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 |
|
|
is defined by |
Definition |
: |
|
U+003A |
|
is defined as equal to |
|
is defined as equivalent to |
Set construction
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Empty set |
Empty set |
\varnothing ,
\emptyset |
∅ |
U+2205 |
|
|
Set consisting of the elements and so on |
Set (mathematics) |
\{ \} |
|
U+007B/D |
|
|
Set of elements , that satisfy the condition |
\mid |
|
U+007C |
|
|
\colon |
|
U+003A |
Set operations
Set relations
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
is a proper subset of |
Subset |
\subset |
⊂ |
U+2282 |
|
|
\subsetneq |
|
U+228A |
|
|
is a subset of |
\subseteq |
⊆ |
U+2286 |
|
|
is a proper superset of |
Superset |
\supset |
⊃ |
U+2283 |
|
|
\supsetneq |
|
U+228B |
|
|
is a superset of |
\supseteq |
⊇ |
U+2287 |
|
|
Element is in the set |
Element (mathematics) |
\in |
∈ |
U+2208 |
|
|
\ni , \owns |
∋ |
U+220B |
|
|
Element is not in the set |
\notin |
∉ |
U+2209 |
|
|
\not\ni |
|
U+220C |
Note: The symbols and are used inconsistently and often do not exclude the equality of the two quantities.
Number sets
Cardinality
Arithmetic
Arithmetic operators
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
added to |
Addition |
+ |
|
U+002B |
|
|
subtracted from |
Subtraction |
- |
|
U+2212 |
|
|
multiplied by |
Multiplication |
\cdot |
· |
U+22C5 |
|
|
\times |
× |
U+2A2F |
|
|
divided by |
Division (mathematics) |
: |
|
U+003A |
|
|
/ |
⁄ |
U+2215 |
|
|
\div |
÷ |
U+00F7 |
|
|
\frac |
|
U+2044 |
|
|
Negative of the number or the additive inverse of |
Unary minus |
- |
− |
U+2212 |
|
|
Plus or minus |
Plus or minus sign |
\pm |
± |
U+00B1 |
|
|
Minus or plus |
\mp |
|
U+2213 |
|
|
Term is evaluated first |
Bracket |
( ) |
|
U+0028/9 |
|
|
[ ] |
|
U+005B/D |
Equality signs
Comparison
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
is less than |
Comparison (mathematics) |
< |
< |
U+003C |
|
|
is greater than |
> |
> |
U+003E |
|
|
is less than or equal to |
\le , \leq |
≤ |
U+2264 |
|
|
\leqq |
|
U+2266 |
|
|
is greater than or equal to |
\ge , \geq |
≥ |
U+2265 |
|
|
\geqq |
|
U+2267 |
|
|
is much smaller than |
\ll |
|
U+226A |
|
|
is much bigger than |
\gg |
|
U+226B |
Divisibility
Intervals
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Closed interval between and |
Interval (mathematics) |
( )
[ ] |
|
U+0028/9
U+005B/D |
|
|
Open interval between and |
|
|
|
|
Right-open interval between and |
|
|
|
|
Left-open interval between and |
|
|
Elementary functions
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Absolute value of |
Absolute value |
\vert |
|
U+007C |
|
|
Biggest whole number less than or equal to |
Floor and ceiling functions |
[ ] |
|
U+005B/D |
|
|
\lfloor \rfloor |
⌊ ⌋ |
U+230A/B |
|
|
Smallest whole number greater than or equal to |
\lceil \rceil |
⌈ ⌉ |
U+2308/9 |
|
|
Square root of |
Square root |
\sqrt |
√ |
U+221A |
|
-th root of |
nth root |
|
|
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 |
|
|
Real part of complex number |
Complex number |
\Re |
|
U+211C |
|
|
Imaginary part of complex number |
\Im |
|
U+2111 |
|
|
Complex conjugate of |
Complex conjugate |
\bar |
|
U+0305 |
|
|
\ast |
∗ |
U+002A |
|
|
Absolute value of complex number |
Absolute value |
\vert |
|
U+007C |
- Remark: real and complex parts of a complex number are often also denoted by and .
Mathematical constants
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Pi, or Archimedes' constant |
Pi |
\pi |
π |
U+03C0 |
|
|
Euler's constant |
e (mathematics) |
\rm{e} |
|
U+0065 |
|
|
Golden ratio |
Golden ratio |
\varphi |
φ |
U+03C6 |
|
|
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 from to or over all elements in set |
Summation |
\sum |
∑ |
U+2211 |
|
|
Product from to or over all elements in set |
Product (mathematics) |
\prod |
∏ |
U+220F |
|
|
Coproduct from to or over all elements in set |
Coproduct |
\coprod |
|
U+2210 |
|
|
Sequence of elements |
Sequence |
( ) |
|
U+0028/9 |
|
|
Sequence tends to limit |
Limit of a sequence |
\to |
→ |
U+2192 |
|
|
tends to infinity |
Infinity |
\infty |
∞ |
U+221E |
Functions
Limits
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Limit of function as approaches from below |
Limit of a function |
\uparrow |
↑ |
U+2191 |
|
|
\nearrow |
|
U+2197 |
|
|
Limit of function as approaches |
\to |
→ |
U+2192 |
|
|
Limit of function as approaches from above |
\searrow |
|
U+2198 |
|
|
\downarrow |
↓ |
U+2193 |
Asymptotic behaviour
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Function is asymptotically equal to function |
Asymptotic analysis |
\sim |
∼ |
U+223C |
|
|
Function grows slower than |
Big O notation |
o |
|
U+006F |
|
|
Function grows not substantially faster than |
\mathcal{O} |
|
U+1D4AA |
|
|
Function grows as fast as |
\Theta |
Θ |
U+0398 |
|
|
Function grows not substantially slower than |
\Omega |
Ω |
U+03A9 |
|
|
Function grows faster than |
\omega |
ω |
U+03C9 |
Differential calculus
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
First or second derivative of function |
Differentiation (mathematics) |
\prime |
′ |
U+2032 |
|
|
First or second derivative of function with respect to time (in physics) |
\dot , \ddot |
|
U+0307 |
|
|
-th derivative of function |
( ) |
|
U+0028/9 |
|
|
Derivative of function with respect to variable |
d |
|
U+0064 |
|
Total differential of function |
Total differential |
|
|
Partial derivative of function with respect to variable |
Partial derivative |
\partial |
∂ |
U+2202 |
Integral calculus
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
, |
Definite integral between and or over set |
Integral |
\int |
∫ |
U+222B |
|
|
Curve integral along curve |
Curve integral |
\oint |
|
U+222E |
|
|
Surface integral over surface |
Surface integral |
\iint |
|
U+222C |
|
|
Volume integral over volume |
Volume integral |
\iiint |
|
U+222D |
Vector calculus
Topology
Functional analysis
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Topological dual space of topological vector space |
Dual space |
\prime |
′ |
U+2032 |
|
|
Bidual space of normed vector space |
|
|
Completion of metric space |
Complete metric space |
\hat |
|
U+0302 |
|
|
Embedding of topological vector space into |
Embedding |
\hookrightarrow |
|
U+21AA |
Linear algebra and geometry
Elementary geometry
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Line segment between points and |
Line segment |
[ ] |
|
U+005B/D |
|
|
Length of line segment between points and |
\vert |
|
U+007C |
|
|
\overline |
|
U+0305 |
|
|
Vector between points and |
Euclidean vector |
\vec |
|
U+20D7 |
|
|
Angle between line segments and |
Angle |
\angle |
∠ |
U+2220 |
|
|
Triangle with vertices , and |
Triangle |
\triangle |
|
U+25B3 |
|
|
Quadrilateral with vertices , , and |
Quadrilateral |
\square |
|
U+25A1 |
|
|
Lines and are parallel |
Parallel (geometry) |
\parallel |
|
U+2225 |
|
|
Lines and are not parallel |
\nparallel |
|
U+2226 |
|
|
Lines and are orthogonal |
Orthogonality |
\perp |
⊥ |
U+27C2 |
Vectors and matrices
Symbol |
Interpretation |
Article |
LaTeX |
|
Row vector comprising elements through |
Vector (mathematics and physics) |
\begin{pmatrix}
...
\end{pmatrix}
oder
\left(
\begin{array}{...}
...
\end{array}
\right) |
|
Column vector comprising elements through |
|
Matrix comprising elements through |
Matrix (mathematics) |
Vector calculus
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Dot product of vectors and |
Dot product |
\cdot |
· |
U+22C5 |
|
|
( ) |
|
U+0028/9 |
|
|
\langle \rangle |
⟨ ⟩ |
U+27E8/9 |
|
|
Cross product of vectors and |
Cross product |
\times |
× |
U+2A2F |
|
|
[ ] |
|
U+005B/D |
|
|
Triple product of vectors , and |
Triple product |
( ) |
|
U+0028/9 |
|
|
Dyadic product of vectors and |
Dyadic product |
\otimes |
⊗ |
U+2297 |
|
|
Wedge product of vectors and |
Wedge product |
\wedge |
|
U+2227 |
|
|
Length of vector |
Euclidean norm |
\vert |
|
U+007C |
|
|
Norm of vector |
Norm (mathematics) |
\Vert , \| |
|
U+2016 |
|
|
Normalized vector of vector |
Unit vector |
\hat |
|
U+0302 |
Matrix calculus
Vector spaces
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Sum of vector spaces and |
Direct sum of modules |
+ |
|
U+002B |
|
|
Direct sum of vector spaces and |
\oplus |
⊕ |
U+2295 |
|
|
Direct product of vector spaces and |
Direct product |
\times |
× |
U+2A2F |
|
|
Tensor product of vector spaces and |
Tensor product |
\otimes |
⊗ |
U+2297 |
|
|
Quotient space of vector space by subspace |
Quotient space (linear algebra) |
/ |
⁄ |
U+002F |
|
|
Orthogonal complement of subspace |
Orthogonal complement |
\perp |
⊥ |
U+27C2 |
|
|
Dual space of vector space |
Dual space |
\ast |
∗ |
U+002A |
|
|
Annihilator space of the set of vectors |
0 |
|
U+0030 |
|
|
Linear hull of the set of vectors |
Linear hull |
\langle \rangle |
⟨ ⟩ |
U+27E8/9 |
Algebra
Relations
Group theory
Field theory
Ring theory
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Group of units of ring |
Group of units |
\ast |
∗ |
U+2217 |
|
|
\times |
× |
U+2A2F |
|
|
is an ideal of ring |
Ideal (ring theory) |
\vartriangleleft |
|
U+22B2 |
|
|
Quotient ring of ring by ideal |
Quotient ring |
/ |
⁄ |
U+002F |
|
|
Polynomial ring over ring with variable |
Polynomial ring |
[ ] |
|
U+005B/D |
Combinatorics
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Number of permutations of elements |
Factorial |
! |
|
U+0021 |
|
Number of derangements of elements (permutations without fixed points) |
Derangement |
|
Number of involutions without fixed points ( odd) |
Double factorial |
|
|
Number of -combinations of elements without repetition |
Combination |
\binom |
|
U+0028/9 |
|
Number of permutations of elements of which are identical |
Multinomial coefficient |
|
|
Number of -combinations of elements with repetition |
Multiset |
|
|
U+0028/9 |
|
|
Rising factorial from with factors |
Pochhammer symbol |
\overline |
|
U+0305 |
|
Falling factorial from with factors |
\underline |
|
U+0332 |
|
|
Product of all primes up to |
Primorial |
\# |
|
U+0023 |
Stochastics
Probability theory
- 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 |
|
|
Average of the values |
Average |
\bar |
|
U+0305 |
|
|
Average over all values in the set (in physics) |
\langle \rangle |
⟨ ⟩ |
U+27E8/9 |
|
|
Estimator for parameter |
Estimator |
\hat |
|
U+0302 |
Logic
Operators
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Proposition and proposition |
Logical conjunction |
\land |
∧ |
U+2227 |
|
|
Proposition or proposition (or both) |
Logical disjunction |
\lor |
∨ |
U+2228 |
|
|
Proposition follows from proposition and vice versa |
Logical equivalence |
\Leftrightarrow |
⇔ |
U+21D4 |
|
|
\leftrightarrow |
↔ |
U+2194 |
|
|
From proposition follows proposition |
Logical consequence |
\Rightarrow |
⇒ |
U+21D2 |
|
|
\rightarrow |
→ |
U+2192 |
|
|
Either proposition or proposition |
Exclusive or |
\oplus |
⊕ |
U+2295 |
|
|
\veebar |
|
U+22BB |
|
|
\dot\lor |
|
U+2A52 |
|
|
Not proposition |
Logical negation |
\lnot |
¬ |
U+00AC |
|
|
\bar |
|
U+0305 |
Quantifiers
Deduction symbols
Symbol |
Usage |
Interpretation |
Article |
LaTeX |
HTML |
Unicode |
|
|
Proposition can be syntactically derived from proposition |
Propositional calculus |
\vdash |
|
U+22A2 |
|
|
Proposition follows semantically from proposition |
Inference |
\models |
|
U+22A8 |
|
Proposition is universally true |
Tautology (logic) |
|
|
\top |
|
U+22A4 |
|
|
Proposition is contradictory |
Contradiction |
\bot |
⊥ |
U+22A5 |
|
|
Proposition is true, therefore proposition is true |
Deductive reasoning |
\therefore |
|
U+2234 |
|
|
Proposition is true, because is true |
\because |
|
U+2235 |
|
|
End of proof |
Q.E.D. |
\blacksquare |
|
U+220E |
|
\Box |
|
U+25A1 |
See also
References
- Tilo Arens, Frank Hettlich, Christian Karpfinger, Ulrich Kockelkorn, Klaus Lichtenegger, Hellmuth Stachel (2011) (in German), Mathematik (2. ed.), Spektrum Akademischer Verlag, pp. 1483ff., ISBN 3-827-42347-3
- Wolfgang Hackbusch (2010) (in German), Taschenbuch der Mathematik, Band 1 (3. ed.), Springer, pp. 1275ff., ISBN 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.
Note: This article is a translation of the German Wikipedia article de:Liste mathematischer Symbole.
External links