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LaTeX provides almost any mathematical or technical symbol that
anyone uses. For example, if you include $\pi$
in your source,
you will get the pi symbol π. See the Comprehensive
LaTeX Symbol List at
https://ctan.org/tex-archive/info/symbols/comprehensive/.
Here is a list of commonly-used symbols. It is by no means exhaustive. Each symbol is described with a short phrase, and its symbol class, which determines the spacing around it, is given in parenthesis. Unless said otherwise, the commands for these symbols can be used only in math mode. To redefine a command so that it can be used whatever the current mode, see \ensuremath.
\|
∥ Parallel (relation). Synonym: \parallel
.
\aleph
ℵ Aleph, transfinite cardinal (ordinary).
\alpha
α Lowercase Greek letter alpha (ordinary).
\amalg
⨿ Disjoint union (binary)
\angle
∠ Geometric angle (ordinary). Similar: less-than
sign <
and angle bracket \langle
.
\approx
≈ Almost equal to (relation).
\ast
∗ Asterisk operator, convolution, six-pointed
(binary). Synonym: *
, which is often a superscript or
subscript, as in the Kleene star. Similar: \star
, which is
five-pointed, and is sometimes used as a general binary operation, and
sometimes reserved for cross-correlation.
\asymp
≍ Asymptotically equivalent (relation).
\backslash
\ Backslash (ordinary). Similar: set minus \setminus
, and
\textbackslash
for backslash outside of math mode.
\beta
β Lowercase Greek letter beta (ordinary).
\bigcap
⋂ Variable-sized, or n-ary, intersection (operator). Similar:
binary intersection \cap
.
\bigcirc
⚪ Circle, larger (binary). Similar: function
composition \circ
.
\bigcup
⋃ Variable-sized, or n-ary, union (operator). Similar: binary
union \cup
.
\bigodot
⨀ Variable-sized, or n-ary, circled dot operator (operator).
\bigoplus
⨁ Variable-sized, or n-ary, circled plus operator (operator).
\bigotimes
⨂ Variable-sized, or n-ary, circled times operator (operator).
\bigtriangledown
▽ Variable-sized, or n-ary, open triangle pointing down (operator).
\bigtriangleup
△ Variable-sized, or n-ary, open triangle pointing up (operator).
\bigsqcup
⨆ Variable-sized, or n-ary, square union (operator).
\biguplus
⨄ Variable-sized, or n-ary, union operator with a plus (operator). (Note that the name has only one p.)
\bigvee
⋁ Variable-sized, or n-ary, logical-and (operator).
\bigwedge
⋀ Variable-sized, or n-ary, logical-or (operator).
\bot
⊥ Up tack, bottom, least element of a partially ordered
set, or a contradiction (ordinary). See also \top
.
\bowtie
⋈ Natural join of two relations (relation).
\Box
□ Modal operator for necessity; square open box (ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package.
\bullet
• Bullet (binary). Similar: multiplication
dot \cdot
.
\cap
∩ Intersection of two sets (binary). Similar: variable-sized
operator \bigcap
.
\cdot
⋅ Multiplication (binary). Similar: Bullet
dot \bullet
.
\chi
χ Lowercase Greek chi (ordinary).
\circ
∘ Function composition, ring operator (binary). Similar:
variable-sized operator \bigcirc
.
\clubsuit
♣ Club card suit (ordinary).
\complement
∁ Set complement, used as a superscript as in
$S^\complement$
(ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package. Also used:
$S^{\mathsf{c}}$
or $\bar{S}$
.
\cong
≅ Congruent (relation).
\coprod
∐ Coproduct (operator).
\cup
∪ Union of two sets (binary). Similar: variable-sized
operator \bigcup
.
\dagger
† Dagger relation (binary).
\dashv
⊣ Dash with vertical, reversed turnstile (relation). Similar:
turnstile \vdash
.
\ddagger
‡ Double dagger relation (binary).
\Delta
Δ Greek uppercase delta, used for increment (ordinary).
\delta
δ Greek lowercase delta (ordinary).
\Diamond
◇ Large diamond operator (ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package.
\diamond
⋄ Diamond operator (binary). Similar: large
diamond \Diamond
, circle bullet \bullet
.
\diamondsuit
♢ Diamond card suit (ordinary).
\div
÷ Division sign (binary).
\doteq
≐ Approaches the limit (relation). Similar: geometrically equal
to \Doteq
.
\downarrow
↓ Down arrow, converges (relation). Similar:
\Downarrow
double line down arrow.
\Downarrow
⇓ Double line down arrow (relation). Similar:
\downarrow
single line down arrow.
\ell
ℓ Lowercase cursive letter l (ordinary).
\emptyset
∅ Empty set symbol (ordinary). The variant form is
\varnothing
.
\epsilon
ϵ Lowercase lunate epsilon (ordinary). Similar to
Greek text letter. More widely used in mathematics is the script small
letter epsilon \varepsilon
ε. Related:
the set membership relation \in
∈.
\equiv
≡ Equivalence (relation).
\eta
η Lowercase Greek letter (ordinary).
\exists
∃ Existential quantifier (ordinary).
\flat
♭ Musical flat (ordinary).
\forall
∀ Universal quantifier (ordinary).
\frown
⌢ Downward curving arc (ordinary).
\Gamma
Γ uppercase Greek letter (ordinary).
\gamma
γ Lowercase Greek letter (ordinary).
\ge
≥ Greater than or equal to (relation). This is a synonym
for \geq
.
\geq
≥ Greater than or equal to (relation). This is a synonym
for \ge
.
\gets
← Is assigned the value (relation).
Synonym: \leftarrow
.
\gg
≫ Much greater than (relation). Similar: much less
than \ll
.
\hbar
ℏ Planck constant over two pi (ordinary).
\heartsuit
♡ Heart card suit (ordinary).
\hookleftarrow
↩ Hooked left arrow (relation).
\hookrightarrow
↪ Hooked right arrow (relation).
\iff
⟷ If and only if (relation). It is \Longleftrightarrow
with a \thickmuskip
on either side.
\Im
ℑ Imaginary part (ordinary). See: real part \Re
.
\imath
Dotless i; used when you are putting an accent on an i (see Math accents).
\in
∈ Set element (relation). See also: lowercase lunate
epsilon \epsilon
ϵ and small letter script
epsilon \varepsilon
.
\infty
∞ Infinity (ordinary).
\int
∫ Integral (operator).
\iota
ι Lowercase Greek letter (ordinary).
\Join
⨝ Condensed bowtie symbol (relation). Not available in Plain TeX.
\jmath
Dotless j; used when you are putting an accent on a j (see Math accents).
\kappa
κ Lowercase Greek letter (ordinary).
\Lambda
Λ uppercase Greek letter (ordinary).
\lambda
λ Lowercase Greek letter (ordinary).
\land
∧ Logical and (binary). This is a synonym for \wedge
.
See also logical or \lor
.
\langle
⟨ Left angle, or sequence, bracket (opening). Similar:
less-than <
. Matches \rangle
.
\lbrace
{ Left curly brace
(opening). Synonym: \{
. Matches \rbrace
.
\lbrack
[ Left square bracket (opening).
Synonym: [
. Matches \rbrack
.
\lceil
⌈ Left ceiling bracket, like a square bracket but with the bottom
shaved off (opening). Matches \rceil
.
\le
≤ Less than or equal to (relation). This is a synonym
for \leq
.
\leadsto
⇝ Squiggly right arrow (relation). Not available in plain TeX. In LaTeX you need to load the amssymb package.
To get this symbol outside of math mode you can put
\newcommand*{\Leadsto}{\ensuremath{\leadsto}}
in the
preamble and then use \Leadsto
instead.
\Leftarrow
⇐ Is implied by, double-line left arrow (relation). Similar:
single-line left arrow \leftarrow
.
\leftarrow
← Single-line left arrow (relation).
Synonym: \gets
. Similar: double-line left
arrow \Leftarrow
.
\leftharpoondown
↽ Single-line left harpoon, barb under bar (relation).
\leftharpoonup
↼ Single-line left harpoon, barb over bar (relation).
\Leftrightarrow
⇔ Bi-implication; double-line double-headed arrow (relation).
Similar: single-line double headed arrow \leftrightarrow
.
\leftrightarrow
↔ Single-line double-headed arrow (relation). Similar:
double-line double headed arrow \Leftrightarrow
.
\leq
≤ Less than or equal to (relation). This is a synonym
for \le
.
\lfloor
⌊ Left floor bracket (opening). Matches: \floor
.
\lhd
◁ Arrowhead, that is, triangle, pointing left (binary).
Not available in plain TeX. In LaTeX you need to load the amssymb package. For the normal subgroup symbol you should load
amssymb and use \vartriangleleft
(which is a relation
and so gives better spacing).
\ll
≪ Much less than (relation). Similar: much greater
than \gg
.
\lnot
¬ Logical negation (ordinary). Synonym: \neg
.
\longleftarrow
⟵ Long single-line left arrow (relation). Similar: long
double-line left arrow \Longleftarrow
.
\longleftrightarrow
⟷ Long single-line double-headed arrow (relation). Similar: long
double-line double-headed arrow \Longleftrightarrow
.
\longmapsto
⟼ Long single-line left arrow starting with vertical bar
(relation). Similar: shorter version \mapsto
.
\longrightarrow
⟶ Long single-line right arrow (relation). Similar: long
double-line right arrow \Longrightarrow
.
\lor
∨ Logical or (binary). Synonym: wedge \wedge
.
\mapsto
↦ Single-line left arrow starting with vertical bar (relation).
Similar: longer version \longmapsto
.
\mho
℧ Conductance, half-circle rotated capital omega (ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package.
\mid
∣ Single-line vertical bar (relation). A typical use of
\mid
is for a set \{\, x \mid x\geq 5 \,\}
.
Similar: \vert
and |
produce the same single-line
vertical bar symbol but without any spacing (they fall in class
ordinary) and you should not use them as relations but instead only as
ordinals, i.e., footnote symbols. For absolute value, see the entry
for \vert
and for norm see the entry for \Vert
.
\models
⊨ Entails, or satisfies; double turnstile, short double dash
(relation). Similar: long double dash \vDash
.
\mp
∓ Minus or plus (relation).
\mu
μ Lowercase Greek letter (ordinary).
\nabla
∇ Hamilton’s del, or differential, operator (ordinary).
\natural
♮ Musical natural notation (ordinary).
\ne
≠ Not equal (relation). Synonym: \neq
.
\nearrow
↗ North-east arrow (relation).
\neg
¬ Logical negation (ordinary).
Synonym: \lnot
. Sometimes instead used for
negation: \sim
.
\neq
≠ Not equal (relation). Synonym: \ne
.
\ni
∋ Reflected membership epsilon; has the member
(relation). Synonym: \owns
. Similar: is a member
of \in
.
\not
Long solidus, or slash, used to overstrike a following operator (relation).
Many negated operators are available that don’t require \not
,
particularly with the amssymb package. For example, \notin
is typographically preferable to \not\in
.
\notin
∉ Not an element of (relation). Similar: not subset
of \nsubseteq
.
\nu
ν Lowercase Greek letter (ordinary).
\nwarrow
↖ North-west arrow (relation).
\odot
⊙ Dot inside a circle (binary). Similar: variable-sized
operator \bigodot
.
\oint
∮ Contour integral, integral with circle in the middle (operator).
\Omega
Ω uppercase Greek letter (ordinary).
\omega
ω Lowercase Greek letter (ordinary).
\ominus
⊖ Minus sign, or dash, inside a circle (binary).
\oplus
⊕ Plus sign inside a circle (binary). Similar: variable-sized
operator \bigoplus
.
\oslash
⊘ Solidus, or slash, inside a circle (binary).
\otimes
⊗ Times sign, or cross, inside a circle (binary). Similar:
variable-sized operator \bigotimes
.
\owns
∋ Reflected membership epsilon; has the member
(relation). Synonym: \ni
. Similar: is a member
of \in
.
\parallel
∥ Parallel (relation). Synonym: \|
.
\partial
∂ Partial differential (ordinary).
\perp
⟂ Perpendicular (relation). Similar: \bot
uses the
same glyph but the spacing is different because it is in the class
ordinary.
\phi
ϕ Lowercase Greek letter (ordinary). The variant form is
\varphi
φ.
\Pi
Π uppercase Greek letter (ordinary).
\pi
π Lowercase Greek letter (ordinary). The variant form is
\varpi
ϖ.
\pm
± Plus or minus (binary).
\prec
≺ Precedes (relation). Similar: less than <
.
\preceq
⪯ Precedes or equals (relation). Similar: less than or
equals \leq
.
\prime
′ Prime, or minute in a time expression (ordinary).
Typically used as a superscript: $f^\prime$
; $f^\prime$
and $f'$
produce the same result. An advantage of the second
is that $f'''$
produces the desired symbol, that is, the same
result as $f^{\prime\prime\prime}$
, but uses rather less
typing. You can only use \prime
in math mode. Using the right
single quote '
in text mode produces a different character
(apostrophe).
\prod
∏ Product (operator).
\propto
∝ Is proportional to (relation)
\Psi
Ψ uppercase Greek letter (ordinary).
\psi
ψ Lowercase Greek letter (ordinary).
\rangle
⟩ Right angle, or sequence, bracket (closing).
Similar: greater than >
. Matches:\langle
.
\rbrace
} Right curly brace
(closing). Synonym: \}
. Matches \lbrace
.
\rbrack
] Right square bracket
(closing). Synonym: ]
. Matches \lbrack
.
\rceil
⌉ Right ceiling bracket (closing). Matches \lceil
.
\Re
ℜ Real part, real numbers, cursive capital R (ordinary). Related:
double-line, or blackboard bold, R \mathbb{R}
; to access
this, load the amsfonts package.
\restriction
↾ Restriction of a function (relation). Synonym:
\upharpoonright
. Not available in plain TeX. In LaTeX you need to load the amssymb package.
\revemptyset
⦰ Reversed empty set symbol (ordinary). Related:
\varnothing
. Not available in plain TeX. In LaTeX you need to load the stix package.
\rfloor
⌋ Right floor bracket, a right square bracket with the top cut
off (closing). Matches \lfloor
.
\rhd
◁ Arrowhead, that is, triangle, pointing right (binary).
Not available in plain TeX. In LaTeX you need to load the amssymb package. For the normal subgroup symbol you should instead
load amssymb and use \vartriangleright
(which is a
relation and so gives better spacing).
\rho
ρ Lowercase Greek letter (ordinary). The variant form is
\varrho
ϱ.
\Rightarrow
⇒ Implies, right-pointing double line arrow
(relation). Similar: right single-line arrow \rightarrow
.
\rightarrow
→ Right-pointing single line arrow (relation).
Synonym: \to
. Similar: right double line
arrow \Rightarrow
.
\rightharpoondown
⇁ Right-pointing harpoon with barb below the line (relation).
\rightharpoonup
⇀ Right-pointing harpoon with barb above the line (relation).
\rightleftharpoons
⇌ Right harpoon up above left harpoon down (relation).
\searrow
↘ Arrow pointing southeast (relation).
\setminus
⧵ Set difference, reverse solidus or reverse slash,
like \ (binary). Similar: backslash \backslash
and also
\textbackslash
outside of math mode.
\sharp
♯ Musical sharp (ordinary).
\Sigma
Σ uppercase Greek letter (ordinary).
\sigma
σ Lowercase Greek letter (ordinary). The variant form is
\varsigma
ς.
\sim
∼ Similar, in a relation (relation).
\simeq
≃ Similar or equal to, in a relation (relation).
\smallint
∫ Integral sign that does not change to a larger size in a display (operator).
\smile
⌣ Upward curving arc, smile (ordinary).
\spadesuit
♠ Spade card suit (ordinary).
\sqcap
⊓ Square intersection symbol (binary). Similar:
intersection cap
.
\sqcup
⊔ Square union symbol (binary). Similar:
union cup
. Related: variable-sized
operator \bigsqcup
.
\sqsubset
⊏ Square subset symbol (relation). Similar:
subset \subset
. Not available in plain TeX. In LaTeX you need to load the amssymb package.
\sqsubseteq
⊑ Square subset or equal symbol (binary). Similar: subset or
equal to \subseteq
.
\sqsupset
⊐ Square superset symbol (relation). Similar:
superset \supset
. Not available in plain TeX. In LaTeX you need to load the amssymb package.
\sqsupseteq
⊒ Square superset or equal symbol (binary).
Similar: superset or equal \supseteq
.
\star
⋆ Five-pointed star, sometimes used as a general binary
operation but sometimes reserved for cross-correlation (binary).
Similar: the synonyms asterisk *
and \ast
, which
are six-pointed, and more often appear as a superscript or subscript,
as with the Kleene star.
\subset
⊂ Subset (occasionally, is implied by) (relation).
\subseteq
⊆ Subset or equal to (relation).
\succ
≻ Comes after, succeeds (relation). Similar: is less
than >
.
\succeq
⪰ Succeeds or is equal to (relation). Similar: less
than or equal to \leq
.
\sum
∑ Summation (operator). Similar: Greek capital
sigma \Sigma
.
\supset
⊃ Superset (relation).
\supseteq
⊇ Superset or equal to (relation).
\surd
√ Radical symbol (ordinary). The LaTeX command
\sqrt{...}
typesets the square root of the argument, with a bar
that extends to cover the argument.
\swarrow
↙ Southwest-pointing arrow (relation).
\tau
τ Lowercase Greek letter (ordinary).
\theta
θ Lowercase Greek letter (ordinary). The variant form is
\vartheta
ϑ.
\times
× Primary school multiplication sign (binary). See
also \cdot
.
\to
→ Right-pointing single line arrow (relation).
Synonym: \rightarrow
.
\top
⊤ Top, greatest element of a partially ordered set
(ordinary). See also \bot
.
\triangle
△ Triangle (ordinary).
\triangleleft
◁ Not-filled triangle pointing left
(binary). Similar: \lhd
. For the normal subgroup symbol you
should load amssymb and use \vartriangleleft
(which
is a relation and so gives better spacing).
\triangleright
▷ Not-filled triangle pointing right
(binary). For the normal subgroup symbol you should instead load
amssymb and use \vartriangleright
(which is a
relation and so gives better spacing).
\unlhd
⊴ Left-pointing not-filled underlined arrowhead, that is,
triangle, with a line under (binary). Not available in plain TeX. In LaTeX you need to load the amssymb package. For the
normal subgroup symbol load amssymb and
use \vartrianglelefteq
(which is a relation and so gives
better spacing).
\unrhd
⊵ Right-pointing not-filled underlined arrowhead, that is,
triangle, with a line under (binary). Not available in plain TeX. In LaTeX you need to load the amssymb package. For the
normal subgroup symbol load amssymb and
use \vartrianglerighteq
(which is a relation and so gives
better spacing).
\Uparrow
⇑ Double-line upward-pointing arrow
(relation). Similar: single-line up-pointing
arrow \uparrow
.
\uparrow
↑ Single-line upward-pointing arrow, diverges
(relation). Similar: double-line up-pointing
arrow \Uparrow
.
\Updownarrow
⇕ Double-line upward-and-downward-pointing arrow
(relation). Similar: single-line upward-and-downward-pointing
arrow \updownarrow
.
\updownarrow
↕ Single-line upward-and-downward-pointing arrow
(relation). Similar: double-line upward-and-downward-pointing
arrow \Updownarrow
.
\upharpoonright
↾ Up harpoon, with barb on right side
(relation). Synonym: \restriction
.
Not available in plain TeX. In LaTeX you need to load the amssymb package.
\uplus
⊎ Multiset union, a union symbol with a plus symbol in
the middle (binary). Similar: union \cup
. Related:
variable-sized operator \biguplus
.
\Upsilon
Υ uppercase Greek letter (ordinary).
\upsilon
υ Lowercase Greek letter (ordinary).
\varepsilon
ε Small letter script epsilon (ordinary). This is
more widely used in mathematics than the non-variant lunate epsilon form
\epsilon
ϵ. Related: set
membership \in
.
\vanothing
∅ Empty set symbol. Similar: \emptyset
. Related:
\revemptyset
. Not available in plain TeX. In LaTeX you need to load the amssymb package.
\varphi
φ Variant on the lowercase Greek letter (ordinary).
The non-variant form is \phi
ϕ.
\varpi
ϖ Variant on the lowercase Greek letter (ordinary).
The non-variant form is \pi
π.
\varrho
ϱ Variant on the lowercase Greek letter (ordinary).
The non-variant form is \rho
ρ.
\varsigma
ς Variant on the lowercase Greek letter
(ordinary). The non-variant form is
\sigma
σ.
\vartheta
ϑ Variant on the lowercase Greek letter
(ordinary). The non-variant form is
\theta
θ.
\vdash
⊢ Provable; turnstile, vertical and a dash
(relation). Similar: turnstile rotated a
half-circle \dashv
.
\vee
∨ Logical or; a downwards v shape (binary). Related:
logical and \wedge
. Similar: variable-sized
operator \bigvee
.
\Vert
‖ Vertical double bar (ordinary). Similar: vertical single
bar \vert
.
For a norm symbol, you can use the mathtools package and put in
your preamble
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
. This gives you
three command variants for double-line vertical bars that are correctly
horizontally spaced: if in the document body you write the starred
version $\norm*{M^\perp}$
then the height of the vertical bars
will match the height of the argument, whereas with
\norm{M^\perp}
the bars do not grow with the height of the
argument but instead are the default height, and \norm[size
command]{M^\perp}
also gives bars that do not grow but are set to
the size given in the size command, e.g., \Bigg
.
\vert
| Single line vertical bar (ordinary). Similar: double-line
vertical bar \Vert
. For such that, as in the definition of a
set, use \mid
because it is a relation.
For absolute value you can use the mathtools package and in your
preamble put
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
. This gives you
three command variants for single-line vertical bars that are correctly
horizontally spaced: if in the document body you write the starred
version $\abs*{\frac{22}{7}}$
then the height of the
vertical bars will match the height of the argument, whereas with
\abs{\frac{22}{7}}
the bars do not grow with the height of
the argument but instead are the default height, and
\abs[size command]{\frac{22}{7}}
also gives bars that
do not grow but are set to the size given in the size command,
e.g., \Bigg
.
\wedge
∧ Logical and (binary). Synonym: \land
. See also
logical or \vee
. Similar: variable-sized
operator \bigwedge
.
\wp
℘ Weierstrass p (ordinary).
\wr
≀ Wreath product (binary).
\Xi
Ξ uppercase Greek letter (ordinary).
\xi
ξ Lowercase Greek letter (ordinary).
\zeta
ζ Lowercase Greek letter (ordinary).
The following symbols are most often used in plain text but LaTeX provides versions to use in mathematical text.
\mathdollar
Dollar sign in math mode: $.
\mathparagraph
Paragraph sign (pilcrow) in math mode, ¶.
\mathsection
Section sign in math mode §.
\mathsterling
Sterling sign in math mode: £.
\mathunderscore
Underscore in math mode: _.
• Blackboard bold: | Doublestruck characters. | |
• Calligraphic: | Cursive characters. | |
• \boldmath & \unboldmath: | Symbols in boldface. | |
• Dots: | Ellipses, etc. |