It has been suggested that this article be merged into Glossary of mathematical symbols. (Discuss) Proposed since August 2023.

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 &times;.
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 &#x2A2F; where #x indicates that the value in hexadecimal.

Numbers

Number sets

Symbol Unicode character Articles with usage LaTeX HTML Unicode Hex
𝔸 Algebraic number \mathbb{A} &Aopf; U+1D538
Complex number \mathbb{C}, \Complex &Copf; U+2102
Quaternion \mathbb{H} &quaternions; U+210D
Natural number \mathbb{N}, \N &Nopf; U+2115
𝕆 Octonion \mathbb{O} &Oopf; U+1D546
Rational number \mathbb{Q}, \Q &Qopf; U+211A
Real number \mathbb{R}, \R, \Reals &Ropf; U+211D
𝕊 Sedenion \mathbb{S} &Sopf; U+1D54A
Integer \mathbb{Z}, \Z &Zopf; U+2124

Intervals

Symbol Usage LaTeX HTML Unicode Hex
( )
[ ]
&lpar; &rpar;
&lsqb; &rsqb;
U+0028/9
U+005B/D

Mathematical constants

For symbols of additional mathematical constants, see Mathematical constant.

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

Complex numbers

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Complex number \Im &image; U+2111
Im \operatorname{Im} Im
\Re &Rfr; U+211C
Re \operatorname{Re} Re
◌̄ Complex conjugate \bar &#x304; U+0304
◌̄̄ \bar{\bar{)) &#x304;&#x304;
◌̅ \overline &#x305; U+0305
◌̅̅ \overline{\overline{)) &#x305;&#x305;
* {}^\ast &ast; U+002A
| Absolute value \vert &VerticalLine; U+007C
Polar coordinate system \arg
Remark: real and imaginary parts of a complex number are often also denoted by and .

Elementary arithmetic operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex Notes
+ Addition + &plus; U+002B
Subtraction - &minus; U+2212
Multiplication \cdot &sdot; U+22C5
\times &times; U+2A2F
∶  or  : Division (mathematics) :\colon &ratio; or &colon; U+003A or U+2236 In LaTeX, : added space around the colon that \colon does not .
/ &#x2215; U+2215
÷ \div &divide; U+00F7
\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: ab
Multiplicative inverse ^{-1} U+207B
Additive inverse - &minus; U+2212
± Plus or minus sign \pm &plusmn; U+00B1
\mp &mnplus; U+2213

Elementary functions

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

Arithmetic comparison

See also: Order relations, Set relations
Symbol Unicode character Usage LaTeX HTML Unicode Hex
< < &lt; U+003C
> > &gt; U+003E
\le, \leq &le; U+2264
\ge, \geq &ge; U+2265
\leqq &LessFullEqual; U+2266
\geqq &GreaterFullEqual; U+2267
\leqslant &LessSlantEqual U+2A7D
\geqslant &GreaterSlantEqual U+2A7E
\ll &NestedLessLess; U+226A
\gg &NestedGreaterGreater; U+226B
\lesssim &lsim; U+2272
\gtrsim &GreaterTilde; U+2273
\lessapprox &lessapprox; U+2A85
\gtrapprox &gap; U+2A86
Symbol Unicode character Usage LaTeX HTML Unicode Hex
\lessgtr &LessGreater U+2276
\gtrless &GreaterLess; U+2277
\lesseqgtr &LessEqualGreater; U+22DA
\gtreqless &GreaterEqualLess; U+22DB
\lesseqqgtr &lesseqqgtr; U+2A8B
\gtreqqless &gtreqqless; U+2A8C

Number theory

Divisibility and modulo

Symbol Unicode character Usage LaTeX HTML Unicode Hex
\mid &VerticalBar; U+2223
\nmid &NotVerticalBar; U+2224
\perp &perp; U+22A5
\sqcap &SquareIntersection; U+2293
\wedge &and; U+2227
\sqcup &SquareUnion; U+2294
\vee &or; U+2228
Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex Other information
Modulo operation \equiv &equiv; U+2261
mod \mod m mod <math>\mod</math> without a trailing symbol (e.g. ) will produce an error.
(mod) \pmod m (mod) <math>\pmod</math> without a trailing symbol (e.g. ) will produce an error.
gcd Greatest common divisor \gcd gcd

Combinatorics

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
! Factorial ! &excl; U+0021
Derangement
Double factorial
( ) Combination \binom &lpar; &rpar; U+0028/9
Multinomial coefficient
(( )) Multiset (( )) &lpar; &rpar; U+0028/9
◌̄ Pochhammer symbol \bar &#x304; U+0304
◌̅ \overline &#x305; U+0305
◌̲ \underline &#x332; U+0332
# Primorial \# &num; U+0023

Stochastics

Probability theory

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Probability measure P U+2119
Conditional probability \mid &VerticalLine; U+007C
/ U+2215
𝔼 Expected value E &Eopf; U+1D53C
𝕍 Variance V &Vopf; U+1D54D
σ Standard deviation \sigma &sigma; U+03C3
Covariance
ρ Correlation \rho &rho; U+03C1
Probability distribution \sim &sim; U+223C
\approx &asymp; U+2248
Independence (probability theory) \perp &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
◌̅ Average \bar &#x304; U+0304
◌̅ \overline &#x305; U+0305
⟨ ⟩ \langle \rangle &lang; &rang; U+27E8/9
◌̂ Estimator \hat ̂ U+0302

Calculus

Sequences and series

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Summation \sum &sum; U+2211
Multiplication \prod &prod; U+220F
Coproduct \coprod &Coproduct; U+2210
( ) Sequence ( ) &lpar; &rpar; U+0028/9
Limit of a sequence \to \rarr &rarr; U+2192
Infinity \infty &infin; U+221E

Limits

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Limit of a function \to
\rightarrow
&rarr;
&rightarrow;
U+2192
\longrightarrow &LongRightArrow; U+27F6
\uparrow &uarr;
&ShortUpArrow;
U+2191
\nearrow &UpperRightArrow; U+2197
\searrow &LowerRightArrow; U+2198
\downarrow &darr;
&ShortDownArrow;
U+2193
\swarrow &LowerLeftArrow; U+2199
\leftarrow &larr;
&ShortLeftArrow;
U+2190
\longleftarrow &longleftarrow; U+27F5
\nwarrow &UpperLeftArrow; U+2196
^+ &#8314; U+207A
^- &#8315; U+207B
\lim
Limit inferior and limit superior \liminf
\limsup

Differential calculus

Main article: Differential calculus

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex


Lagrange's notation
Prime (symbol)
'
^\prime
&prime; U+2032


''
^{\prime\prime}
&Prime; U+2033


'''
^{\prime\prime\prime}
&tprime; U+2034


''''
^{\prime\prime\prime\prime}
&qprime; U+2057
^{IV} ^V ^{VI} <sup>IV</sup>
^{iv} ^v ^{vi} <sup>iv</sup>
⁽ ⁾ ^{( )} <sup>( )</sup> U+207D/E
◌̇ Newton's notation \dot &#x0307; U+0307
◌̈ \ddot &#x0308; U+0308
d Leibniz's notation d d U+0064
Partial derivative \partial &part; U+2202
∂ and | \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
, Integral \int &int; U+222B
Surface integral \iint &Int; U+222C
Volume integral \iiint &tint; U+222D
Curve integral \oint &ContourIntegral; U+222E
\oiint \oiint Surface integral \oiint &DoubleContourIntegral; U+222F
\oiiint \oiiint Volume integral \oiiint &Cconint; U+2230

Vector calculus

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Gradient \nabla &nabla; U+2207
Divergence
Curl (mathematics)
Laplace operator \Delta &Delta; U+2206
D'Alembert operator \square &#9633; U+25A1

Asymptotic behaviour

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Asymptotic analysis \sim &sim; U+223C
o Big O notation o U+006F
𝒪 \mathcal{O} &Oscr; U+1D4AA
Θ \Theta &Theta; U+0398
Ω \Omega &Omega; U+03A9
ω \omega &omega; U+03C9

Linear algebra

Vectors and matrices

Symbol Articles with usage LaTeX
Vector (mathematics and physics) \begin{pmatrix}
...
\end{pmatrix}

or

\left(
\begin{array}{...}
...
\end{array}
\right)
Matrix (mathematics)

Vector operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Dot product

Inner product space

\cdot &sdot; U+22C5
( ) ( ) &lpar; &rpar; U+0028/9
⟨ ⟩
\langle \rangle &lang; &rang; U+27E8/9
Cross product \times &times; U+2A2F
[ ] [ ] &lsqb; &rsqb; U+005B/D
( ) Triple product ( ) &lpar; &rpar; U+0028/9
Dyadic product \otimes &otimes; U+2297
Exterior algebra \wedge &and; U+2227
| | Euclidean norm \vert &VerticalLine; U+007C

Norm (mathematics) \Vert\|
\lVert \rVert
&Vert; U+2016
̂ Unit vector \hat{} &#x302; U+0302

Matrix operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Matrix multiplication \cdot &sdot; U+22C5
Hadamard product \circ &SmallCircle; U+2218
Hadamard division \oslash &osol; U+2298
* Khatri-Rao product * &ast; U+002A
Kronecker product \otimes &otimes; U+2297
Transposed matrix ^\intercal &intercal; U+22BA
^\top &top; U+22A4
T ^{\mathrm T} U+0054
* Conjugate transpose ^\ast &ast; U+002A
^\dagger &dagger; U+2020
H ^H U+0048
Inverse matrix ^{-1} U+207B
+ Moore–Penrose pseudoinverse ^+ &plus; U+002B
| A | Determinant |, \vert &VerticalLine; U+007C
det \det det
Matrix norm \|, \Vert &Vert; U+2016

Vector spaces

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
+ Direct sum of modules

Linear subspace

+ &plus; U+002B
\oplus &oplus; U+2295
Direct product \times &times; U+2A2F
Tensor product \otimes &otimes; U+2297
/ Quotient space (linear algebra) / &frasl; U+002F
Orthogonal complement ^\perp &perp; U+27C2
* Dual space ^\ast &lowast; U+002A
0 ^0 U+0030
⟨ ⟩ Linear hull \langle \rangle &lang; &rang; U+27E8/9
dim Dimension (linear algebra) \dim dim
ker Kernel (linear algebra) \ker ker
Pr Projection (linear algebra) \Pr Pr

Functional analysis

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Dual space ^\prime &prime; U+2032/3
◌̂ Complete metric space \hat{} U+0302
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
= Equality = &equals; U+003D
# Apartness relation \# &num; U+0023
Inequality \neq
\ne
\not=
&ne; U+2260
Identity \equiv &equiv; U+2261
Approximation \approx &asymp; U+2248
Equivalence class \sim &sim; U+223C
Proportionality \propto &prop; U+221D
Bijection \widehat{=} &wedgeq; U+2259
Asks "is it equal to" \overset{?}{=} &questeq; U+225F
Equal to by definition \overset{\operatorname{def)){=} &#x225D; U+225D
\triangleq &trie; U+225C
Assignment := &coloneq; U+2254
=: &eqcolon; U+2255
Approaches the limit \doteq &esdot; U+2250
Relational operator == &Equal; U+2A75

Logical operators

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Logical conjunction \land &and; U+2227
Logical disjunction \lor &or; U+2228
Logical equivalence \Leftrightarrow &hArr; U+21D4
\leftrightarrow &harr; U+2194
\iff &Longleftrightarrow; U+27FA
Logical consequence \Rightarrow &rArr; U+21D2
\rightarrow &rarr; U+2192
\implies &DoubleLongRightArrow; U+27F9
\Longrightarrow
Exclusive or \oplus &oplus; U+2295
\veebar &veebar; U+22BB
\dot\lor U+2A52
¬ Logical negation \lnot &not; U+00AC
◌̄ \bar &#x304; U+0304
̅ \overline &#x305; U+0305
◌̸
\not
(ex: \not= \not\in)
&#x338;
(ex: =&#x338; &isin;&#x338;)
U+0338
Converse implication \leftarrow &ShortLeftArrow; U+2190
Linear logic \multimap &mumap; 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
Universal quantification \forall &forall; U+2200
\bigwedge &Wedge; U+22C0
Existential quantification \exists &exist; U+2203
\bigvee &xvee; U+22C1
∃! Uniqueness quantification \exists! &exist;! U+2203!
\dot\bigvee U+2A52
Existential quantification \nexists &NotExists; U+2204

Deduction symbols

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Logical consequence, Propositional calculus \vdash &vdash; U+22A2
Logical consequence, Inference \models &DoubleRightTee; U+22A8
Tautology (logic)
\top &top; U+22A4
Contradiction \bot &perp; U+22A5
Deductive reasoning \therefore &therefore; U+2234
\because &because; U+2235

End of proof symbols

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
...as desired. Q.E.D. \blacksquare &#x25A0; U+25A0
\Box &squ; U+25A1
Tombstone &#x220E; U+220E

Formal language and strings

Main article: Formal language

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
ε Empty string \varepsilon &epsi; U+03B5
| | String length \vert &VerticalLine; U+007C
+ Concatenation + &plus; U+002B
\cdot &sdot; U+22C5
¬ Formal language \lnot &not; U+00AC
* Kleene star ^\ast &lowast; U+002A
+ Free monoid ^+ &plus; U+002B
Squiggle operator \sim &sim; U+223C
⟦⟧ Squiggle operator [\![ ]\!] &LeftDoubleBracket; &RightDoubleBracket; U+27E6/7

Functions and category theory

Functions

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Function (mathematics) \to &rarr; U+2192
\mapsto &mapstoright; U+21A6
( ) Image (mathematics) ( ) &lpar; &rpar; U+0028/9
[ ] [ ] &lbrack; or &rbrack; U+005B/D
| Restriction (mathematics) \vert &VerticalLine; U+007C
Free variable \cdot &sdot; U+22C5
Inverse function -1 U+207B
Function composition \circ &#8728; U+2218
Convolution \ast &lowast; U+2217
◌̂ Fourier transform \hat U+0302
Multimap \multimap &mumap; U+22B8

Morphisms

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Morphism \to &rarr; U+2192
\mapsto &mapstoright; U+21A6
Isomorphism \tilde{\rightarrow} U+2972
Monomorphism \hookrightarrow &#8618 U+21AA
Epimorphism \twoheadrightarrow &#8608 U+21A0
hom Morphism \hom hom

Constructions

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Product (category theory) \prod &prod; U+220F
Coproduct \coprod &Coproduct; U+2210
Biproduct \oplus &CirclePlus; U+2295
× Pullback (category theory) \times &times; U+00D7
lim Limit (category theory) \lim lim
projlim Inverse limit \projlim projlim
\varprojlim
injlim Direct limit \injlim injlim
\varinjlim

Set theory

Definition symbols

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
: Definition \colon &colon; U+003A

Set construction

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Empty set \varnothing &varnothing;
&empty;
U+2205
\emptyset
{ } Set (mathematics) \{ \}
\lbrace \rbrace
&lcub; &rcub; U+007B/D
| \mid &VerticalLine; U+007C
: \colon &colon; U+003A
:
Comparison of separators (the symbol between the variable and predicate)
Rendered result Latex code Notes on separator
\{x\in X : P(x)\} : inserts whitespace that \colon does not.
\{x\in X \colon P(x)\}
\{x\in X \mid P(x)\} \mid inserts whitespace that \vert does not.
\{x\in X \vert P(x)\} \vert and | are synonyms in LaTeX.
\{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 \mid |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\} 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
Intersection (set theory) \cap &cap; U+2229
\bigcap &xcap;
&Intersection;
U+22C2
Union (set theory) \cup &cup; U+222A
\bigcup &xcup;
&Union;
U+22C3
Difference (set theory) \setminus &setminus;
&smallsetminus;
U+2216
\smallsetminus
Symmetric difference \triangle &Delta; U+2206
\ominus &CircleMinus; U+2296
Cartesian product \times &times; U+2A2F
Intersection (set theory) \dot\cap &capdot; U+2A40
\sqcap &SquareIntersection; U+2293
\capwedge &capand; U+2A44
Disjoint union \dot\cup &cupdot; U+228D
\uplus &uplus; U+228E
\sqcup &SquareUnion; U+2294
Transversal intersection \mlcp &mlcp; U+2ADB
Complement (set theory) ^\complement &complement; U+2201
C ^{\mathrm C} &complement; U+2201
◌̄ \bar{} &#x304; U+0304
◌̅ \overline{} U+0305
Power set \wp &wp; U+2118
𝒫 \mathcal{P} &Pscr; U+1D4AB
𝔓 \mathfrak{P} &Pfr; U+1D513
Infimum and supremum \bigwedge
\bigwedge\limits_{}
&Wedge; U+22C0
\bigvee
\bigvee\limits_{}
&xvee; U+22C1

Set relations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Subset \subset &sub; U+2282
\subsetneq &subne; U+228A
\subseteq &sube; U+2286
AB \subsetcirc &#x27C3; U+27C3
Superset \supset &sup; U+2283
\supsetneq &supne; U+228B
\supseteq &supe; U+2287
AB \supsetcirc &#x27C4; U+27C4
\not\subset &nsub; U+2284
Superset \not\supset &nsup; U+2285
\not\subseteq &NotSubsetEqual; U+2288
Superset \not\supseteq &NotSupersetEqual; U+2289
Element (mathematics) \in &isin; U+2208
\ni, \owns &ni; U+220B
\notin, \not\in &notin; U+2209
\not\ni &NotReverseElement; U+220C
Substring \sqsubset &SquareSubset; U+228F
\sqsupset &SquareSuperset; U+2290
\sqsubseteq &sqsubseteq; U+2291
\sqsupseteq &SquareSupersetEqual; U+2292

Note: The symbols and 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
| | Cardinality \vert &VerticalLine; U+007C
# \# &num; U+0023
𝔠 Cardinality of the continuum \mathfrak{c} &cfr; U+1D520
, , ... Aleph number \aleph &aleph; U+2135
, , ... Beth number \beth &beth; U+2136

Equivalence classes/relations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
[ ] Equivalence class [ ] &lsqb; &rsqb; U+005B/D
/ Quotient set / &sol; U+002F
Equivalence relation \sim &sim;, &Tilde; U+223C
\backsim &bsim; U+223D
\not\sim, \nsim &nsim; U+2241
\eqsim &EqualTilde; U+2242
\simeq &TildeEqual; U+2243
\cong &TildeFullEqual; U+2245
\not\cong, \ncong &NotTildeFullEqual; U+2247

Order theory

Comparisons

See also: Arithmetic comparison, Set relations
Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Order relation \leq, \le &leq;, &le; U+2264
\geq, \ge &geq;, &ge; U+2265
\nless &nlt;, &NotLess; U+226E
\ngtr &ngt;, &NotGreater; U+226F
\not\leq, \nleq &nle;, &NotLessEqual; U+2270
\not\geq, \ngeq &nge;, &NotGreaterEqual; U+2271
Inequality (mathematics) \lesssim &lsim;, &LessTilde; U+2272
\gtrsim &gsim;, &GreaterTilde; U+2273
\not\lesssim &NotLessTilde; U+2274
\not\gtrsim &NotGreaterTilde; U+2275
Successor ordinal \prec &prec; U+227A
\succ &succ; U+227B
\preccurlyeq &PrecedesSlantEqual; U+227C
\succcurlyeq &SucceedsSlantEqual; U+227D
\precsim &PrecedesTilde; U+227E
\succsim &SucceedsTilde; U+227F
\preceq &PrecedesEqual; U+2AAF
\succeq &SucceedsEqual; U+2AB0
\curlyeqprec &curlyeqprec; U+22DE
\curlyeqsucc &curlyeqsucc; U+22DF
Partially ordered set \sqsubset &sqsubset;
&SquareSubset;
U+228F
\sqsupset &sqsupset;
&SquareSuperset;
U+2290
\sqsubseteq &sqsubseteq;
&SquareSubsetEqual;
U+2291
\sqsupseteq &sqsupseteq;
&SquareSupersetEqual;
U+2292
\not\sqsubseteq &NotSquareSubsetEqual; U+22E2
\not\sqsupseteq &NotSquareSupersetEqual; U+22E3

Binary relations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
; ; Composition of relations ; &semi; U+003B
Operation (mathematics) \bullet &bull; U+2219
\ast &lowast; U+2217
Converse relation T
Complementary relation \bar{R}
+ Transitive closure + U+002B
* Reflexive closure \ast &lowast; U+002A

Algebra

Group theory

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
Group isomorphism \simeq U+2243
\cong &cong; U+2245
Direct product \times &times; U+2A2F
Semidirect product \rtimes &rtimes; U+22CA
Wreath product \wr &VerticalTilde; U+2240
Subgroup \leq &le; U+2264
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