List of mathematical symbols by subject
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 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 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.
- Interpretation
- A short textual description of the meaning of the formula in the previous column.
- Article
- The Wikipedia article discussing 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 (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>.
- 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.
Set theory
Definition symbols
Symbol | Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|
is defined by | Definition | \colon |
∶ |
U+003A | ||
is defined as equal to | ||||||
is defined as equivalent to |
Set construction
Symbol | Unicode 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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∪ | Union of the sets A and B | Union (set theory) | \cup |
∪ |
U+222A | ||
⋃ | N-Ary union of sets | Union (set theory) | \bigcup |
|
U+22C3 | ||
∩ | Intersection A and B | Intersection (set theory) | \cap |
∩ |
U+2229 | ||
⋂ | N-Ary intersection of sets | Intersection (set theory) | \bigcap |
|
U+22C2 | ||
∖ | Difference of sets A and B | Difference (set theory) | \setminus |
|
U+2216 | ||
∆ | Symmetric difference of sets A and B | Symmetric difference | \triangle |
Δ |
U+2206 | ||
⨯ | Cartesian product of sets A and B | Cartesian product | \times |
× |
U+2A2F | ||
⊍ | Disjoint union of sets A and B | Disjoint union | \dot\cup |
|
U+228D | ||
⊎ | \uplus |
⊎ |
U+228E | ||||
⊔ | \sqcup |
|
U+2294 | ||||
⩀ | Intersection of the sets A and B | Intersection (set theory) | \dot\cap |
|
U+2A40 | ||
⊓ | Intersection of the sets A and B | Intersection (set theory) | \sqcap |
|
U+2293 | ||
⩄ | Intersection of the sets A and B | Intersection (set theory) | \capwedge |
⩄ |
U+2A44 | ||
⫛ | Transversal intersection of sets A and B | Transversal intersection | \mlcp |
⫛ |
U+2ADB | ||
∁ | Complement of the set A | Complement (set theory) | \mathrm{C} |
|
U+2201 | ||
◌̅ | \overline{A} |
|
U+0305 | ||||
𝒫 | Power set of the set A | Power set | \mathcal{P} |
|
U+1D4AB | ||
𝔓 | \mathfrak{P} |
|
U+1D513 | ||||
℘ | \wp |
|
U+2118 | ||||
⋀ | This is the greatest lower bound, infimum, or meet of all elements operated on. | Infimum and supremum | \bigwedge |
|
U+22C0 | ||
⋁ | This is the least upper bound, supremum, or join of all elements operated on. [1] | \bigvee |
|
U+22C1 |
Set relations
Symbol | Unicode 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 | |||
⟃ | A ⟃ B | is an open subset of |
|
|
U+27C3 | ||
⊃ | is a proper superset of | Superset | \supset |
⊃ |
U+2283 | ||
⊋ | \supsetneq |
U+228B | |||||
⊇ | is a superset of | \supseteq |
⊇ |
U+2287 | |||
⟄ | A ⟄ B | is an open subset of |
|
|
U+27C3 | ||
⊄ | is not a proper subset of | \not\subset |
U+2284 | ||||
⊅ | is not a proper superset of | Superset | \not\supset |
U+2285 | |||
⊈ | is not a subset of | \not\subseteq |
U+2288 | ||||
⊉ | is not a superset of | Superset | \not\supseteq |
U+2289 | |||
∈ | 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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
𝔸 | Algebraic numbers | Algebraic number | \mathbb{A} |
U+1D538 | |||
ℂ | Complex numbers | Complex number | \mathbb{C} |
U+2102 | |||
ℍ | Quaternions | Quaternion | \mathbb{H} |
U+210D | |||
ℕ | Natural numbers | Natural number | \mathbb{N} |
U+2115 | |||
𝕁 | Nonnegative ("whole") numbers | \mathbb{J} |
U+1D541 | ||||
𝕎 | \mathbb{W} |
U+1D54E | |||||
ℚ | Rational numbers | Rational number | \mathbb{Q} |
U+211A | |||
ℝ | Real numbers | Real number | \mathbb{R} |
U+211D | |||
ℤ | Integers | Integer | \mathbb{Z} |
U+2124 |
Cardinality
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
| | | Cardinality of the set | Cardinality | \vert |
U+007C | |||
# | \# |
U+0023 | |||||
𝔠 | Cardinality of the continuum | Cardinality of the continuum | \mathfrak{c} |
U+1D520 | |||
ℵ | , , ... | Infinite cardinals | Aleph number | \aleph |
U+2135 | ||
ℶ | , , ... | Beth numbers | Beth number | \beth |
U+2136 |
Arithmetic
Arithmetic operators
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
+ | added to | Addition | + |
+ |
U+002B | ||
− | subtracted to | 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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
= | equals | Equality (mathematics) | = |
U+003D | |||
≠ | does not equal | Inequality (mathematics) | \neq |
≠ |
U+2260 | ||
≡ | is identical to | Identity (mathematics) | \equiv |
≡ |
U+2261 | ||
≈ | is approximately equal to | Approximation | \approx |
≈ |
U+2248 | ||
∼ | is similar to | Equivalence class | \sim |
∼ |
U+223C | ||
∝ | is proportional to | Proportionality (mathematics) | \propto |
∝ |
U+221D | ||
≙ | corresponds to | Correspondence (mathematics) | \widehat{=} |
U+2259 | |||
≟ | is equal to ? | Questioning equal sign | \overset{?}{=} |
U+225F |
Comparison
Symbol | Unicode 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 | |||
≷ | is greater than or less than or is different than [2] |
Wiktionary:≷ | \gtrless |
≷ |
U+2277 |
Divisibility
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∣ | divides | Divisibility | \mid |
U+2223 | |||
∤ | does not divide | \nmid |
U+2224 | ||||
⊥ | and are relatively prime | Relatively prime | \perp |
⊥ |
U+22A5 | ||
⊓ | Greatest common divisor of and | Greatest common divisor | \sqcap |
U+2293 | |||
∧ | \wedge |
∧ |
U+2227 | ||||
⊔ | Least common multiple of and | Least common multiple | \sqcup |
∧ |
U+2294 | ||
∨ | \vee |
∨ |
U+2228 | ||||
≡ | and are congruent modulo | Modular arithmetic | \equiv |
≡ |
U+2261 |
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 | Unicode 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 | \sqrt[n]{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 | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
ℜ | Real part of complex number | Complex number | \Re |
U+211C | |||
ℑ | 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 | |||
Argument of | Argument (complex analysis) | \arg |
- Remark: real and imaginary parts of a complex number are often also denoted by and .
Mathematical constants
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
π | Pi, or Archimedes' constant | Pi | \pi |
{{pi}} |
U+03C0 | ||
e or e | e | Euler's constant | e (mathematics) | e or \rm{e} |
{{mvar|e}} or {{math|e}} |
U+0065 | |
φ | Golden ratio | Golden ratio | \varphi |
φ |
U+03C6 | ||
i or i | i | Imaginary unit (square root of −1) | Imaginary unit | i or \rm{i} |
{{mvar|i}} or {{math|i}} |
U+0069 |
See also: mathematical constant for symbols of additional mathematical constants.
Calculus
Sequences and series
Symbol | Unicode 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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
→ | Function maps from set to set | Function (mathematics) | \to |
→ |
U+2192 | ||
↦ | Function maps element to element | \mapsto |
&mapstoright; |
U+21A6 | |||
( ) | Image of element under function | Image (mathematics) | ( ) |
( or ) |
U+0028/9 | ||
Image of set under function | |||||||
[ ] | [ ] |
[ or ] |
U+005B/D | ||||
| | Restriction of function to set | Restriction (mathematics) | \vert |
| |
U+007C | ||
⋅ | Placeholder for a variable as argument of function | Free variable | \cdot |
U+22C5 | |||
⁻ | Inverse function of | Inverse function | -1 |
U+207B | |||
∘ | Composition of functions and ; | Function composition | \circ |
∘ |
U+2218 | ||
∗ | Convolution of functions and | Convolution | \ast |
∗ |
U+2217 | ||
◌̂ | Fourier transform of function | Fourier transform | \hat |
U+0302 |
Limits
Symbol | Unicode 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 | ||||
⁺ | Limit of a function as approaches from the right | ^+ |
⁺ |
U+207A | |||
⁻ | Limit of a function as approaches from the left | ^- |
⁻ |
U+207B | |||
Asymptotic behaviour
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∼ | Function is asymptotically equal to function | Asymptotic analysis | \sim |
∼ |
U+223C | ||
o | Function grows slower than | Big O notation | o |
U+006F | |||
𝒪 | Function grows not substantially faster than | \mathcal{O} |
U+1D4AA | ||||
Θ | Function grows as fast as | \Theta |
Θ |
U+0398 | |||
Ω | Function grows not substantially slower than | \Omega |
Ω |
U+03A9 | |||
ω | Function grows faster than | \omega |
ω |
U+03C9 |
Differential calculus
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
′ ″ | First or second derivative of function | Lagrange's notation | \prime |
′ |
U+2032,U+2033 | ||
Alternative notation for fourth, fifth, or sixth derivative of function | ^{V} |
<sup>Ⅳ</sup> |
|||||
( ) | Alternative notation for fourth, fifth, or -th derivative of function | ( ) |
<sup>( )</sup> |
U+0028/9 | |||
◌̇ | First or second derivative of function with respect to time (in physics) | Newton's notation | \dot , \ddot |
U+0307 | |||
d | An infinitesimally small change in | Leibniz's notation | d |
d |
U+0064 | ||
Derivative of function with respect to variable | |||||||
Second derivative of function with respect to variable | |||||||
Total differential of function | |||||||
∂ | Partial derivative of function with respect to variable | Partial derivative | \partial |
∂ |
U+2202 |
Integral calculus
Symbol | Unicode 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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∇ | Gradient of function | Gradient | \nabla |
∇ |
U+2207 | ||
Divergence of vector field | Divergence | ||||||
Curl of vector field | Curl (mathematics) | ||||||
∆ | Laplace operator of function | Laplace operator | \Delta |
Δ |
U+2206 | ||
□ | D'Alembert operator of function | D'Alembert operator | \square |
U+25A1 |
Topology
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∂ | Boundary of set | Boundary (topology) | \partial |
∂ |
U+2202 | ||
˚ | Interior of set | Interior (topology) | \circ |
° |
U+02DA | ||
◌̅ | Closure of set | Closure (topology) | \overline |
U+0305 | |||
◌̇ | Punctured neighbourhood of point | Punctured neighbourhood | \dot |
— U+0307 |
Functional analysis
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
′ | Topological dual space of topological vector space | Dual space | \prime |
′ |
U+2032/3 | ||
″ | 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 | Unicode 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 and Affine space |
\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 | Usage | Article | LaTeX |
---|---|---|---|
Row vector comprising elements through | Vector (mathematics and physics) | \begin{pmatrix} ... \end{pmatrix} or \left( \begin{array}{...} ... \end{array} \right) | |
Column vector comprising elements through | |||
Matrix comprising elements through | Matrix (mathematics) |
Vector calculus
Symbol | Unicode 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 | ||
∧ | Exterior product of vectors and | Exterior algebra | \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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
⋅ | Product of matrices and | Matrix multiplication | \cdot |
· |
U+22C5 | ||
∘ | Hadamard product of matrices and | Hadamard product (matrices) | \circ |
U+2218 | |||
⊘ | Hadamard division of matrices and | Hadamard product (matrices) | \oslash |
U+2298 | |||
⊗ | Kronecker product of matrices and | Kronecker product | \otimes |
⊗ |
U+2297 | ||
T | Transposed matrix of matrix | Transposed matrix | ^T |
U+0054 | |||
⊺ | \intercal |
U+22BA | |||||
H | Conjugate transpose of matrix | Conjugate transpose | ^H |
U+0048 | |||
* | \ast |
∗ |
U+002A | ||||
† | \dagger |
† |
U+2020 | ||||
⁻ | Inverse matrix of matrix | Inverse matrix | -1 |
U+207B | |||
+ | Moore–Penrose pseudoinverse of matrix | Moore–Penrose pseudoinverse | + |
+ |
U+002B | ||
| A | | Determinant of Matrix | Determinant | \vert |
U+007C | |||
‖ | Norm of matrix | Matrix norm | \Vert , \| |
U+2016 |
Vector spaces
Symbol | Unicode 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 | ||
0 | 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
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∘ | Composition of relations and | Composition of relations | \circ |
U+2218 | |||
Operation of elements and (general) | Operation (mathematics) | ||||||
• | \bullet |
• |
U+2219 | ||||
∗ | \ast |
∗ |
U+2217 | ||||
≤ | Order relation between elements and | Order relation | \leq |
≤ |
U+2264 | ||
≺ | Element is a predecessor of element | Successor ordinal | \prec |
U+227A | |||
≻ | Element is a successor of element | \succ |
U+227B | ||||
∼ | Equivalence relation between elements and | Equivalence relation | \sim |
∼ |
U+223C | ||
[ ] | Equivalence class of element | Equivalence class | [ ] |
U+005B/D | |||
/ | Quotient set of set by equivalence relation | Quotient set | / |
⁄ |
U+002F | ||
⁻ | Inverse relation of relation | Inverse relation | -1 |
U+207B | |||
+ | Transitive closure of relation | Transitive closure | + |
U+002B | |||
* | Reflexive closure of relation | Reflexive closure | \ast |
∗ |
U+002A |
Group theory
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
≃ | Groups and are isomorphic | Group isomorphism | \simeq |
U+2243 | |||
≅ | \cong |
≅ |
U+2245 | ||||
⨯ | Direct product of groups and | Direct product | \times |
× |
U+2A2F | ||
⋊ | Semidirect product of groups and | Semidirect product | \rtimes |
U+22CA | |||
≀ | Wreath product of groups and | Wreath product | \wr |
U+2240 | |||
≤ | is a subgroup of group | Subgroup | \leq |
≤ |
U+2264 | ||
< | U is a proper subgroup of group G | \lt |
< |
U+003C | |||
⊲ | N is a normal subgroup of group G | Normal subgroup | \vartriangleleft |
U+22B3 | |||
⊴ | N is a normal subgroup of G and possibly equal to G | Normal subgroup | \trianglelefteq |
U+22B4 | |||
⋪ | N is not a normal subgroup of group G | Normal subgroup | \not\vartriangleleft |
U+22EA | |||
⋬ | N is not a normal subgroup of G | Normal subgroup | \not\trianglelefteq |
U+22EC | |||
⊳ | N is a normal subgroup of group G | Normal subgroup | \vartriangleright |
U+22B3 | |||
⊵ | N is a normal subgroup of group G | Normal subgroup | \trianglerighteq |
U+22B5 | |||
⋫ | N is not a normal subgroup of group G | Normal subgroup | \not\vartriangleright |
U+22EB | |||
⋭ | N is not a normal subgroup of group G | Normal subgroup | \not\trianglerighteq |
U+22ED | |||
/ | Quotient group of group G by normal subgroup | Quotient group | / |
⁄ |
U+002F | ||
: | Index of subgroup U in group | Index of a subgroup | \colon |
U+003A | |||
⟨ ⟩ | Subgroup generated by set E | Generating set of a group | \langle \rangle |
⟨ ⟩ |
U+27E8/9 | ||
[ ] | Commutator of elements g and h | Commutator | [ ] |
U+005B/D |
Field theory
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
/ | Extension of field over field | Field extension | / |
⁄ |
U+002F | ||
| | \mid |
U+007C | |||||
: | \colon |
U+003A | |||||
Degree of field extension over | Degree of a field extension | ||||||
̅ | Algebraic closure of field | Algebraic closure | \overline |
U+0305 | |||
( ) | Extension of a field by adding an algebraic element | Field extension, Algebraic number field | ( ) |
U+0028/9 | |||
𝕂 | Field of real or complex numbers | Field (mathematics) | \mathbb{K} |
U+1D542 | |||
𝔽 | Finite field | Finite field | \mathbb{F} |
U+1D53D |
Ring theory
Symbol | Unicode 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 (Uncommon, needs to be defined before the first use) |
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 | |||
[ ] | Ring of formal power series and ring of formal Laurent series | Formal power series | [[ ]] |
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
Symbol | Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|
Probability of event | Probability measure | P |
U+2119 | |||
Probability of event given event | Conditional probability | \mid |
U+007C | |||
Expected value of the random variable | Expected value | E |
U+1D53C | |||
Variance of the random variable | Variance | V |
U+1D54D | |||
Standard deviation of the random variable | Standard deviation | \sigma |
σ |
U+03C3 | ||
Covariance of random variables and | Covariance | |||||
Correlation of random variables and | Correlation | \rho |
ρ |
U+03C1 | ||
Random variable has distribution | Probability distribution | \sim |
∼ |
U+223C | ||
Random variable has distribution approximately | \approx |
≈ |
U+2248 | |||
Event is independent from event | Independence (probability theory) | \perp |
⊥ |
U+22A5 |
- Remark: for operators there are several notational variants; instead of round brackets also square brackets are used
Logic
Operators
Symbol | Unicode 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 | |||||
← | If B then A, or not B without A. It is not to be confused with the assignment operator in computer science. | Converse implication | \leftarrow |
← |
U+2190 |
Quantifiers
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
∀ | For all elements | Universal quantification | \forall |
∀ |
U+2200 | ||
⋀ | \bigwedge |
U+22C0 | |||||
∃ | At least one element exists | Existential quantification | \exists |
∃ |
U+2203 | ||
⋁ | \bigvee |
U+22C1 | |||||
∃! | Exactly one element exists | Uniqueness quantification | \exists! |
∃! |
U+2203 ! | ||
⩒ | \dot\bigvee |
U+2A52 | |||||
∄ | No element exists | Existential quantification | \nexists |
U+2204 |
Deduction symbols
Symbol | Unicode symbol |
Usage | Interpretation | Article | LaTeX | HTML | Unicode |
---|---|---|---|---|---|---|---|
⊢ | Proposition can be syntactically derived from proposition | Propositional calculus, Turnstile | \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 |
Alphanumeric Symbols
Digits
Name | Digits |
---|---|
Double-struck | 𝟘 𝟙 𝟚 𝟛 𝟜 𝟝 𝟞 𝟟 𝟠 𝟡 |
Alphabets
Name | Sub-type | Alphabet |
---|---|---|
Double-struck | 𝔸 𝔹 ℂ 𝔻 𝔼 𝔽 𝔾 ℍ 𝕀 𝕁 𝕂 𝕃 𝕄 ℕ 𝕆 ℙ ℚ ℝ 𝕊 𝕋 𝕌 𝕍 𝕎 𝕏 𝕐 ℤ | |
𝕒 𝕓 𝕔 𝕕 𝕖 𝕗 𝕘 𝕙 𝕚 𝕛 𝕜 𝕝 𝕞 𝕟 𝕠 𝕡 𝕢 𝕣 𝕤 𝕥 𝕦 𝕧 𝕨 𝕩 𝕪 𝕫 | ||
Script/Calligraphy | 𝒜 ℬ 𝒞 𝒟 ℰ ℱ 𝒢 ℋ ℐ 𝒥 𝒦 ℒ ℳ 𝒩 𝒪 𝒫 𝒬 ℛ 𝒮 𝒯 𝒰 𝒱 𝒲 𝒳 𝒴 𝒵 | |
𝒶 𝒷 𝒸 𝒹 ℯ 𝒻 ℊ 𝒽 𝒾 𝒿 𝓀 𝓁 𝓂 𝓃 ℴ 𝓅 𝓆 𝓇 𝓈 𝓉 𝓊 𝓋 𝓌 𝓍 𝓎 𝓏 | ||
Bold | 𝓐 𝓑 𝓒 𝓓 𝓔 𝓕 𝓖 𝓗 𝓘 𝓙 𝓚 𝓛 𝓜 𝓝 𝓞 𝓟 𝓠 𝓡 𝓢 𝓣 𝓤 𝓥 𝓦 𝓧 𝓨 𝓩 | |
𝓪 𝓫 𝓬 𝓭 𝓮 𝓯 𝓰 𝓱 𝓲 𝓳 𝓴 𝓵 𝓶 𝓷 𝓸 𝓹 𝓺 𝓻 𝓼 𝓽 𝓾 𝓿 𝔀 𝔁 𝔂 𝔃 | ||
Fraktur | 𝔄 𝔅 ℭ 𝔇 𝔈 𝔉 𝔊 ℌ ℑ 𝔍 𝔎 𝔏 𝔐 𝔑 𝔒 𝔓 𝔔 ℜ 𝔖 𝔗 𝔘 𝔙 𝔚 𝔛 𝔜 ℨ | |
𝔞 𝔟 𝔠 𝔡 𝔢 𝔣 𝔤 𝔥 𝔦 𝔧 𝔨 𝔩 𝔪 𝔫 𝔬 𝔭 𝔮 𝔯 𝔰 𝔱 𝔲 𝔳 𝔴 𝔵 𝔶 𝔷 | ||
Bold | 𝕬 𝕭 𝕮 𝕯 𝕰 𝕱 𝕲 𝕳 𝕴 𝕵 𝕶 𝕷 𝕸 𝕹 𝕺 𝕻 𝕼 𝕽 𝕾 𝕿 𝖀 𝖁 𝖂 𝖃 𝖄 𝖅 | |
𝖆 𝖇 𝖈 𝖉 𝖊 𝖋 𝖌 𝖍 𝖎 𝖏𝖐 𝖑 𝖒 𝖓 𝖔 𝖕 𝖖 𝖗 𝖘 𝖙 𝖚 𝖛 𝖜 𝖝 𝖞 𝖟 | ||
Mono-space | 𝙰 𝙱 𝙲 𝙳 𝙴 𝙵 𝙶 𝙷 𝙸 𝙹 𝙺 𝙻 𝙼 𝙽 𝙾 𝙿 𝚀 𝚁 𝚂 𝚃 𝚄 𝚅 𝚆 𝚇 𝚈 𝚉 | |
𝚊 𝚋 𝚌 𝚍 𝚎 𝚏 𝚐 𝚑 𝚒 𝚓 𝚔 𝚕 𝚖 𝚗 𝚘 𝚙 𝚚 𝚛 𝚜 𝚝 𝚞 𝚟 𝚠 𝚡 𝚢 𝚣 | ||
Greek | Α Β Γ ᴦ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Ῥ ☧ Σ Ϲ Τ Υ υ Φ Χ Ψ Ω | |
α β ᵝ ᵦ γ ᵞ ᵧ δ ᵟ ε ϵ ϶ ζ η Ͱ ͱ θ ϑ ϴ ᶿ ι ᶥ ℩ κ ϰ λ ᴧ μ µ ν ξ ο π ϖ ρ ῥ ῤ ϱ ϼ ᴩ ᵨ σ ς ϲ Ͻ ͻ Ͼ ͼ Ͽ ͽ τ ϒ φ ϕ χ ᵡ ᵪ ψ ᴪ ω | ||
Italic | 𝛢 𝛣 𝛤 𝛥 𝛦 𝛧 𝛨 𝛩 𝛪 𝛫 𝛬 𝛭 𝛮 𝛯 𝛰 𝛱 𝛲 𝛳 𝛴 𝛵 𝛶 𝛷 𝛸 𝛹 𝛺 𝛻 | |
𝛼 𝛽 𝛾 𝛿 𝜕 𝜀 𝜖 𝜁 𝜂 𝜃 𝜗 𝜄 𝜅 𝜆 𝜇 𝜈 𝜉 𝜊 𝜋 𝜛 𝜌 𝜚 𝜍 𝜎 𝜏 𝜐 𝜑 𝜙 𝜒 𝜘 𝜓 𝜔 | ||
Non-Latin Italic | 𝛼 𝛽 𝛤 𝛾 𝛥 𝛿 𝜀 𝜁 𝜂 𝛩 𝜃 𝛳 𝜗 𝜄 𝜅 𝜘 𝛬 𝜆 𝜇 𝜈 𝛯 𝜉 𝛱 𝜋 𝜌 𝜚 𝛴 𝜎 𝜍 𝜏 𝛶 𝜐 𝛷 𝜑 𝜙 𝜒 𝛹 𝜓 𝛺 𝜔 | |
Bold | 𝚨 𝚩 𝚪 𝚫 𝚬 𝚭 𝚮 𝚯 𝚰 𝚱 𝚲 𝚳 𝚴 𝚵 𝚶 𝚷 𝚸 𝚹 𝚺 𝚻 𝚼 𝚽 𝚾 𝚿 𝛀 𝛁 | |
𝛂 𝛃 𝛄 𝛅 𝛛 𝛆 𝛜 𝛇 𝛈 𝛉 𝛝 𝛊 𝛋 𝛞 𝛌 𝛍 𝛎 𝛏 𝛐 𝛑 𝛡 𝛒 𝛠 𝛓 𝛔 𝛕 𝛖 𝛗 𝛟 𝛘 𝛙 𝛚 | ||
Bold Italic | 𝜜 𝜝 𝜞 𝜟 𝜠 𝜡 𝜢 𝜣 𝜤 𝜥 𝜦 𝜧 𝜨 𝜩 𝜪 𝜫 𝜬 𝜭 𝜮 𝜯 𝜰 𝜱 𝜲 𝜳 𝜴 𝜵 | |
𝜶 𝜷 𝜸 𝜹 𝝏 𝜺 𝝐 𝜻 𝜼 𝜽 𝝑 𝜾 𝜿 𝝀 𝝁 𝝂 𝝃 𝝄 𝝅 𝝕 𝝆 𝝔 𝝇 𝝈 𝝉 𝝊 𝝋 𝝓 𝝌 𝝒 𝝍 𝝎 |
Greek Letters
Name | Greek Letter | Bold | Italic | Bold Italic | Sans-Serif Bold | Sans-Serif Bold Italic | ALP | ALP Underbar | Double struck bold | Misc |
---|---|---|---|---|---|---|---|---|---|---|
Alpha | Α α | 𝚨 𝛂 | 𝛢 𝛼 | 𝜜 𝜶 | 𝝖 𝝰 | 𝞐 𝞪 | ⍺ | ⍶ | ||
Beta | Β β ᵝ ᵦ | 𝚩 𝛃 | 𝛣 𝛽 | 𝜝 𝜷 | 𝝗 𝝱 | 𝞑 𝞫 | ||||
Gamma | Γ γ ᴦ ᵞ ᵧ | 𝚪 𝛄 | 𝛤 𝛾 | 𝜞 𝜸 | 𝝘 𝝲 | 𝞒 𝞬 | ℾ ℽ | |||
Delta | Δ δ ᵟ | 𝚫 𝛅 | 𝛥 𝛿 | 𝜟 𝜹 | 𝝙 𝝳 | 𝞓 𝞭 | ||||
Epsilon | Ε ε ϵ ϶ | 𝚬 𝛆 | 𝛦 𝜀 | 𝜠 𝜺 | 𝝚 𝝴 | 𝞔 𝞮 | ||||
Zeta | Ζ ζ | 𝚭 𝛇 | 𝛧 𝜁 | 𝜡 𝜻 | 𝝛 𝝵 | 𝞕 𝞯 | ||||
Eta | Η η Ͱ ͱ | 𝚮 𝛈 | 𝛨 𝜂 | 𝜢 𝜼 | 𝝜 𝝶 | 𝞖 𝞰 | ||||
Theta | Θ θ ϑ ϴ ᶿ | 𝚯 𝛉 𝚹 𝛝 | 𝛩 𝜃 𝛳 𝜗 | 𝜣 𝜽 𝜭 𝝑 | 𝝝 𝝷 𝚹 𝞋 | 𝞗 𝞱 𝜭 𝟅 | ||||
Iota | Ι ι ᶥ ℩ | 𝚰 𝛊 | 𝛪 𝜄 | 𝜤 𝜾 | 𝝞 𝝸 | 𝞘 𝞲 | ||||
Kappa | Κ κ ϰ | 𝚱 𝛋 𝛞 | 𝛫 𝜅 𝜘 | 𝜥 𝜿 𝝒 | 𝝟 𝝹 𝞌 | 𝞙 𝞳 𝟆 | ||||
Lambda | Λ λ ᴧ | 𝚲 𝛌 | 𝛬 𝜆 | 𝜦 𝝀 | 𝝠 𝝺 | 𝞚 𝞴 | ||||
Mu | Μ μ µ | 𝚳 𝛍 | 𝛭 𝜇 | 𝜧 𝝁 | 𝝡 𝝻 | 𝞛 𝞵 | ||||
Nu | Ν ν | 𝚴 𝛎 | 𝛮 𝜈 | 𝜨 𝝂 | 𝝢 𝝼 | 𝞜 𝞶 | ||||
Xi | Ξ ξ | 𝚵 𝛏 | 𝛯 𝜉 | 𝜩 𝝃 | 𝝣 𝝽 | 𝞝 𝞷 | ||||
Omicron | Ο ο | 𝚶 𝛐 | 𝛰 𝜊 | 𝜪 𝝄 | 𝝤 𝝾 | 𝞞 𝞸 | ||||
Pi | Π π ϖ | 𝚷 𝛑 | 𝛱 𝜋 | 𝜫 𝝅 | 𝝥 𝝿 | 𝞟 𝞹 | ℿ ℼ | ∏ ∐ | ||
Rho | Ρ ρ Ῥ ῥ ῤ ϱ ϼ ᴩ ᵨ ☧ | 𝚸 𝛒 𝛠 | 𝛲 𝜌 𝜚 | 𝜬 𝝆 𝝔 | 𝝦 𝞀 𝞎 | 𝞠 𝞺 𝟈 | ⍴ | |||
Sigma | Σ σ ς Ϲ ϲ Ͻ ͻ Ͼ ͼ Ͽ ͽ | 𝚺 𝛔 𝛓 | 𝛴 𝜎 𝜍 | 𝜮 𝝈 𝝇 | 𝝨 𝞂 𝞁 | 𝞢 𝞼 𝞻 | ∑ | |||
Tau | Τ τ | 𝚻 𝛕 | 𝛵 𝜏 | 𝜯 𝝉 | 𝝩 𝞃 | 𝞣 𝞽 | ||||
Upsilon | Υ υ ϒ | 𝚼 𝛖 | 𝛶 𝜐 | 𝜰 𝝊 | 𝝪 𝞄 | 𝞤 𝞾 | ||||
Phi | Φ φ ϕ | 𝚽 𝛗 𝛟 | 𝛷 𝜑 𝜙 | 𝜱 𝝋 𝝓 | 𝝫 𝞅 𝞍 | 𝞥 𝞿 𝟇 | ||||
Chi | Χ χᵡᵪ☧ | 𝚾 𝛘 | 𝛸 𝜒 | 𝜲 𝝌 | 𝝬 𝞆 | 𝞦 𝟀 | ||||
Psi | Ψ ψ ᴪ | 𝚿 𝛙 | 𝛹 𝜓 | 𝜳 𝝍 | 𝝭 𝞇 | 𝞧 𝟁 | ||||
Omega | Ω ω | 𝛀 𝛚 | 𝛺 𝜔 | 𝜴 𝝎 | 𝝮 𝞈 | 𝞨 𝟂 |
See also
- List of mathematical symbols
- Greek letters used in mathematics, science, and engineering
- ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)
- Language of mathematics
- Latin letters used in mathematics
- List of mathematical abbreviations
- Mathematical alphanumeric symbols
- Mathematical constants and functions
- Mathematical notation
- Mathematical operators and symbols in Unicode
- Notation in probability and statistics
- Physical constants
- Table of logic symbols
- Table of mathematical symbols by introduction date
- Unicode block
References
- Davey, B.A.; Priestley, H.A. (2002). Introduction to lattices and order (2 ed.). Cambridge: Cambridge University Press. pp. xii + 298. ISBN 0-521-78451-4.
- Serrasqueiro, José Adelino (1906). Tratado de Algebra Elementar (in Portuguese). p. 7.
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.
Note: This article is a translation of the German Wikipedia article de:Liste mathematischer Symbole.
External links
- Tex
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Wikimedia Commons has media related to Mathematical symbols. |
- "Comprehensive List of Mathematical Symbols" (PDF). Retrieved 2020-08-08.
- Scott Pakin (25 June 2020). "The Comprehensive LaTeX Symbol List" (PDF; 4,4 MB). The Comprehensive TeX Archive Network (CTAN). Retrieved 8 August 2020.
- 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”
- Tex and Unicode