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 <sup></sup> and <sub></sub>. The character × whose HTML code is times 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
${\displaystyle \mathbb {A} }$	𝔸	Algebraic number	\mathbb{A}	𝔸	U+1D538
${\displaystyle \mathbb {C} }$	ℂ	Complex number	\mathbb{C}, \Complex	ℂ	U+2102
${\displaystyle \mathbb {H} }$	ℍ	Quaternion	\mathbb{H}, \mathbb{H}	ℍ	U+210D
${\displaystyle \mathbb {N} }$	ℕ	Natural number	\mathbb{N}, \N	ℕ	U+2115
${\displaystyle \mathbb {O} }$	𝕆	Octonion	\mathbb{O}	𝕆	U+1D546
${\displaystyle \mathbb {Q} }$	ℚ	Rational number	\mathbb{Q}, \Q	ℚ	U+211A
${\displaystyle \mathbb {R} }$	ℝ	Real number	\mathbb{R}, \R, \Reals	ℝ	U+211D
${\displaystyle \mathbb {S} }$	𝕊	Sedenion	\mathbb{S}	𝕊	U+1D54A
${\displaystyle \mathbb {Z} }$	ℤ	Integer	\mathbb{Z}, \Z	ℤ	U+2124

Intervals

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

Mathematical constants

For symbols of additional mathematical constants, see Mathematical constant.

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

Complex numbers

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

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

Elementary arithmetic operations

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

Elementary functions

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

Arithmetic comparison

See also: Order relations, Set relations

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

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

Number theory

Divisibility and modulo

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

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

Combinatorics

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

Stochastics

Probability theory

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${\displaystyle P}$		${\displaystyle P(A)}$	Probability measure	P		U+2119
${\displaystyle \mid }$		${\displaystyle P(A\mid B)}$	Conditional probability	\mid	|	U+007C
${\displaystyle /}$		${\displaystyle P(A/B)}$		/		U+2215
${\displaystyle E}$	𝔼	${\displaystyle E(X)}$	Expected value	E	𝔼	U+1D53C
${\displaystyle V}$	𝕍	${\displaystyle V(X)}$	Variance	V	𝕍	U+1D54D
${\displaystyle \sigma }$	σ	${\displaystyle \sigma (X)}$	Standard deviation	\sigma	σ	U+03C3
		${\displaystyle \sigma (X,Y)}$	Covariance
${\displaystyle \rho }$	ρ	${\displaystyle \rho (X,Y)}$	Correlation	\rho	ρ	U+03C1
${\displaystyle \sim }$	∼	${\displaystyle X\sim F}$	Probability distribution	\sim	∼	U+223C
${\displaystyle \approx }$	≈	${\displaystyle X\approx F}$		\approx	≈	U+2248
${\displaystyle {\displaystyle \perp }}$	⊥	${\displaystyle A\perp B}$	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
${\displaystyle {\bar {~}}}$	◌̅	${\displaystyle {\bar {x}}}$	Average	\bar	̄	U+0304
${\displaystyle {\overline {~~}}}$	◌̅	${\displaystyle {\overline {m}}}$		\overline	̅	U+0305
${\displaystyle \langle ~~\rangle }$	⟨ ⟩	${\displaystyle \langle X\rangle }$		\langle \rangle	⟨ ⟩	U+27E8/9
${\displaystyle {\hat {~}}}$	◌̂	${\displaystyle {\hat {p}}}$	Estimator	\hat	̂	U+0302

Calculus

Sequences and series

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

Limits

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

Differential calculus

Main article: Differential calculus

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${\displaystyle {}'}$  ${\displaystyle {}^{\prime }}$	′	${\displaystyle f'}$  ${\displaystyle f^{\prime }}$	Lagrange's notation Prime (symbol)	' ^\prime	′	U+2032
${\displaystyle {}''}$  ${\displaystyle {}^{\prime \prime }}$	″	${\displaystyle f''}$  ${\displaystyle f^{\prime \prime }}$		'' ^{\prime\prime}	″	U+2033
${\displaystyle {}'''}$  ${\displaystyle {}^{\prime \prime \prime }}$	‴	${\displaystyle f'''}$  ${\displaystyle f^{\prime \prime \prime }}$		''' ^{\prime\prime\prime}	‴	U+2034
${\displaystyle {}''''}$  ${\displaystyle {}^{\prime \prime \prime \prime }}$	⁗	${\displaystyle f''''}$  ${\displaystyle f^{\prime \prime \prime \prime }}$		'''' ^{\prime\prime\prime\prime}	⁗	U+2057
${\displaystyle ^{IV}\;{}^{V}\;{}^{VI}}$		${\displaystyle f^{IV},f^{V},f^{VI}}$		^{IV} ^V ^{VI}	<sup>IV</sup>
${\displaystyle ^{iv}\;{}^{v}\;{}^{vi}}$		${\displaystyle f^{iv},f^{v},f^{vi}}$		^{iv} ^v ^{vi}	<sup>iv</sup>
${\displaystyle {}^{(~)}}$	⁽ ⁾	${\displaystyle f^{(4)},f^{(5)},f^{(n)}}$		^{( )}	<sup>( )</sup>	U+207D/E
${\displaystyle {\dot {~~}}}$	◌̇	${\displaystyle {\dot {f}}}$	Newton's notation	\dot	&#x0307;	U+0307
${\displaystyle {\ddot {~~}}}$	◌̈	${\displaystyle {\ddot {f}}}$		\ddot	&#x0308;	U+0308
${\displaystyle d}$	d	${\displaystyle dx}$	Leibniz's notation	d	d	U+0064
		${\displaystyle df}$
		${\displaystyle {\frac {df}{dx}}}$
		${\displaystyle {\frac {d}{dx}}f}$
		${\displaystyle {\frac {d^{2}}{dx^{2}}}f}$
${\displaystyle \partial }$	∂	${\displaystyle \partial _{x}f}$	Partial derivative	\partial	&part;	U+2202
${\displaystyle \left.{\frac {\partial }{\partial x}}\right\vert _{x}}$	∂ and |	${\displaystyle \left.{\frac {\partial f}{\partial x}}\right\vert _{x=x_{0}}}$		\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
${\displaystyle \int }$	∫	${\displaystyle \int _{a}^{b}}$  , ${\displaystyle \int _{G}}$	Integral	\int	∫	U+222B
${\displaystyle \iint }$	∬	${\displaystyle \iint _{\mathcal {F}}}$	Surface integral	\iint	∬	U+222C
${\displaystyle \iiint }$	∭	${\displaystyle \iiint _{V}}$	Volume integral	\iiint	∭	U+222D
${\displaystyle \oint }$	∮	${\displaystyle \oint _{\gamma }}$	Curve integral	\oint	∮	U+222E
	∯	${\displaystyle \gamma }$	Surface integral	\oiint	∯	U+222F
	∰	${\displaystyle \gamma }$	Volume integral	\oiiint	∰	U+2230

Vector calculus

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

Asymptotic behaviour

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

Linear algebra

Vectors and matrices

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

Vector operations

Symbol	Unicode character	Usage	Articles with usage	LaTeX	HTML	Unicode Hex
${\displaystyle \cdot }$	⋅	${\displaystyle v\cdot w}$	Dot product Inner product space	\cdot	⋅	U+22C5
${\displaystyle (~~)}$	( )	${\displaystyle (v,w)}$		( )	( )	U+0028/9
${\displaystyle \langle ~~\rangle }$	⟨ ⟩	${\displaystyle \langle v,w\rangle }$  ${\displaystyle \langle v\,|\,w\rangle }$		\langle \rangle	⟨ ⟩	U+27E8/9
${\displaystyle \times }$	⨯	${\displaystyle v\times w}$	Cross product	\times	×	U+2A2F
${\displaystyle [~~]}$	[ ]	${\displaystyle [v,w]}$		[ ]	[ ]	U+005B/D
${\displaystyle (~~)}$	( )	${\displaystyle (u,v,w)}$	Triple product	( )	( )	U+0028/9
${\displaystyle \otimes }$	⊗	${\displaystyle v\otimes w}$	Dyadic product	\otimes	⊗	U+2297
${\displaystyle \wedge }$	∧	${\displaystyle v\wedge w}$	Exterior algebra	\wedge	∧	U+2227
${\displaystyle |~~|}$	| |