List of mathematical symbols by subject

This list of mathematical symbols by subject shows a selection of the most common symbols that are used in modern mathematical notation within formulas, grouped by mathematical topic. As it is virtually impossible to list all the symbols ever used in mathematics, 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 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.
Interpretation
A short textual description of the meaning of the formula in the previous column.
Article
The Wikipedia article that discusses the meaning (semantics) of the symbol.
LaTeX
The LaTeX command that creates the icon. Characters from the ASCII character set can be used directly, with a few exceptions (pound sign #, backslash \, braces {}, and percent sign %). High-and low-position is indicated via the characters ^ and _ 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 can &#xnnnn by specifying the Unicode code point of the next column. High-and low-position can be indicated via <sup></sup> and <sub></sub>.
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 the opening and the closing forms are specified.

Set theory

Definition symbols

Symbol Usage Interpretation Article LaTeX HTML Unicode
: A : B A is defined by B Definition : U+003A
A := B A is defined as equal to B
A :\Leftrightarrow B A is defined as equivalent to B

Set construction

Symbol Usage Interpretation Article LaTeX HTML Unicode
\varnothing Empty set Empty set \varnothing,
\emptyset
&empty; U+2205
\{ ~ \} \{ a,b,\ldots \} Set consisting of the elements a, b and so on Set (mathematics) \{ \} U+007B/D
\mid \{ a \mid T(a) \} Set of elements a, that satisfy the condition T(a) \mid U+007C
\colon \{ a \, \colon T(a) \} \colon U+003A

Set operations

Symbol Usage Interpretation Article LaTeX HTML Unicode
\cup A \cup B Union of the sets A and B Union (set theory) \cup &cup; U+222A
\cap A \cap B Intersection of the sets A and B Intersection (set theory) \cap &cap; U+2229
\setminus A \setminus B Difference of sets A and B Difference (set theory) \setminus U+2216
\triangle A \, \triangle \, B Symmetric difference of sets A and B Symmetric difference \triangle &Delta; U+2206
\times A \times B Cartesian product of sets A and B Cartesian product \times &times; U+2A2F
\dot{\cup} A \, \dot{\cup} \, B Disjoint union of sets A and B Disjoint union \dot\cup U+228D
\sqcup A \sqcup B Disjoint intersection of sets A and B \sqcup U+2294
{}^{\mathrm C} A^{\mathrm C} Complement of the set A Complement (set theory) \mathrm{C} U+2201
\overline{~~} \overline{A} \bar U+0305
\mathcal{P} \mathcal{P}(A) Power set of the set A Power set \mathcal{P} U+1D4AB
\mathfrak{P} \mathfrak{P}(A) \mathfrak{P} U+1D513

Set relations

Symbol Usage Interpretation Article LaTeX HTML Unicode
\subset A \subset B A is a proper subset of B Subset \subset &sub; U+2282
\subsetneq A \subsetneq B \subsetneq U+228A
\subseteq A \subseteq B A is a subset of B \subseteq &sube; U+2286
\supset A \supset B A is a proper superset of B Superset \supset &sup; U+2283
\supsetneq A \supsetneq B \supsetneq U+228B
\supseteq A \supseteq B A is a superset of B \supseteq &supe; U+2287
\in a \in A Element a is in the set A Element (mathematics) \in &isin; U+2208
\ni A \ni a \ni, \owns &ni; U+220B
\notin a \notin A Element a is not in the set A \notin &notin; U+2209
\not\ni A \not\ni a \not\ni U+220C

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

Number sets

Symbol Usage Interpretation Article LaTeX HTML Unicode
\N Natural numbers Natural number \mathbb{N} U+2115
\Z Integers Integer \mathbb{Z} U+2124
\Q Rational numbers Rational number \mathbb{Q} U+211A
\mathbb A Algebraic numbers Algebraic number \mathbb{A} U+1D538
\R Real numbers Real number \mathbb{R} U+211D
\C Complex numbers Complex number \mathbb{C} U+2102
\H Quaternions Quaternion \mathbb{H} U+210D

Cardinality

Symbol Usage Interpretation Article LaTeX HTML Unicode
|~~| |A| Cardinality of the set A Cardinality \vert U+007C
\# \# A \# U+0023
\mathfrak{c} Cardinality of the continuum Cardinality of the continuum \mathfrak{c} U+1D520
\aleph \aleph_0, \aleph_1, ... Infinite cardinals Aleph number \aleph U+2135
\beth \beth_0, \beth_1, ... Beth numbers Beth number \beth U+2136

Arithmetic

Arithmetic operators

Symbol Usage Interpretation Article LaTeX HTML Unicode
+ a + b a added to b Addition + U+002B
- a - b b subtracted from a Subtraction - U+2212
\cdot a \cdot b a multiplied by b Multiplication \cdot &middot; U+22C5
\times a \times b \times &times; U+2A2F
: a : b a divided by b Division (mathematics) : U+003A
/ a/b / &frasl; U+2215
\div a \div b \div &divide; U+00F7
\frac{~~}{~~} \tfrac{a}{b} \frac U+2044
- -a Negative of the number a or the additive inverse of a Unary minus - &minus; U+2212
\pm \pm a Plus or minus a Plus or minus sign \pm &plusmn; U+00B1
\mp \mp a Minus or plus a \mp U+2213
(~) (a) Term  a is evaluated first Bracket ( ) U+0028/9
[~] [a] [ ] U+005B/D

Equality signs

Symbol Usage Interpretation Article LaTeX HTML Unicode
= a = b a equals b Equality (mathematics) = U+003D
\neq a \neq b a does not equal b Inequality (mathematics) \neq &ne; U+2260
\equiv a \equiv b a is identical to b Identity (mathematics) \equiv &equiv; U+2261
\approx a \approx b a is approximately equal to b Approximation \approx &asymp; U+2248
\sim a \sim b a is proportional to b Proportionality (mathematics) \sim &sim; U+223C
\propto a \propto b \propto &prop; U+221D
\widehat{=} a \, \widehat{=} \, b a corresponds to b Correspondence (mathematics) \widehat{=} U+2259
See also: Equals sign

Comparison

Symbol Usage Interpretation Article LaTeX HTML Unicode
< a < b a is less than b Comparison (mathematics) < &lt; U+003C
> a > b a is greater than b > &gt; U+003E
\leq a \leq b a is less than or equal to b \le, \leq &le; U+2264
\leqq a \leqq b \leqq U+2266
\geq a \geq b a is greater than or equal to b \ge, \geq &ge; U+2265
\geqq a \geqq b \geqq U+2267
\ll a \ll b a is much smaller than b \ll U+226A
\gg a \gg b a is much bigger than b \gg U+226B

Divisibility

Symbol Usage Interpretation Article LaTeX HTML Unicode
\mid a \mid b a divides b Divisibility \mid U+2223
\nmid a \nmid b a does not divide b \nmid U+2224
\perp a \perp b a and b are relatively prime Relatively prime \perp &perp; U+22A5
\sqcap a \sqcap b Greatest common divisor of a and b Greatest common divisor \sqcap U+2293
\wedge a \wedge b \wedge U+2227
\sqcup a \sqcup b Least common multiple of a and b Least common multiple \sqcup U+2294
\vee a \vee b \vee U+2228
\equiv \scriptstyle a \, \equiv \, b \pmod m a and b are congruent modulo m Modular arithmetic \equiv &equiv; U+2261

Intervals

Symbol Usage Interpretation Article LaTeX HTML Unicode
[~~] [a,b] Closed interval between a and b Interval (mathematics) ( )
[ ]
U+0028/9
U+005B/D
]~~[ ]a,b[ Open interval between a and b
(~~) (a,b)
[~~[ [a,b[ Right-open interval between a and b
[~~) [a,b)
]~~] ]a,b] Left-open interval between a and b
(~~] (a,b]

Elementary functions

Symbol Usage Interpretation Article LaTeX HTML Unicode
| ~~ | | x | Absolute value of x Absolute value \vert U+007C
\left[ ~~ \right] \left[ x \right] Biggest whole number less than or equal to x Floor and ceiling functions [ ] U+005B/D
\lfloor ~~ \rfloor \lfloor x \rfloor \lfloor \rfloor &lfloor; &rfloor; U+230A/B
\lceil ~~ \rceil \lceil x \rceil Smallest whole number greater than or equal to x \lceil \rceil &lceil; &rceil; U+2308/9
\sqrt{\,} \sqrt{x} Square root of x Square root \sqrt &radic; U+221A
\sqrt[n]{x} n-th root of x nth root
\% x \, \% x percent Percent \% U+0025

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

Complex numbers

Symbol Usage Interpretation Article LaTeX HTML Unicode
\Re \Re(z) Real part of complex number z Complex number \Re U+211C
\Im \Im(z) Imaginary part of complex number z \Im U+2111
\bar{~} \bar{z} Complex conjugate of z Complex conjugate \bar U+0305
{}^\ast z^\ast \ast &lowast; U+002A
| ~~ | | z | Absolute value of complex number z Absolute value \vert U+007C
Remark: real and complex parts of a complex number are often also denoted by \operatorname{Re} and \operatorname{Im}.

Mathematical constants

Symbol Usage Interpretation Article LaTeX HTML Unicode
\pi Pi, or Archimedes' constant Pi \pi &pi; U+03C0
\rm{e} Euler's constant e (mathematics) \rm{e} U+0065
\varphi Golden ratio Golden ratio \varphi &phi; U+03C6
\rm{i} Imaginary unit (square root of −1) Imaginary unit \rm{i} U+0069

See also: mathematical constant for symbols of additional mathematical constants.

Calculus

Sequences and series

Symbol Usage Interpretation Article LaTeX HTML Unicode
\sum \sum_{i=1}^n, \sum_{i \in I} Sum from i=1 to n or over all elements i in set I Summation \sum &sum; U+2211
\prod \prod_{i=1}^n, \prod_{i \in I} Product from i=1 to n or over all elements i in set I Product (mathematics) \prod &prod; U+220F
\coprod \coprod_{i=1}^n, \coprod_{i \in I} Coproduct from i=1 to n or over all elements i in set I Coproduct \coprod U+2210
( ~~ ) ( a_n ) Sequence of elements a_1, a_2, \ldots Sequence ( ) U+0028/9
\to a_n \to a Sequence (a_n) tends to limit a Limit of a sequence \to &rarr; U+2192
\infty n \to \infty n tends to infinity Infinity \infty &infin; U+221E

Functions

Symbol Usage Interpretation Article LaTeX HTML Unicode
\to f \colon A \to B Function f maps from set A to set B Function (mathematics) \to &rarr; U+2192
A \, \stackrel f\to \, B
\mapsto f \colon x \mapsto y Function f maps element x to element y \mapsto U+21A6
x \, \stackrel f\mapsto \, y
( ~~ ) f(x) Image of element x under function f Image (mathematics) ( ) U+0028/9
f(X) Image of set X under function f
[ ~~ ] f[X] [ ] U+005B/D
\vert f \vert_X Restriction of function f to set X Restriction (mathematics) \vert U+007C
\cdot f(\cdot) Placeholder for a variable as argument of function f Free variable \cdot U+22C5
{}^{-1} f^{-1} Inverse function of f Inverse function -1 U+207B
\circ f \circ g Composition of functions f and g Function composition \circ U+2218
\ast f \ast g Convolution of functions f and g Convolution \ast &lowast; U+2217
\hat{~} \hat{f} Fourier transform of function f Fourier transform \hat U+0302

Limits

Symbol Usage Interpretation Article LaTeX HTML Unicode
\uparrow \lim_{x \uparrow a} f(x) Limit of function f as x approaches a from below Limit of a function \uparrow &uarr; U+2191
\nearrow \lim_{x \nearrow a} f(x) \nearrow U+2197
\to \lim_{x \to a} f(x) Limit of function f as x approaches a \to &rarr; U+2192
\searrow \lim_{x \searrow a} f(x) Limit of function f as x approaches a from above \searrow U+2198
\downarrow \lim_{x \downarrow a} f(x) \downarrow &darr; U+2193

Asymptotic behaviour

Symbol Usage Interpretation Article LaTeX HTML Unicode
\sim f \sim g Function f is asymptotically equal to function g Asymptotic analysis \sim &sim; U+223C
o f \in o(g) Function f grows slower than g Big O notation o U+006F
\mathcal{O} f \in \mathcal{O}(g) Function f grows not substantially faster than g \mathcal{O} U+1D4AA
\Theta f \in \Theta(g) Function f grows as fast as g \Theta &Theta; U+0398
\Omega f \in \Omega(g) Function f grows not substantially slower than g \Omega &Omega; U+03A9
\omega f \in \omega(g) Function f grows faster than g \omega &omega; U+03C9

Differential calculus

Symbol Usage Interpretation Article LaTeX HTML Unicode
{}' f', f'' First or second derivative of function f Differentiation (mathematics) \prime &prime; U+2032
\cdot \dot f, \ddot f First or second derivative of function f with respect to time (in physics) \dot, \ddot U+0307
{}^{(~)} f^{(n)} n-th derivative of function f ( ) U+0028/9
d \frac{df}{dx} Derivative of function f with respect to variable x d U+0064
df Total differential of function f Total differential
\partial \frac{\partial\!f}{\partial x} Partial derivative of function f with respect to variable x Partial derivative \partial &part; U+2202

Integral calculus

Symbol Usage Interpretation Article LaTeX HTML Unicode
\int \int_a^b , \displaystyle \int_G Definite integral between a and b or over set G Integral \int &int; U+222B
\oint \oint_\gamma Curve integral along curve \gamma Curve integral \oint U+222E
\iint \iint_{\mathcal F} Surface integral over surface \mathcal F Surface integral \iint U+222C
\iiint \iiint_V Volume integral over volume V Volume integral \iiint U+222D

Vector calculus

Symbol Usage Interpretation Article LaTeX HTML Unicode
\nabla \nabla f Gradient of function f Gradient \nabla &nabla; U+2207
\nabla \cdot F Divergence of vector field F Divergence
\nabla \times F Curl of vector field F Curl (mathematics)
\Delta \Delta f Laplace operator of function f Laplace operator \Delta &Delta; U+2206
\square \square f D'Alembert operator of function f D'Alembert operator \square U+25A1

Topology

Symbol Usage Interpretation Article LaTeX HTML Unicode
\partial \partial U Boundary of set U Boundary (topology) \partial &part; U+2202
{}^\circ U^\circ Interior of set U Interior (topology) \circ &deg; U+02DA
\overline{~~} \overline{U} Closure of set U Closure (topology) \bar U+0305
\dot{~} \dot{U}(x) Punctured neighbourhood U of point x Punctured neighbourhood \dot U+0307

Functional analysis

Symbol Usage Interpretation Article LaTeX HTML Unicode
{}' V' Topological dual space of topological vector space V Dual space \prime &prime; U+2032
{}'' V'' Bidual space of normed vector space V
\hat{~} \hat{X} Completion of metric space X Complete metric space \hat U+0302
\hookrightarrow X \hookrightarrow Y Embedding of topological vector space X into Y Embedding \hookrightarrow U+21AA

Linear algebra and geometry

Elementary geometry

Symbol Usage Interpretation Article LaTeX HTML Unicode
[~~] [AB] Line segment between points A and B Line segment [ ] U+005B/D
|~~| |AB| Length of line segment between points A and B \vert U+007C
\overline{~~} \overline{AB} \overline U+0305
\overrightarrow{~~} \overrightarrow{AB} Vector between points A and B Euclidean vector \vec U+20D7
\angle \angle ABC Angle between line segments BA and BC Angle \angle &ang; U+2220
\triangle \triangle ABC Triangle with vertices A, B and C Triangle \triangle U+25B3
\square \square \mathit{ABCD} Quadrilateral with vertices A, B, C and D Quadrilateral \square U+25A1
\parallel g \parallel h Lines g and h are parallel Parallel (geometry) \parallel U+2225
\nparallel g \nparallel h Lines g and h are not parallel \nparallel U+2226
\perp g \perp h Lines g and h are orthogonal Orthogonality \perp &perp; U+27C2

Vectors and matrices

Symbol Interpretation Article LaTeX
\begin{pmatrix} v_1, \ldots , v_n \end{pmatrix} Row vector comprising elements v_1 through v_n Vector (mathematics and physics) \begin{pmatrix}
...
\end{pmatrix}

oder

\left(
\begin{array}{...}
...
\end{array}
\right)
\begin{pmatrix} v_1 \\ \vdots \\ v_m \end{pmatrix} Column vector comprising elements v_1 through v_m
\begin{pmatrix} a_{11} & \!\ldots\! & a_{1n} \\ \vdots & \!\ddots\! & \vdots \\ a_{m1} & \!\ldots\! & a_{mn} \end{pmatrix} Matrix comprising elements a_{11} through a_{mn} Matrix (mathematics)

Vector calculus

Symbol Usage Interpretation Article LaTeX HTML Unicode
\cdot v \cdot w Dot product of vectors v and w Dot product \cdot &middot; U+22C5
(~~) (v,w) ( ) U+0028/9
\langle ~~ \rangle \langle v,w \rangle
\langle v\,|\,w \rangle
\langle \rangle &lang; &rang; U+27E8/9
\times v \times w Cross product of vectors v and w Cross product \times &times; U+2A2F
[~~] [v,w] [ ] U+005B/D
(~~) (u,v,w) Triple product of vectors u, v and w Triple product ( ) U+0028/9
\otimes v \otimes w Dyadic product of vectors v and w Dyadic product \otimes &otimes; U+2297
\wedge v \wedge w Wedge product of vectors v and w Wedge product \wedge U+2227
|~~| | v | Length of vector v Euclidean norm \vert U+007C
\|~~\| \| v \| Norm of vector v Norm (mathematics) \Vert, \| U+2016
\hat{~} \hat{v} Normalized vector of vector v Unit vector \hat U+0302

Matrix calculus

Symbol Usage Interpretation Article LaTeX HTML Unicode
\cdot A \cdot B Product of matrices A and B Matrix multiplication \cdot &middot; U+22C5
\circ A \circ B Hadamard product of matrices A and B Hadamard product (matrices) \circ U+2218
\otimes A \otimes B Kronecker product of matrices A and B Kronecker product \otimes &otimes; U+2297
{}^{\mathrm T} A^{\mathrm T} Transposed matrix of matrix A Transposed matrix T U+0054
{}^{\mathrm H} A^{\mathrm H} Conjugate transpose of matrix A Conjugate transpose H U+0048
{}^\ast A^\ast \ast &lowast; U+002A
{}^\dagger A^\dagger \dagger &dagger; U+2020
{}^{-1} A^{-1} Inverse matrix of matrix A Inverse matrix -1 U+207B
{}^{+} A^{+} Moore–Penrose pseudoinverse of matrix A Moore–Penrose pseudoinverse + U+002B
| ~~ | | A | Determinant of Matrix A Determinant \vert U+007C
\| ~~ \| \| A \| Norm of matrix A Matrix norm \Vert, \| U+2016

Vector spaces

Symbol Usage Interpretation Article LaTeX HTML Unicode
+ V + W Sum of vector spaces V and W Direct sum of modules + U+002B
\oplus V \oplus W Direct sum of vector spaces V and W \oplus &oplus; U+2295
\times V \times W Direct product of vector spaces V and W Direct product \times &times; U+2A2F
\otimes V \otimes W Tensor product of vector spaces V and W Tensor product \otimes &otimes; U+2297
/ V \, / \, U Quotient space of vector space V by subspace U Quotient space (linear algebra) / &frasl; U+002F
{}^\perp U^\perp Orthogonal complement of subspace U Orthogonal complement \perp &perp; U+27C2
{}^\ast V^{\ast} Dual space of vector space V Dual space \ast &lowast; U+002A
{}^0 X^0 Annihilator space of the set of vectors X 0 U+0030
\langle ~~ \rangle \langle X \rangle Linear hull of the set of vectors X Linear hull \langle \rangle &lang; &rang; U+27E8/9

Algebra

Relations

Symbol Usage Interpretation Article LaTeX HTML Unicode
\circ R \circ S Composition of relations R and S Composition of relations \circ U+2218
a \circ b Operation of elements a and b (general) Operation (mathematics)
\bullet a \bullet b \bullet &bull; U+2219
\ast a \ast b \ast &lowast; U+2217
\leq a \leq b Order relation between elements a and b Order relation \leq &le; U+2264
\prec a \prec b Element a is a predecessor of element b Successor ordinal \prec U+227A
\succ a \succ b Element a is a successor of element b \succ U+227B
\sim a \sim b Equivalence relation between elements a and b Equivalence relation \sim &sim; U+223C
[ ~~ ] [ a ] Equivalence class of element a Equivalence class [ ] U+005B/D
/ M / \sim Quotient set of set M by equivalence relation \sim Quotient set / &frasl; U+002F
{}^{-1} R^{-1} Inverse relation of relation R Inverse relation -1 U+207B
{}^{+} R^{+} Transitive closure of relation R Transitive closure + U+002B
{}^\ast R^\ast Reflexive closure of relation R Reflexive closure \ast &lowast; U+002A

Group theory

Symbol Usage Interpretation Article LaTeX HTML Unicode
\simeq G \simeq H Groups G and H are isomorphic Group isomorphism \simeq U+2243
\cong G \cong H \cong &cong; U+2245
\times G \times H Direct product of groups G and H Direct product \times &times; U+2A2F
\rtimes G \rtimes H Semidirect product of groups G and H Semidirect product \rtimes U+22CA
\wr G \, \wr \, H Wreath product of groups G and H Wreath product \wr U+2240
\leq U \leq G U is a subgroup of group G Subgroup \leq &le; U+2264
< U < G U is a proper subgroup of group G \lt &lt; U+003C
\vartriangleleft N \vartriangleleft G N is a normal subgroup of group G Normal subgroup \vartriangleleft U+22B2
/ G / N Quotient group of group G by normal subgroup N Quotient group / &frasl; U+002F
\colon ( G \colon U ) Index of subgroup U in group G Index of a subgroup \colon U+003A
\langle ~~ \rangle \langle E \rangle Subgroup generated by set E Generating set of a group \langle \rangle &lang; &rang; U+27E8/9
[ ~~ ] [ g, h ] Commutator of elements g and h Commutator [ ] U+005B/D

Field theory

Symbol Usage Interpretation Article LaTeX HTML Unicode
/ L / K Extension of field L over field K Field extension / &frasl; U+002F
\mid L \mid K \mid U+007C
\colon L \colon K \colon U+003A
[ L \colon K ] Degree of field extension L over K Degree of a field extension
\overline{~~} \overline{K} Algebraic closure of field K Algebraic closure \bar U+0305
\mathbb{K} Field of real or complex numbers Field (mathematics) \mathbb{K} U+1D542
\mathbb{F} Finite field Finite field \mathbb{F} U+1D53D

Ring theory

Symbol Usage Interpretation Article LaTeX HTML Unicode
{}^\ast R^\ast Group of units of ring R Group of units \ast &lowast; U+2217
{}^\times R^\times \times &times; U+2A2F
\vartriangleleft I \vartriangleleft R I is an ideal of ring R Ideal (ring theory) \vartriangleleft U+22B2
/ R / I Quotient ring of ring R by ideal I Quotient ring / &frasl; U+002F
[ ~~ ] R[ X ] Polynomial ring over ring R with variable X Polynomial ring [ ] U+005B/D

Combinatorics

Symbol Usage Interpretation Article LaTeX HTML Unicode
! n! Number of permutations of n elements Factorial ! U+0021
!n Number of derangements of n elements (permutations without fixed points) Derangement
n!! Number of involutions without fixed points (n odd) Double factorial
\tbinom{~}{~} \tbinom{n}{k} Number of k-combinations of n elements without repetition Combination \binom U+0028/9
\tbinom{n}{k_1, \ldots , k_r} Number of permutations of n elements of which k_1, \ldots , k_r are identical Multinomial coefficient
\left(\!\tbinom{~}{~}\!\right) \left(\!\tbinom{n}{k}\!\right) Number of k-combinations of n elements with repetition Multiset U+0028/9
\overline{~~} n^{\overline{m}} Rising factorial from n with m factors Pochhammer symbol \overline U+0305
n^{\underline{m}} Falling factorial from n with m factors \underline U+0332
\# n \# Product of all primes up to n Primorial \# U+0023

Stochastics

Probability theory

Symbol Usage Interpretation Article LaTeX HTML Unicode
P P(A) Probability of event A Probability measure P U+2119
\mid P(A \mid B) Probability of event A given event B Conditional probability \mid U+007C
E E(X) Expected value of the random variable X Expected value E U+1D53C
V V(X) Variance of the random variable X Variance V U+1D54D
\sigma \sigma(X) Standard deviation of the random variable X Standard deviation \sigma &sigma; U+03C3
\sigma(X,Y) Covariance of random variables X and Y Covariance
\rho \rho(X,Y) Correlation of random variables X and Y Correlation \rho &rho; U+03C1
\sim X \sim F Random variable X has distribution F Probability distribution \sim &sim; U+223C
\approx X \approx F Random variable X has distribution F approximately \approx &asymp; U+2248
Remark: for operators there are several notational variants; instead of round brackets also square brackets are used

Statistics

Symbol Usage Interpretation Article LaTeX HTML Unicode
\bar{~} \bar{x} Average of the values x_1, \ldots , x_n Average \bar U+0305
\langle ~~ \rangle \langle X \rangle Average over all values in the set X (in physics) \langle \rangle &lang; &rang; U+27E8/9
\hat{~} \hat{p} Estimator for parameter p Estimator \hat U+0302

Logic

Operators

Symbol Usage Interpretation Article LaTeX HTML Unicode
\land A \land B Proposition A and proposition B Logical conjunction \land &and; U+2227
\lor A \lor B Proposition A or proposition B (or both) Logical disjunction \lor &or; U+2228
\Leftrightarrow A \Leftrightarrow B Proposition A follows from proposition B and vice versa Logical equivalence \Leftrightarrow &hArr; U+21D4
\leftrightarrow A \leftrightarrow B \leftrightarrow &harr; U+2194
\Rightarrow A \Rightarrow B From proposition A follows proposition B Logical consequence \Rightarrow &rArr; U+21D2
\rightarrow A \rightarrow B \rightarrow &rarr; U+2192
\oplus A \oplus B Either proposition A or proposition B Exclusive or \oplus &oplus; U+2295
\veebar A \, \veebar \, B \veebar U+22BB
\dot\lor A \, \dot\lor \, B \dot\lor U+2A52
\lnot \lnot A Not proposition A Logical negation \lnot &not; U+00AC
\overline{~~} \overline{A} \bar U+0305

Quantifiers

Symbol Usage Interpretation Article LaTeX HTML Unicode
\forall \forall\,x For all elements x Universal quantification \forall &forall; U+2200
\bigwedge \bigwedge_x \bigwedge U+22C0
\exists \exists\,x At least one element x exists Existential quantification \exists &exist; U+2203
\bigvee \bigvee_x \bigvee U+22C1
\exists ! \exists !\,x Exactly one element x exists Uniqueness quantification \exists &exist; U+2203
\bigvee^\centerdot \bigvee^\centerdot_x \dot\bigvee U+2A52
\nexists \nexists\,x No element x exists Existential quantification \nexists U+2204

Deduction symbols

Symbol Usage Interpretation Article LaTeX HTML Unicode
\vdash A \vdash B Proposition B can be syntactically derived from proposition A Propositional calculus \vdash U+22A2
\models A \models B Proposition B follows semantically from proposition A Inference \models U+22A8
\models A Proposition A is universally true Tautology (logic)
\top A \top \top U+22A4
\bot A \bot Proposition A is contradictory Contradiction \bot &perp; U+22A5
\therefore A \therefore B Proposition A is true, therefore proposition B is true Deductive reasoning \therefore U+2234
\because A \because B Proposition A is true, because B is true \because U+2235
\blacksquare End of proof Q.E.D. \blacksquare U+220E
\Box \Box U+25A1

See also

References

Note: This article is a translation of the German Wikipedia article de:Liste mathematischer Symbole.

External links

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