or  :	$a:b$	Division (mathematics)	:, \colon	∶ or :	U+003A or U+2236	In LaTeX, : added space around the colon $a:b$ that \colon does not $a\colon b$.
$/$	∕	$a/b$		/	∕	U+2215
$\div$	÷	$a\div b$		\div	÷	U+00F7
${\frac {~~}{~~}}$	⁄	${\frac {a}{b}}$		\frac{a}{b} \tfrac{a}{b} (inline) \dfrac{a}{b} (display) \cfrac{a}{b} (continued fraction)	&frasl;	U+2044	<sup>a</sup>⁄<sub>b</sub> renders as: a⁄b
${}^{-1}$	⁻	$a^{-1}$	Multiplicative inverse	^{-1}		U+207B
$-$	−	$-a$	Additive inverse	-	&minus;	U+2212
$\pm$	±	$\pm a$	Plus or minus sign	\pm	&plusmn;	U+00B1
$\mp$	∓	$\mp a$		\mp	&mnplus;	U+2213

Elementary functions

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${\sqrt {\,}}$	√	${\sqrt {x}}$	Square root	\sqrt{}	√	U+221A
${\sqrt[{3}]{\,}}$	∛	${\sqrt[{3}]{x}}$	Cube root	\sqrt[3]{x}	&x221B;	U+221B
${\sqrt[{4}]{\,}}$	∜	${\sqrt[{4}]{x}}$	Fourth root	\sqrt[4]{x}	&x221C;	U+221C
${\sqrt[{n}]{\,}}$		${\sqrt[{n}]{x}}$	nth root	\sqrt[n]{}
$\%$	%	$x\,\%$	Percentage	\%	%	U+0025
$(~~)$	( )	$(x)$	Order of operations	( )	( )	U+0028/9
		$\left({\frac {1}{2}}\right)$		\left( \right)
$[~~]$	[ ]	$[x]$	Bracket	[ ]	[ ]	U+005B/D
$|~~|$	| |	$|x|$	Absolute value	|, \vert	|	U+007C
$\left\{~~\right\}$	{ }	$\left\{x\right\}$	Fractional part	\{ \} \lbrace \rbrace	{ }	U+007B/D
$\lceil ~~\rceil$	⌈ ⌉	$\lceil x\rceil$	Floor and ceiling functions	\lceil \rceil	⌈ ⌉	U+2308/9
$\lfloor ~~\rfloor$	⌊ ⌋	$\lfloor x\rfloor$		\lfloor \rfloor	⌊ ⌋	U+230A/B
$\ulcorner ~~\urcorner$	⌜ ⌝	$\ulcorner x\urcorner$		\ulcorner \urcorner	⌜ ⌝	U+231C/D
$\llcorner ~~\lrcorner$	⌞ ⌟	$\llcorner x\lrcorner$		\llcorner \lrcorner	⌞ ⌟	U+231E/F
$\frown$	⌢​	${\stackrel {\frown }{x}}$	Cap product	\frown	⌢	U+2322
$\smile$	⌣​	${\stackrel {\smile }{x}}$	Cup product	\smile	⌣	U+2323
$\exp$	exp	$\exp x$	Exponential function	\exp	exp
$\log$	log	$\log _{b}x$	Logarithm	\log or \log_{}	log or log<sub></sub>
$\ln$	ln	$\ln x$	Natural logarithm	\ln	ln
$\lg$	lg	$\lg x$	Binary logarithm	\lg	lg
$\min$	min	$\min\{1,2\}$	Maxima and minima	\min	min
$\max$	max	$\max\{1,2\}$		\max	max
$\inf$	inf	$\inf\{1,2\}$	Infimum and supremum	\inf	inf
$\sup$	sup	$\sup\{1,2\}$		\sup	sup
$\liminf$	liminf	$\liminf _{n\to \infty }x_{n}$	Limit inferior and limit superior	\liminf	liminf
$\varliminf$	lim	$\varliminf x_{n}$		\varliminf	<u>lim</u>
$\limsup$	limsup	$\limsup _{n\to \infty }x_{n}$		\limsup	limsup
$\varlimsup$	lim	$\varlimsup x_{n}$		\varlimsup	<span style="text-decoration:overline;">lim</span>
$\gcd$	gcd	$\gcd(1,2)$	Greatest common divisor	\gcd	gcd

Note: the power function is not represented by its own icon, but by the positioning of the exponent as a superscript.

Trigonometric functions

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\sin$	sin	$\sin x$	Sine and cosine	\sin	sin
$\cos$	cos	$\cos x$		\cos	cos
$\tan$	tan	$\tan x$	Tangent	\tan	tan
$\sec$	sec	$\sec x$	Trigonometric functions	\sec	sec
$\csc$	csc	$\csc x$		\csc	csc
$\cot$	cot	$\cot x$		\cot	cot
$\arcsin$	sin	$\arcsin x$	Inverse trigonometric functions	\arcsin	arcsin
$\arccos$	arccos	$\arccos x$		\arccos	arccos
$\arctan$	arctan	$\arctan x$		\arctan	arctan
$\operatorname {arcsec}$	arcsec	$\operatorname {arcsec} x$		\arcsec	arcsec
$\operatorname {arccsc}$	arccsc	$\operatorname {arccsc} x$		\arccsc	arccsc
$\operatorname {arccot}$	arccot	$\operatorname {arccot} x$		\arccot	arccot
$\sinh$	sinh	$\sinh x$	Hyperbolic functions	\sinh	sinh
$\cosh$	cosh	$\cosh x$		\cosh	cosh
$\tanh$	tanh	$\tanh x$		\tanh	tanh
$\coth$	coth	$\coth x$		\coth	coth

Arithmetic comparison

See also: Order relations, Set relations

Symbol	Unicode character	Usage	LaTeX	HTML	Unicode Hex
$<$	<	$a<b$	<	&lt;	U+003C
$>$	>	$a>b$	>	&gt;	U+003E
$\leq$	≤	$a\leq b$	\le, \leq	&le;	U+2264
$\geq$	≥	$a\geq b$	\ge, \geq	&ge;	U+2265
$\leqq$	≦	$a\leqq b$	\leqq	&LessFullEqual;	U+2266
$\geqq$	≧	$a\geqq b$	\geqq	&GreaterFullEqual;	U+2267
$\leqslant$	⩽	$a\leqslant b$	\leqslant	&LessSlantEqual	U+2A7D
$\geqslant$	⩾	$a\geqslant b$	\geqslant	&GreaterSlantEqual	U+2A7E
$\ll$	≪	$a\ll b$	\ll	&NestedLessLess;	U+226A
$\gg$	≫	$a\gg b$	\gg	&NestedGreaterGreater;	U+226B
$\lesssim$	≲	$a\lesssim b$	\lesssim	&lsim;	U+2272
$\gtrsim$	≳	$a\gtrsim b$	\gtrsim	&GreaterTilde;	U+2273
$\lessapprox$	⪅	$a\lessapprox b$	\lessapprox	&lessapprox;	U+2A85
$\gtrapprox$	⪆	$a\gtrapprox b$	\gtrapprox	&gap;	U+2A86

Symbol	Unicode character	Usage	LaTeX	HTML	Unicode Hex
$\lessgtr$	≶	$a\lessgtr b$	\lessgtr	&LessGreater	U+2276
$\gtrless$	≷	$a\gtrless b$	\gtrless	≷	U+2277
$\lesseqgtr$	⋚	$a\lesseqgtr b$	\lesseqgtr	⋚	U+22DA
$\gtreqless$	⋛	$a\gtreqless b$	\gtreqless	⋛	U+22DB
$\lesseqqgtr$	⪋	$a\lesseqqgtr b$	\lesseqqgtr	⪋	U+2A8B
$\gtreqqless$	⪌	$a\gtreqqless b$	\gtreqqless	⪌	U+2A8C

Number theory

Divisibility and modulo

Symbol	Unicode character	Usage	LaTeX	HTML	Unicode Hex
$\mid$	∣	$a\mid b$	\mid	∣	U+2223
$\nmid$	∤	$a\nmid b$	\nmid	∤	U+2224
$\perp$	⊥	$a\perp b$	\perp	⊥	U+22A5
$\sqcap$	⊓	$a\sqcap b$	\sqcap	⊓	U+2293
$\wedge$	∧	$a\wedge b$	\wedge	∧	U+2227
$\sqcup$	⊔	$a\sqcup b$	\sqcup	⊔	U+2294
$\vee$	∨	$a\vee b$	\vee	∨	U+2228

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex	Other information
$\equiv$	≡	$a\equiv b$	Modulo operation	\equiv	≡	U+2261
$\mod m$	mod	$a\mod m$		\mod m	mod		<math>\mod</math> without a trailing symbol (e.g. $m$) will produce an error.
${\pmod {m}}$	(mod)	$a{\pmod {m}}$		\pmod m	(mod)		<math>\pmod</math> without a trailing symbol (e.g. $m$) will produce an error.
$\gcd$	gcd	$\gcd(1,2)$	Greatest common divisor	\gcd	gcd

Combinatorics

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$!$	!	$n!$	Factorial	!	!	U+0021
		$!n$	Derangement
		$n!!$	Double factorial
${\tbinom {~}{~}}$	( )	${\tbinom {n}{k}}$	Combination	\binom	( )	U+0028/9
		${\tbinom {n}{k_{1},\ldots ,k_{r}}}$	Multinomial coefficient
$\left(\!{\tbinom {~}{~}}\!\right)$	(( ))	$\left(\!{\tbinom {n}{k}}\!\right)$	Multiset	(( ))	( )	U+0028/9
${\overline {~}}$	◌̄	$n^{\bar {m}}$	Pochhammer symbol	\bar	̄	U+0304
	◌̅	$n^{\overline {m}}$		\overline	̅	U+0305
	◌̲	$n^{\underline {m}}$		\underline	̲	U+0332
$\#$	#	$n\#$	Primorial	\#	#	U+0023

Stochastics

Probability theory

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$P$		$P(A)$	Probability measure	P		U+2119
$\mid$		$P(A\mid B)$	Conditional probability	\mid	|	U+007C
$/$		$P(A/B)$		/		U+2215
$E$	𝔼	$E(X)$	Expected value	E	𝔼	U+1D53C
$V$	𝕍	$V(X)$	Variance	V	𝕍	U+1D54D
$\sigma$	σ	$\sigma (X)$	Standard deviation	\sigma	σ	U+03C3
		$\sigma (X,Y)$	Covariance
$\rho$	ρ	$\rho (X,Y)$	Correlation	\rho	ρ	U+03C1
$\sim$	∼	$X\sim F$	Probability distribution	\sim	∼	U+223C
$\approx$	≈	$X\approx F$		\approx	≈	U+2248
${\displaystyle \perp }$	⊥	$A\perp B$	Independence (probability theory)	\perp	⊥	U+22A5

Remark: for operators there are several notational variants; instead of round brackets also square brackets are used

Statistics

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${\bar {~}}$	◌̅	${\bar {x}}$	Average	\bar	̄	U+0304
${\overline {~~}}$	◌̅	${\overline {m}}$		\overline	̅	U+0305
$\langle ~~\rangle$	⟨ ⟩	$\langle X\rangle$		\langle \rangle	⟨ ⟩	U+27E8/9
${\hat {~}}$	◌̂	${\hat {p}}$	Estimator	\hat	̂	U+0302

Calculus

Sequences and series

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\sum$	∑	$\sum _{i=1}^{n},\sum _{i\in I}$	Summation	\sum	∑	U+2211
$\prod$	∏	$\prod _{i=1}^{n},\prod _{i\in I}$	Multiplication	\prod	∏	U+220F
$\coprod$	∐	$\coprod _{i=1}^{n},\coprod _{i\in I}$	Coproduct	\coprod	∐	U+2210
$(~~)$	( )	$(a_{n})$	Sequence	( )	( )	U+0028/9
$\to$	→	$a_{n}\to a$	Limit of a sequence	\to \rarr	→	U+2192
$\infty$	∞	$n\to \infty$	Infinity	\infty	∞	U+221E

Limits

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\to$	→	$\lim _{x\to a}f(x)$	Limit of a function	\to \rightarrow	→ →	U+2192
$\longrightarrow$	⟶	$x\longrightarrow a$		\longrightarrow	⟶	U+27F6
$\uparrow$	↑	$\lim _{x\uparrow a}f(x)$		\uparrow	↑ ↑	U+2191
$\nearrow$	↗	$\lim _{x\nearrow a}f(x)$		\nearrow	↗	U+2197
$\searrow$	↘	$\lim _{x\searrow a}f(x)$		\searrow	↘	U+2198
$\downarrow$	↓	$\lim _{x\downarrow a}f(x)$		\downarrow	↓ ↓	U+2193
$\swarrow$	↙	$a\swarrow x$		\swarrow	↙	U+2199
$\leftarrow$	←	$a\leftarrow x$		\leftarrow	← ←	U+2190
$\longleftarrow$	⟵	$a\longleftarrow x$		\longleftarrow	⟵	U+27F5
$\nwarrow$	↖	$a\nwarrow x$		\nwarrow	↖	U+2196
$^{+}$	⁺	$\lim _{x\to a^{+}}f(x)$		^+	⁺	U+207A
$^{-}$	⁻	$\lim _{x\to a^{-}}f(x)$		^-	⁻	U+207B
$\lim$		$\lim _{n\to \infty }x_{n}$		\lim
$\liminf$		$\liminf _{n\to \infty }x_{n}$	Limit inferior and limit superior	\liminf
$\limsup$		$\limsup _{n\to \infty }x_{n}$		\limsup

Differential calculus

Main article: Differential calculus

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${}'$ ${}^{\prime }$	′	$f'$ $f^{\prime }$	Lagrange's notation Prime (symbol)	' ^\prime	′	U+2032
${}''$ ${}^{\prime \prime }$	″	$f''$ $f^{\prime \prime }$		'' ^{\prime\prime}	″	U+2033
${}'''$ ${}^{\prime \prime \prime }$	‴	$f'''$ $f^{\prime \prime \prime }$		''' ^{\prime\prime\prime}	‴	U+2034
${}''''$ ${}^{\prime \prime \prime \prime }$	⁗	$f''''$ $f^{\prime \prime \prime \prime }$		'''' ^{\prime\prime\prime\prime}	⁗	U+2057
$^{IV}\;{}^{V}\;{}^{VI}$		$f^{IV},f^{V},f^{VI}$		^{IV} ^V ^{VI}	<sup>IV</sup>
$^{iv}\;{}^{v}\;{}^{vi}$		$f^{iv},f^{v},f^{vi}$		^{iv} ^v ^{vi}	<sup>iv</sup>
${}^{(~)}$	⁽ ⁾	$f^{(4)},f^{(5)},f^{(n)}$		^{( )}	<sup>( )</sup>	U+207D/E
${\dot {~~}}$	◌̇	${\dot {f}}$	Newton's notation	\dot	&#x0307;	U+0307
${\ddot {~~}}$	◌̈	${\ddot {f}}$		\ddot	&#x0308;	U+0308
$d$	d	$dx$	Leibniz's notation	d	d	U+0064
		$df$
		${\frac {df}{dx}}$
		${\frac {d}{dx}}f$
		${\frac {d^{2}}{dx^{2}}}f$
$\partial$	∂	$\partial _{x}f$	Partial derivative	\partial	&part;	U+2202
$\left.{\frac {\partial }{\partial x}}\right\vert _{x}$	∂ and |	$\left.{\frac {\partial f}{\partial x}}\right\vert _{x=x_{0}}$		\left. \frac{\partial }{\partial x} \right\vert_x	&part; and &VerticalLine;	U+2202 and U+007C

Integral calculus

See also: Extensions of the integral symbol

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\int$	∫	$\int _{a}^{b}$ , $\int _{G}$	Integral	\int	∫	U+222B
$\iint$	∬	$\iint _{\mathcal {F}}$	Surface integral	\iint	∬	U+222C
$\iiint$	∭	$\iiint _{V}$	Volume integral	\iiint	∭	U+222D
$\oint$	∮	$\oint _{\gamma }$	Curve integral	\oint	∮	U+222E
	∯	$\gamma$	Surface integral	\oiint	∯	U+222F
	∰	$\gamma$	Volume integral	\oiiint	∰	U+2230

Vector calculus

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\nabla$	∇	$\nabla f$	Gradient	\nabla	∇	U+2207
		$\nabla \cdot F$	Divergence
		$\nabla \times F$	Curl (mathematics)
$\Delta$	∆	$\Delta f$	Laplace operator	\Delta	Δ	U+2206
$\square$	□	$\square f$	D'Alembert operator	\square	□	U+25A1

Asymptotic behaviour

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\sim$	∼	$f\sim$	Asymptotic analysis	\sim	∼	U+223C
$o$	o	$f\in o(g)$	Big O notation	o		U+006F
${\mathcal {O}}$	𝒪	$f\in {\mathcal {O}}(g)$		\mathcal{O}	𝒪	U+1D4AA
$\Theta$	Θ	$f\in \Theta (g)$		\Theta	Θ	U+0398
$\Omega$	Ω	$f\in \Omega (g)$		\Omega	Ω	U+03A9
$\omega$	ω	$f\in \omega (g)$		\omega	ω	U+03C9

Linear algebra

Vectors and matrices

Symbol	Articles with usage	LaTeX
${\begin{pmatrix}v_{1},\ldots ,v_{n}\end{pmatrix}}$	Vector (mathematics and physics)	\begin{pmatrix} ... \end{pmatrix} or \left( \begin{array}{...} ... \end{array} \right)
${\begin{pmatrix}v_{1}\\\vdots \\v_{m}\end{pmatrix}}$
${\begin{pmatrix}a_{11}&\!\ldots \!&a_{1n}\\\vdots &\!\ddots \!&\vdots \\a_{m1}&\!\ldots \!&a_{mn}\end{pmatrix}}$	Matrix (mathematics)

Vector operations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\cdot$	⋅	$v\cdot w$	Dot product Inner product space	\cdot	⋅	U+22C5
$(~~)$	( )	$(v,w)$		( )	( )	U+0028/9
$\langle ~~\rangle$	⟨ ⟩	$\langle v,w\rangle$ $\langle v\,|\,w\rangle$		\langle \rangle	⟨ ⟩	U+27E8/9
$\times$	⨯	$v\times w$	Cross product	\times	×	U+2A2F
$[~~]$	[ ]	$[v,w]$		[ ]	[ ]	U+005B/D
$(~~)$	( )	$(u,v,w)$	Triple product	( )	( )	U+0028/9
$\otimes$	⊗	$v\otimes w$	Dyadic product	\otimes	⊗	U+2297
$\wedge$	∧	$v\wedge w$	Exterior algebra	\wedge	∧	U+2227
$|~~|$	| |	$|v|$	Euclidean norm	\vert	|	U+007C
$\|~~\|$	‖	$\|v\|$ $\lVert v\rVert$	Norm (mathematics)	\Vert, \| \lVert \rVert	‖	U+2016
${\hat {~}}$	̂	${\hat {v}}$	Unit vector	\hat{}	̂	U+0302

Matrix operations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\cdot$	⋅	$A\cdot B$	Matrix multiplication	\cdot	⋅	U+22C5
$\circ$	∘	$A\circ B$	Hadamard product	\circ	∘	U+2218
$\oslash$	⊘	$A\oslash B$	Hadamard division	\oslash	⊘	U+2298
$*$	*	$A*B$	Khatri-Rao product	*	*	U+002A
$\otimes$	⊗	$A\otimes B$	Kronecker product	\otimes	⊗	U+2297
${}^{\intercal }$	⊺	$A^{\intercal }$	Transposed matrix	^\intercal	⊺	U+22BA
${}^{\top }$	⊤	$A^{\top }$		^\top	⊤	U+22A4
${}^{\mathrm {T} }$	T	$A^{\mathrm {T} }$		^{\mathrm T}		U+0054
${}^{\ast }$	*	$A^{\ast }$	Conjugate transpose	^\ast	*	U+002A
${}^{\dagger }$	†	$A^{\dagger }$		^\dagger	†	U+2020
${}^{\mathrm {H} }$	H	$A^{\mathrm {H} }$		^H		U+0048
${}^{-1}$	⁻	$A^{-1}$	Inverse matrix	^{-1}		U+207B
${}^{+}$	+	$A^{+}$	Moore–Penrose pseudoinverse	^+	+	U+002B
$|~~|$	| A |	$|A|$	Determinant	|, \vert	|	U+007C
$\det$	det	$\det A$		\det	det
$\|~~\|$	‖	$\|A\|$	Matrix norm	\|, \Vert	‖	U+2016

Vector spaces

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$+$	+	$V+W$	Direct sum of modules Linear subspace	+	+	U+002B
$\oplus$	⊕	$V\oplus W$		\oplus	⊕	U+2295
$\times$	⨯	$V\times W$	Direct product	\times	×	U+2A2F
$\otimes$	⊗	$V\otimes W$	Tensor product	\otimes	⊗	U+2297
$/$	/	$V\,/\,U$	Quotient space (linear algebra)	/	⁄	U+002F
${}^{\perp }$	⟂	$U^{\perp }$	Orthogonal complement	^\perp	⊥	U+27C2
${}^{\ast }$	*	$V^{\ast }$	Dual space	^\ast	∗	U+002A
${}^{0}$	0	$X^{0}$		^0		U+0030
$\langle ~~\rangle$	⟨ ⟩	$\langle X\rangle$	Linear hull	\langle \rangle	⟨ ⟩	U+27E8/9
$\dim$	dim	$\dim X$	Dimension (linear algebra)	\dim	dim
$\ker$	ker	$\ker L$	Kernel (linear algebra)	\ker	ker
$\Pr$	Pr	$\Pr {}_{1}(x,y)$	Projection (linear algebra)	\Pr	Pr

Functional analysis

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${}'$	′	$V'$	Dual space	^\prime	′	U+2032/3
${}''$	″	$V''$
${\hat {~}}$	◌̂	${\hat {X}}$	Complete metric space	\hat{}		U+0302
$\hookrightarrow$	↪	$X\hookrightarrow Y$	Embedding	\hookrightarrow		U+21AA

Logic

See also: List of logic symbols, Wikipedia:WikiProject Logic/Standards for notation, and MOS:MATH § TONE

The current Wikipedia guidelines advise against unnecessary use of ∀, ∃, and ⇔ and instead recommend writing out "for all", "there exists", and "if and only if." The same is true of abbreviations such as "iff", "s.t.", and "WLOG".

Equality signs

See also: Equals sign

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$=$	=	$a=b$	Equality	=	=	U+003D
$\#$	#	$a\,\#\,b$	Apartness relation	\#	#	U+0023
$\neq$	≠	$a\neq b$	Inequality	\neq \ne \not=	≠	U+2260
$\equiv$	≡	$a\equiv b$	Identity	\equiv	≡	U+2261
$\approx$	≈	$a\approx b$	Approximation	\approx	≈	U+2248
$\sim$	∼	$a\sim b$	Equivalence class	\sim	∼	U+223C
$\propto$	∝	$a\propto b$	Proportionality	\propto	∝	U+221D
${\widehat {=}}$	≙	$a\,{\widehat {=}}\,b$	Bijection	\widehat{=}	≙	U+2259
${\overset {?}{=}}$	≟	$a\,{\overset {?}{=}}\,b$	Asks "is it equal to"	\overset{?}{=}	≟	U+225F
${\overset {\operatorname {def} }{=}}$	≝	$a\,{\overset {\operatorname {def} }{=}}\,b$	Equal to by definition	\overset{\operatorname{def}}{=}	≝	U+225D
$\triangleq$	≜	$a\,\triangleq \,b$		\triangleq	≜	U+225C
$:=$	≔	$a\,:=\,b$	Assignment	:=	≔	U+2254
$=:$	≕	$a\,=:\,b$		=:	≕	U+2255
$\doteq$	≐	$x_{n}\doteq \,b$	Approaches the limit	\doteq	≐	U+2250
$==$	⩵	$x\,==\,y$	Relational operator	==	⩵	U+2A75

Logical operators

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\land$	∧	$A\land B$	Logical conjunction	\land	∧	U+2227
$\lor$	∨	$A\lor B$	Logical disjunction	\lor	∨	U+2228
$\Leftrightarrow$	⇔	$A\Leftrightarrow B$	Logical equivalence	\Leftrightarrow	⇔	U+21D4
$\leftrightarrow$	↔	$A\leftrightarrow B$		\leftrightarrow	↔	U+2194
$\iff$	⟺	$A\iff B$		\iff	⟺	U+27FA
$\Rightarrow$	⇒	$A\Rightarrow B$	Logical consequence	\Rightarrow	⇒	U+21D2
$\rightarrow$	→	$A\rightarrow B$		\rightarrow	→	U+2192
$\implies$	⟹	$A\implies B$		\implies	⟹	U+27F9
$\Longrightarrow$		$A\Longrightarrow B$		\Longrightarrow
$\oplus$	⊕	$A\oplus B$	Exclusive or	\oplus	⊕	U+2295
$\veebar$	⊻	$A\,\veebar \,B$		\veebar	⊻	U+22BB
${\dot {\lor }}$	⩒	$A\,{\dot {\lor }}\,B$		\dot\lor		U+2A52
$\lnot$	¬	$\lnot A$	Logical negation	\lnot	¬	U+00AC
${\bar {~}}$	◌̄	${\bar {A}}$		\bar	̄	U+0304
${\overline {~~}}$	̅	${\overline {A}}$		\overline	̅	U+0305
$\not$	◌̸	$\not =$ $\not \in$		\not (ex: \not= \not\in)	̸ (ex: ≠ ∉)	U+0338
$\leftarrow$	←	$A\leftarrow B$	Converse implication	\leftarrow	←	U+2190
$\multimap$	⊸	$A\multimap B$	Linear logic	\multimap	⊸	U+22B8
⅋	⅋	A ⅋ B	Linear logic	\upand (No Wikipedia support)	&x214B;	U+214B

See also: Further symbols for binary connectives

Quantifiers

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\forall$	∀	$\forall \,x$	Universal quantification	\forall	∀	U+2200
$\bigwedge$	⋀	$\bigwedge _{x}$		\bigwedge	⋀	U+22C0
$\exists$	∃	$\exists \,x$	Existential quantification	\exists	∃	U+2203
$\bigvee$	⋁	$\bigvee _{x}$		\bigvee	⋁	U+22C1
$\exists !$	∃!	$\exists !\,x$	Uniqueness quantification	\exists!	∃!	U+2203!
$\bigvee ^{\centerdot }$	⩒	$\bigvee _{x}^{\centerdot }$		\dot\bigvee		U+2A52
$\nexists$	∄	$\nexists \,x$	Existential quantification	\nexists	∄	U+2204

Deduction symbols

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\vdash$	⊢	$A\vdash B$	Logical consequence, Propositional calculus	\vdash	⊢	U+22A2
$\models$	⊨	$A\models B$	Logical consequence, Inference	\models	⊨	U+22A8
		$\models A$	Tautology (logic)
$\top$	⊤	$A\top$		\top	⊤	U+22A4
$\bot$	⊥	$A\bot$	Contradiction	\bot	⊥	U+22A5
$\therefore$	∴	$A\therefore B$	Deductive reasoning	\therefore	∴	U+2234
$\because$	∵	$A\because B$		\because	∵	U+2235

End of proof symbols

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\blacksquare$	■	...as desired. $\blacksquare$	Q.E.D.	\blacksquare	■	U+25A0
$\Box$	□			\Box	□	U+25A1
${\displaystyle }$	∎		Tombstone		∎	U+220E

Formal language and strings

Main article: Formal language

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\varepsilon$	ε	$\varepsilon s=s$	Empty string	\varepsilon	ε	U+03B5
$|~~|$	| |	$|s|$	String length	\vert	|	U+007C
$+$	+	$s+t$	Concatenation	+	+	U+002B
$\cdot$	⋅	$s\cdot t$		\cdot	⋅	U+22C5
$\lnot$	¬	$\lnot L$	Formal language	\lnot	¬	U+00AC
${}^{\ast }$	*	$V^{\ast }$	Kleene star	^\ast	∗	U+002A
${}^{+}$	+	$V^{+}$	Free monoid	^+	+	U+002B
$\sim$	∼	$a\sim b$	Squiggle operator	\sim	∼	U+223C
$[\![~~]\!]$	⟦⟧	$[\![s]\!]$	Squiggle operator	[\![ ]\!]	⟦ ⟧	U+27E6/7

Functions and category theory

Functions

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\to$	→	$f\colon A\to B$	Function (mathematics)	\to	→	U+2192
		$A\,{\stackrel {f}{\to }}\,B$
$\mapsto$	↦	$f\colon x\mapsto y$		\mapsto	&mapstoright;	U+21A6
		$x\,{\stackrel {f}{\mapsto }}\,y$
$(~~)$	( )	$f(x)$	Image (mathematics)	( )	( )	U+0028/9
		$f(X)$
$[~~]$	[ ]	$f[X]$		[ ]	[ or ]	U+005B/D
$\vert$	|	$f\vert _{X}$	Restriction (mathematics)	\vert	|	U+007C
$\cdot$	⋅	$f(\cdot )$	Free variable	\cdot	⋅	U+22C5
${}^{-1}$	⁻	$f^{-1}$	Inverse function	-1		U+207B
$\circ$	∘	$f\circ g$	Function composition	\circ	∘	U+2218
$\ast$	∗	$f\ast g$	Convolution	\ast	∗	U+2217
${\hat {~}}$	◌̂	${\hat {f}}$	Fourier transform	\hat		U+0302
$\multimap$	⊸	$f:X\multimap Y$	Multimap	\multimap	⊸	U+22B8

Morphisms

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\to$	→	$f\colon X\to Y$	Morphism	\to	→	U+2192
		$X\,{\stackrel {f}{\to }}\,Y$
$\mapsto$	↦	$f\colon x\mapsto y$		\mapsto	&mapstoright;	U+21A6
		$x\,{\stackrel {f}{\mapsto }}\,y$
${\overset {\sim }{\rightarrow }}$	⥲	$f\colon X{\overset {\sim }{\rightarrow }}Y$	Isomorphism	\tilde{\rightarrow}		U+2972
$\hookrightarrow$	↪	$f\colon X\hookrightarrow Y$	Monomorphism	\hookrightarrow	&#8618	U+21AA
		$X\,{\stackrel {f}{\hookrightarrow }}\,Y$
$\twoheadrightarrow$	↠	$f\colon X\twoheadrightarrow Y$	Epimorphism	\twoheadrightarrow	&#8608	U+21A0
		$X\,{\stackrel {f}{\twoheadrightarrow }}\ Y$
$\hom$	hom	$\hom _{C}(X,Y)$	Morphism	\hom	hom

Constructions

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\prod$	∏	$\prod X_{i}$	Product (category theory)	\prod	∏	U+220F
$\coprod$	∐	$\coprod X_{i}$	Coproduct	\coprod	∐	U+2210
$\oplus$	⊕	$\oplus X_{i}$	Biproduct	\oplus	⊕	U+2295
$\times$	×	$A\times _{C}B$	Pullback (category theory)	\times	×	U+00D7
$\lim$	lim	$\lim F$	Limit (category theory)	\lim	lim
$\projlim$	projlim	$\projlim F$	Inverse limit	\projlim	projlim
$\varprojlim$		$\varprojlim F$		\varprojlim
$\injlim$	injlim	$\injlim F$	Direct limit	\injlim	injlim
$\varinjlim$		$\varinjlim F$		\varinjlim

Set theory

Definition symbols

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\colon$	:	$A\colon B$	Definition	\colon	:	U+003A
		$A\colon =B$
		$A\colon \Leftrightarrow B$

Set construction

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\varnothing$	∅	$\varnothing =\{\;\}$	Empty set	\varnothing	∅ ∅	U+2205
$\emptyset$				\emptyset
$\{~\}$	{ }	$\{a,b,\ldots \}$	Set (mathematics)	\{ \} \lbrace \rbrace	{ }	U+007B/D
$\mid$	|	$\{a\mid T(a)\}$		\mid	|	U+007C
$\colon$	:	$\{a\colon T(a)\}$		\colon	:	U+003A
$:$		$\{a:T(a)\}$		:

Comparison of separators (the symbol between the variable and predicate)

Rendered result	Latex code	Notes on separator
$\{x\in X:P(x)\}$	\{x\in X : P(x)\}	: inserts whitespace that \colon does not.
$\{x\in X\colon P(x)\}$	\{x\in X \colon P(x)\}
$\{x\in X\mid P(x)\}$	\{x\in X \mid P(x)\}	\mid inserts whitespace that \vert does not.
$\{x\in X\vert P(x)\}$	\{x\in X \vert P(x)\}	\vert and | are synonyms in LaTeX.
$\{x\in X\vline P(x)\}$	\{x\in X \vline P(x)\}	\mid inserts whitespace that \vline does not.
$\left\{\sum _{n=1}^{\infty }x^{n}:|x|<1\right\}$	\left\{\sum_{n=1}^{\infty} x^n : |x|<1\right\}
$\left\{\sum _{n=1}^{\infty }x^{n}\mid |x|<1\right\}$	\left\{\sum_{n=1}^\infty x^n \mid |x|<1\right\}
$\left\{\sum _{n=1}^{\infty }x^{n}\;{\Bigg |}\;|x|<1\right\}$	\left\{\sum_{n=1}^\infty x^n \;\Bigg|\; |x|<1\right\}	\;\Bigg|\; is used since neither \middle\mid, \Bigg\mid, nor \Bigg\vline render in Wikipedia.
$\left\{\left.\sum _{n=1}^{\infty }x^{n}\;\right|\;|x|<1\right\}$	\left\{\left.\sum_{n=1}^\infty x^n \;\right|\; |x|<1\right\}	Using \left. \right| or \left| \right. is potentially an alternative to manual scaling.

Set operations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\cap$	∩	$A\cap B$	Intersection (set theory)	\cap	∩	U+2229
$\bigcap$	⋂	$\bigcap _{S\in P}S$		\bigcap	⋂ ⋂	U+22C2
$\cup$	∪	$A\cup B$	Union (set theory)	\cup	∪	U+222A
$\bigcup$	⋃	$\bigcup _{S\in P}S$		\bigcup	⋃ ⋃	U+22C3
$\setminus$	∖	$A\setminus B$	Difference (set theory)	\setminus	∖ ∖	U+2216
$\smallsetminus$		$A\smallsetminus B$		\smallsetminus
$\triangle$	∆	$A\,\triangle \,B$	Symmetric difference	\triangle	Δ	U+2206
$\ominus$	⊖	$A\ominus B$		\ominus	⊖	U+2296
$\times$	⨯	$A\times B$	Cartesian product	\times	×	U+2A2F
${\dot {\cap }}$	⩀	$A\,{\dot {\cap }}\,B$	Intersection (set theory)	\dot\cap	⩀	U+2A40
$\sqcap$	⊓	$A\sqcap B$		\sqcap	⊓	U+2293
${\displaystyle }$	⩄	${\displaystyle }$		\capwedge	⩄	U+2A44
${\dot {\cup }}$	⊍	$A\,{\dot {\cup }}\,B$	Disjoint union	\dot\cup	⊍	U+228D
$\uplus$	⊎	$A\uplus B$		\uplus	⊎	U+228E
$\sqcup$	⊔	$A\sqcup B$		\sqcup	⊔	U+2294
${\displaystyle }$	⫛	${\displaystyle }$	Transversal intersection	\mlcp	⫛	U+2ADB
${}^{\complement }$	∁	$A^{\complement }$	Complement (set theory)	^\complement	∁	U+2201
${}^{\mathrm {C} }$	C	$A^{\mathrm {C} }$		^{\mathrm C}	∁	U+2201
${\bar {~}}$	◌̄	${\bar {z}}$		\bar{}	̄	U+0304
${\overline {~~}}$	◌̅	${\overline {A}}$		\overline{}		U+0305
$\wp$	℘	$\wp (A)$	Power set	\wp	℘	U+2118
${\mathcal {P}}$	𝒫	${\mathcal {P}}(A)$		\mathcal{P}	𝒫	U+1D4AB
${\mathfrak {P}}$	𝔓	${\mathfrak {P}}(A)$		\mathfrak{P}	𝔓	U+1D513
$\bigwedge$	⋀	$\bigwedge \limits _{x\in A}$	Infimum and supremum	\bigwedge \bigwedge\limits_{}	⋀	U+22C0
$\bigvee$	⋁	$\bigvee \limits _{x\in A}$		\bigvee \bigvee\limits_{}	⋁	U+22C1

Set relations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\subset$	⊂	$A\subset B$	Subset	\subset	⊂	U+2282
$\subsetneq$	⊊	$A\subsetneq B$		\subsetneq	⊊	U+228A
$\subseteq$	⊆	$A\subseteq B$		\subseteq	⊆	U+2286
${\displaystyle }$	⟃	A ⟃ B		\subsetcirc	⟃	U+27C3
$\supset$	⊃	$A\supset B$	Superset	\supset	⊃	U+2283
$\supsetneq$	⊋	$A\supsetneq B$		\supsetneq	⊋	U+228B
$\supseteq$	⊇	$A\supseteq B$		\supseteq	⊇	U+2287
${\displaystyle }$	⟄	A ⟄ B		\supsetcirc	⟄	U+27C4
$\not \subset$	⊄	$A\not \subset B$		\not\subset	⊄	U+2284
$\not \supset$	⊅	$A\not \supset B$	Superset	\not\supset	⊅	U+2285
$\not \subseteq$	⊈	$A\not \subseteq B$		\not\subseteq	⊈	U+2288
$\not \supseteq$	⊉	$A\not \supseteq B$	Superset	\not\supseteq	⊉	U+2289
$\in$	∈	$a\in A$	Element (mathematics)	\in	∈	U+2208
$\ni$	∋	$A\ni a$		\ni, \owns	∋	U+220B
$\notin$	∉	$a\notin A$		\notin, \not\in	∉	U+2209
$\not \ni$	∌	$A\not \ni a$		\not\ni	∌	U+220C
$\sqsubset$	⊏	$A\sqsubset B$	Substring	\sqsubset	⊏	U+228F
$\sqsupset$	⊐	$A\sqsupset B$		\sqsupset	⊐	U+2290
$\sqsubseteq$	⊑	$A\sqsubseteq B$		\sqsubseteq	⊑	U+2291
$\sqsupseteq$	⊒	$A\sqsupseteq B$		\sqsupseteq	⊒	U+2292

Note: The symbols $\subset$ and $\supset$ are used inconsistently and often do not exclude the equality of the two quantities.

Cardinality

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$|~~|$	| |	$|A|$	Cardinality	\vert	|	U+007C
$\#$	#	$\#A$		\#	#	U+0023
${\mathfrak {c}}$	𝔠		Cardinality of the continuum	\mathfrak{c}	𝔠	U+1D520
$\aleph$	ℵ	$\aleph _{0}$, $\aleph _{1}$, ...	Aleph number	\aleph	ℵ	U+2135
$\beth$	ℶ	$\beth _{0}$, $\beth _{1}$, ...	Beth number	\beth	ℶ	U+2136

Equivalence classes/relations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$[~~]$	[ ]	$[a]$	Equivalence class	[ ]	[ ]	U+005B/D
$/$	/	$M/\!\sim$	Quotient set	/	/	U+002F
$\sim$	∼	$a\sim b$	Equivalence relation	\sim	∼, ∼	U+223C
$\backsim$	∽	$a\backsim b$		\backsim	∽	U+223D
$\nsim$	≁	$a\nsim b$		\not\sim, \nsim	≁	U+2241
$\eqsim$	≂	$a\eqsim b$		\eqsim	≂	U+2242
$\simeq$	≃	$a\simeq b$		\simeq	≃	U+2243
$\cong$	≅	$a\cong b$		\cong	≅	U+2245
$\ncong$	≇	$a\ncong b$		\not\cong, \ncong	≇	U+2247

Order theory

Comparisons

See also: Arithmetic comparison, Set relations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\leq$	≤	$a\leq b$	Order relation	\leq, \le	≤, ≤	U+2264
$\geq$	≥	$a\geq b$		\geq, \ge	≥, ≥	U+2265
$\nless$	≮	$a\nless b$		\nless	≮, ≮	U+226E
$\ngtr$	≯	$a\ngtr b$		\ngtr	≯, ≯	U+226F
$\nleq$	≰	$a\nleq b$		\not\leq, \nleq	≰, ≰	U+2270
$\ngeq$	≱	$a\ngeq b$		\not\geq, \ngeq	≱, ≱	U+2271
$\lesssim$	≲	$a\lesssim b$	Inequality (mathematics)	\lesssim	≲, ≲	U+2272
$\gtrsim$	≳	$a\gtrsim b$		\gtrsim	≳, ≳	U+2273
$\not \lesssim$	≴	$a\not \lesssim b$		\not\lesssim	≴	U+2274
$\not \gtrsim$	≵	$a\not \gtrsim b$		\not\gtrsim	≵	U+2275
$\prec$	≺	$a\prec b$	Successor ordinal	\prec	≺	U+227A
$\succ$	≻	$a\succ b$		\succ	≻	U+227B
$\preccurlyeq$	≼	$a\preccurlyeq b$		\preccurlyeq	≼	U+227C
$\succcurlyeq$	≽	$a\succcurlyeq b$		\succcurlyeq	≽	U+227D
$\precsim$	≾	$a\precsim b$		\precsim	≾	U+227E
$\succsim$	≿	$a\succsim b$		\succsim	≿	U+227F
$\preceq$	⪯	$a\preceq b$		\preceq	⪯	U+2AAF
$\succeq$	⪰	$a\succeq b$		\succeq	⪰	U+2AB0
$\curlyeqprec$	⋞	$a\curlyeqprec b$		\curlyeqprec	⋞	U+22DE
$\curlyeqsucc$	⋟	$a\curlyeqsucc b$		\curlyeqsucc	⋟	U+22DF
$\sqsubset$	⊏	$a\sqsubset b$	Partially ordered set	\sqsubset	⊏ ⊏	U+228F
$\sqsupset$	⊐	$a\sqsupset b$		\sqsupset	⊐ ⊐	U+2290
$\sqsubseteq$	⊑	$a\sqsubseteq b$		\sqsubseteq	⊑ ⊑	U+2291
$\sqsupseteq$	⊒	$a\sqsupseteq b$		\sqsupseteq	⊒ ⊒	U+2292
$\not \sqsubseteq$	⋢	$a\not \sqsubseteq b$		\not\sqsubseteq	⋢	U+22E2
$\not \sqsupseteq$	⋣	$a\not \sqsupseteq b$		\not\sqsupseteq	⋣	U+22E3

Binary relations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
;	;	$R;S$	Composition of relations	;	;	U+003B
$\bullet$	•	$a\bullet b$	Operation (mathematics)	\bullet	•	U+2219
$\ast$	∗	$a\ast b$		\ast	∗	U+2217
${}^{T}$	⁻	$R^{T}$	Converse relation	T
${\bar {}}$	⁻	${\bar {R}}$	Complementary relation	\bar{R}
${}^{+}$	+	$R^{+}$	Transitive closure	+		U+002B
${}^{\ast }$	*	$R^{\ast }$	Reflexive closure	\ast	∗	U+002A

Algebra

Group theory

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\simeq$	≃	$G\simeq H$	Group isomorphism	\simeq		U+2243
$\cong$	≅	$G\cong H$		\cong	≅	U+2245
$\times$	⨯	$G\times H$	Direct product	\times	×	U+2A2F
$\rtimes$	⋊	$G\rtimes H$	Semidirect product	\rtimes	⋊	U+22CA
$\wr$	≀	$G\,\wr \,H$	Wreath product	\wr	≀	U+2240
$\leq$	≤	$U\leq G$	Subgroup	\leq	≤	U+2264
$<$	<	$U<G$		\lt	&lt;	U+003C
$\vartriangleleft$	⊲	$N\vartriangleleft G$	Normal subgroup	\vartriangleleft	&RightTriangle;	U+22B3
$\trianglelefteq$	⊴	$N\trianglelefteq G$		\trianglelefteq	&LeftTriangleEqual;	U+22B4
$\not \vartriangleleft$	⋪	$N\not \vartriangleleft G$		\not\vartriangleleft	&ntriangleleft;	U+22EA
$\not \trianglelefteq$	⋬	$N\not \trianglelefteq G$		\not\trianglelefteq	&NotLeftTriangleEqual;	U+22EC
$\vartriangleright$	⊳	$G\vartriangleright N$		\vartriangleright	&RightTriangle;	U+22B3
$\trianglerighteq$	⊵	$G\trianglerighteq N$		\trianglerighteq	&RightTriangleEqual;	U+22B5
$\not \vartriangleright$	⋫	$G\not \vartriangleright N$		\not\vartriangleright	&NotRightTriangle;	U+22EB
$\not \trianglerighteq$	⋭	$G\not \trianglerighteq N$		\not\trianglerighteq	&NotRightTriangleEqual;	U+22ED
$/$	/	$G/N$	Quotient group	/	&frasl;	U+002F
$\colon$	:	$(G\colon U)$	Index of a subgroup	\colon	&colon;	U+003A
$\langle ~~\rangle$	⟨ ⟩	$\langle E\rangle$	Generating set of a group	\langle \rangle	&lang; &rang;	U+27E8/9
$[~~]$	[ ]	$[g,h]$	Commutator	[ ]	&lsqb; &rsqb;	U+005B/D

Field theory

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$/$	/	$L/K$	Field extension	/	⁄	U+002F
$\mid$	|	$L\mid K$		\mid	|	U+007C
$\colon$	:	$L\colon K$		\colon	:	U+003A
		$[L\colon K]$	Degree of a field extension
${\bar {~}}$	◌̄	${\bar {K}}$	Algebraic closure	\bar	̄	U+0304
${\overline {~~}}$	◌̅	${\overline {K}}$		\overline	̅	U+0305
$()$	( )	$K(\alpha )$	Field extension, Algebraic number field	( )	( )	U+0028/9
$\mathbb {F}$	𝔽		Finite field	\mathbb{F}	𝔽	U+1D53D
$\mathbb {K}$	𝕂		Field (mathematics)	\mathbb{K}	𝕂	U+1D542

Ring theory

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${}^{\ast }$	∗	$R^{\ast }$	Group of units	\ast	∗	U+2217
${}^{\times }$	⨯	$R^{\times }$		\times	×	U+2A2F
$\vartriangleleft$	⊲	$I\vartriangleleft R$	Ideal (ring theory)	\vartriangleleft	⊲	U+22B2
$/$	/	$R/I$	Quotient ring	/	⁄	U+002F
$[~~]$	[ ]	$R[X]$	Polynomial ring	[ ]	[ ]	U+005B/D
$[[~~]]$	[ ]	$R[[X]],R((X))$	Formal power series	[[ ]]	[ ]	U+005B/D
$\deg$	deg	$\deg p(x)$	Degree of a polynomial	\deg	deg;

Geometry

Euclidean geometry

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$[~~]$	[ ]	$[AB]$	Line segment	[ ] \left[ \right]	[ ]	U+005B/D
$|~~|$	| |	$|AB|$		\vert	|	U+007C
${\overline {~~}}$	̅	${\overline {AB}}$		\overline	̅	U+0305
${\underline {~~}}$	̲	${\underline {AB}}$		\underline	̲	U+0332
${\overrightarrow {~~}}$	⃗	${\overrightarrow {AB}}$	Euclidean vector and Affine space	\vec	⃗	U+20D7
$\angle$	∠	$\angle ABC$	Angle	\angle	∠	U+2220
${\displaystyle }$	∡	∡ABC	Angle measure		∡	U+2221
${\displaystyle }$	∟	∟ABC	Right angle		∟	U+221F
${\displaystyle }$	⦜	⦜ABC	Right angle		⦜	U+299C
${\displaystyle }$	⦟	⦟ABC	Acute angle		⦟	U+299F
${\displaystyle }$	⦦	⦦ABC	Obtuse angle, Oblique angle		⦦	U+29A6
${\displaystyle }$	⦞	⦞ABC	Angles		⦞	U+299E
$\parallel$	∥	$g\parallel h$	Parallel (geometry)	\parallel	∥	U+2225
$\nparallel$	∦	$g\nparallel h$		\nparallel	∦	U+2226
$\perp$	⟂	$g\perp h$	Orthogonality	\perp	⊥	U+27C2
$\triangle$	△	$\triangle ABC$	Triangle	\triangle	△	U+25B3
${\displaystyle }$	⊿	⊿ABC	Right triangle		⊿	U+22BF
$\square$	□	$\square {\mathit {ABCD}}$	Quadrilateral	\square	□	U+25A1
${\displaystyle }$	▭	▭ABCD	Rectangle		▭	U+25AD
${\displaystyle }$	⏢	⏢ABCD	Trapezium/Trapezoid		⏢	U+23E2
${\displaystyle }$	▱	▱ABCD	Parallelogram		▱	U+25B1
${\displaystyle }$	◊	◊ABCD	Rhombus, Lozenge		◊	U+25CA
${\displaystyle }$	⬠	⬠ABCDE	Pentagon		⬠	U+2B20
${\displaystyle }$	⬡	⬡ABCDEF	Hexagon		⬡	U+2B21
${\displaystyle }$	⬢	⬢ABCDEF	Hexagon		⬢	U+2B22
${\displaystyle }$	○	○S	Circle		○	U+25CB
${\displaystyle }$	●	●S	Disc		●	U+25CF

Differential geometry

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${\mathcal {L}}$	ℒ	${\mathcal {L}}_{X}\omega$	Lie derivative	\mathcal{L}	ℒ	U+2112
$\mathbin {\lrcorner }$	⌟	$X\mathbin {\lrcorner } \omega$	Interior product	\mathbin{\lrcorner}	⌟	U+231F
$\iota$	𝜄	$\iota _{X}\omega$		\iota	𝜄	U+1D704
$\wedge$	∧	$\omega \wedge \eta$	Wedge product	\wedge	∧	U+2227
$\bigwedge$	⋀	${\textstyle \bigwedge ^{k}}A$		\bigwedge	⋀	U+22C0

Topology

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
$\partial$	∂	$\partial U$	Boundary (topology)	\partial	∂	U+2202
${}^{\circ }$	˚	$U^{\circ }$	Interior (topology)	\circ	°	U+02DA
${\bar {~}}$	◌̄	${\bar {z}}$	Closure (topology)	\bar	̄	U+0304
${\overline {~~}}$	◌̅	${\overline {z}}$		\overline	̅	U+0305
${\dot {~}}$	◌̇	${\dot {U}}(x)$	Punctured neighbourhood	\dot		U+0307

See also

By type of symbol

• List of letters used in mathematics, science, and engineering
  • Greek letters used in mathematics, science, and engineering
  • Latin letters used in mathematics, science, and engineering
• Blackboard bold
• Diacritic

By topic area

• Glossary of mathematical symbols
  • List of logic symbols
• APL syntax and symbols
• List of common physics notations
• Notation in probability and statistics
• Physical constants

General

• List of mathematical abbreviations
• Mathematical notation
• Language of mathematics

Unicode

• Lists of Mathematical operators and symbols in Unicode
  • Mathematical Operators and Supplemental Mathematical Operators
  • List of mathematical symbols
  • Miscellaneous Math Symbols: A, B, Technical
  • Arrow (symbol) and Miscellaneous Symbols and Arrows and arrow symbols
  • ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)
  • Number Forms
  • Geometric Shapes
• Mathematical Alphanumeric Symbols, a Unicode block
  • Mathematical constants and functions
  • Table of mathematical symbols by introduction date
• List of Unicode characters
  • Letterlike Symbols
  • Unicode block

Bibliography

• Tilo Arens; Frank Hettlich; Christian Karpfinger; Ulrich Kockelkorn; Klaus Lichtenegger; Hellmuth Stachel (2011), Mathematik (in German) (2. ed.), Spektrum Akademischer Verlag, pp. 1483ff, ISBN 978-3-827-42347-4
• Wolfgang Hackbusch (2010), Taschenbuch der Mathematik, Band 1 (in German) (3. ed.), Springer, pp. 1275ff, ISBN 978-3-835-10123-4
• Deutsches Institut für Normung: DIN 1302: Allgemeine mathematische Zeichen und Begriffe, Beuth-Verlag, 1999.
• Deutsches Institut für Normung: DIN 1303: Vektoren, Matrizen, Tensoren; Zeichen und Begriffe, Beuth-Verlag, 1987.
• International Standards Organisation: DIN EN ISO 80000-2: Größen und Einheiten – Teil 2: Mathematische Zeichen für Naturwissenschaft und Technik, 2013.

External links

LaTeX and Unicode

• Symbols defined by unicode-math - Lists LaTeX and corresponding Unicode symbols
• Unicode characters and corresponding LaTeX math mode command

LaTeX

• Scott Pakin (25 June 2020). "The Comprehensive LaTeX Symbol List" (PDF; 4,4 MB). The Comprehensive TeX Archive Network (CTAN). Retrieved 8 August 2020.
• Detexify − Online tool: Find LaTeX code for a symbol by drawing it.

Unicode

• Symbols defined by unicode-math
• "Mathematical Operators – Unicode" (PDF). Retrieved 2013-07-20.
• Lists Unicode Block "Mathematical Operators"
• Lists Unicode Block "Supplemental Mathematical Operators"
• Lists Unicode Block "Miscellaneous Mathematical Symbols-A"
• Lists Unicode Block "Miscellaneous Mathematical Symbols-B"
• Lists Unicode Block "Mathematical Alphanumeric Symbols
• Shapecatcher − Online tool: Find Unicode and HTML codes for a symbol by drawing it.