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List of LaTeX mathematical symbols

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All the predefined mathematical symbols from the TeX package are listed below. More symbols are available from extra packages.

Contents

Greek letters

Greek letters
Symbol LaTeX Symbol LaTeX
Α and α \Alpha and \alpha Ν and ν \Nu and \nu
Β and β \Beta and \beta Ξ and ξ \Xi and \xi
Γ and γ \Gamma and \gamma Ο and ο \Omicron and \omicron
Δ and δ \Delta and \delta Π, π and \varpi \Pi, \pi and \varpi
Ε, ε and \varepsilon \Epsilon, \epsilon and \varepsilon Ρ, ρ and \varrho \Rho, \rho and \varrho
Ζ and ζ \Zeta and \zeta Σ, σ and \varsigma\, \Sigma, \sigma and \varsigma
Η and η \Eta and \eta Τ and τ \Tau and \tau
Θ, θ and \vartheta \Theta, \theta and \vartheta Υ and υ \Upsilon and \upsilon
Ι and ι \Iota and \iota Φ, φ, and \varphi \Phi, \phi and \varphi
Κ, κ and \varkappa \Kappa, \kappa and \varkappa Χ and χ \Chi and \chi
Λ and λ \Lambda and \lambda Ψ and ψ \Psi and \psi
Μ and μ \Mu and \mu Ω and ω \Omega and \omega


Archaic Greek letters
Symbol LaTeX
Failed to parse (unknown function\Digamma): \Digamma \Digamma
\digamma \digamma

Unary operators

Unary operators
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
+ \, +   - \, - negation ! \, ! factorial \# \# primorial
      \neg \neg not            

Relation operators

Relation operators
Symbol LaTeX Comment Symbol LaTeX Comment
< \, < is less than > \, > is greater than
\nless \nless is not less than \ngtr \ngtr is not greater than
\leq \leq is less than or equal to \geq \geq is greater than or equal to
\leqslant \leqslant is less than or equal to \geqslant \geqslant is greater than or equal to
\nleq \nleq is neither less than nor equal to \ngeq \ngeq is neither greater than nor equal to
\nleqslant \nleqslant is neither less than nor equal to \ngeqslant \ngeqslant is neither greater than nor equal to
\prec \prec precedes \succ \succ succeeds
\nprec \nprec doesn't precede \nsucc \nsucc doesn't succeed
\preceq \preceq precedes or equals \succeq \succeq succeeds or equals
\npreceq \npreceq neither precedes nor equals \nsucceq \nsucceq neither succeeds nor equals
\ll \ll   \gg \gg  
\lll \lll   \ggg \ggg  
\subset \subset is a proper subset of \supset \supset is a proper superset of
\not\subset \not\subset is not a proper subset of \not\supset \not\supset is not a proper superset of
\subseteq \subseteq is a subset of \supseteq \supseteq is a superset of
\nsubseteq \nsubseteq is not a subset of \nsupseteq \nsupseteq is not a superset of
\sqsubset \sqsubset   \sqsupset \sqsupset  
\sqsubseteq \sqsubseteq   \sqsupseteq \sqsupseteq  
Symbol LaTeX Comment
= \, = is equal to
\doteq \doteq  
\equiv \equiv is equivalent to
\approx \approx is approximately
\cong \cong is congruent to
\simeq \simeq is similar or equal to
˜ \sim is similar to
\propto \propto is proportional to
\neq or \ne \neq or \ne is not equal to
Symbol LaTeX Comment Symbol LaTeX Comment
\parallel \parallel is parallel with \nparallel \nparallel is not parallel with
\asymp \asymp is asymptotic to \bowtie \bowtie  
\vdash \vdash   \dashv \dashv  
\in \in is member of \ni \ni owns, has member
\smile \smile   \frown \frown  
\models \models models \notin \notin is not member of
\perp \perp is perpendicular with \mid \mid divides

Binary operators

Binary operators
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
\pm \pm plus or minus \cap \cap set intersection \diamond \diamond   \oplus \oplus  
\mp \mp minus or plus \cup \cup set union \bigtriangleup \bigtriangleup   \ominus \ominus  
\times \times multiplied by \uplus \uplus multiset addition \bigtriangledown \bigtriangledown   \otimes \otimes  
\div \div divided by \sqcap \sqcap   \triangleleft \triangleleft   \oslash \oslash  
\ast \ast asterisk \sqcup \sqcup   \triangleright \triangleright   \odot \odot  
\star \star   \vee \vee   \bigcirc \bigcirc   \circ \circ  
\dagger \dagger   \wedge \wedge   \bullet \bullet   \setminus \setminus set difference
\ddagger \ddagger   \cdot \cdot   \wr \wr   \amalg \amalg  

Negated binary operators

Negated binary operators
Symbol LaTeX Comment Symbol LaTeX Comment
\neq or \ne \, \neq or \ne is not equal to \notin \notin is not member of
\nless \nless is not less than \ngtr \ngtr is not greater than
\nleq \nleq is not less than or equal to \ngeq \ngeq is not greater than or equal to
\nleqslant \nleqslant   \ngeqslant \ngeqslant  
\nleqq \nleqq   \ngeqq \ngeqq  
\lneq \lneq   \gneq \gneq  
\lneqq \lneqq   \gneqq \gneqq  
\lvertneqq \lvertneqq   \gvertneqq \gvertneqq  
\lnsim \lnsim   \gnsim \gnsim  
\lnapprox \lnapprox   \gnapprox \gnapprox  
\nprec \nprec does not precede \nsucc \nsucc does not succeed
\npreceq \npreceq neither precedes nor equals \nsucceq \nsucceq neither succedes nor equals
\precneqq \precneqq   \succneqq \succneqq  
\precnsim \precnsim   \succnsim \succnsim  
\precnapprox \precnapprox   \succnapprox \succnapprox  
\nsim \nsim is not similar to \ncong \ncong is not congruent to
\nshortmid \nshortmid   \nshortparallel \nshortparallel  
\nmid \nmid   \nparallel \nparallel is not parallel with
\nvdash \nvdash   \nvDash \nvDash  
\nVdash \nVdash   \nVDash \nVDash  
\ntriangleleft \ntriangleleft   \ntriangleright \ntriangleright  
\ntrianglelefteq \ntrianglelefteq   \ntrianglerighteq \ntrianglerighteq  
\nsubseteq \nsubseteq   \nsupseteq \nsupseteq  
\nsubseteqq \nsubseteqq   \nsupseteqq \nsupseteqq  
\subsetneq \subsetneq   \supsetneq \supsetneq  
\varsubsetneq \varsubsetneq   \varsupsetneq \varsupsetneq  
\subsetneqq \subsetneqq   \supsetneqq \supsetneqq  
\varsubsetneqq \varsubsetneqq   \varsupsetneqq \varsupsetneqq  

Set and/or logic notation

Set notation
Symbol LaTeX Comment
\O or \emptyset \,, and \varnothing \, \O or \emptyset, and \varnothing the empty set
\N \N set of natural numbers
\Z \Z set of integers
\Q \Q set of rational numbers
\mathbb{A} \mathbb{A} set of algebraic numbers
\R \R set of real numbers
\C \C set of complex numbers
\mathbb{H} \mathbb{H} set of quaternions
\mathbb{O} \mathbb{O} set of octonions
\mathbb{S} \mathbb{S} set of sedenions
\in \in is member of
\notin \notin is not member of
\ni \ni owns (has member)
\subset \subset is proper subset of
\subseteq \subseteq is subset of
\supset \supset is proper superset of
\supseteq \supseteq is superset of
\cup \cup set union
\cap \cap set intersection
\setminus \setminus set difference
Logic notation
Symbol LaTeX Comment
\exists \exists there exists at least one
\exists! \exists! there exists one and only one
\nexists \nexists there is no
\forall \forall for all
\neg \neg not (logical not)
\lor \lor or (logical or)
\land \land and (logical and)
\Longrightarrow or \implies \Longrightarrow or \implies implies
\Rightarrow \Rightarrow (preferred for right implication)
\Longleftarrow \Longleftarrow is implied by (only if)
\Leftarrow \Leftarrow (preferred for left implication)
\iff \iff is equivalent to (if and only if, iff)
\Leftrightarrow \Leftrightarrow (preferred for equivalence)
\top \top  
\bot \bot  

Geometry

Geometry notation
Symbol LaTeX Comment Symbol LaTeX Comment
\overline{\rm AB} \overline{\rm AB} segment \overrightarrow{\rm AB} \overrightarrow{\rm AB} ray (half-line)
\angle \angle angle \measuredangle \measuredangle measured angle
\triangle \triangle triangle \square \square square
\cong \cong congruent (same shape and size) \ncong \ncong not congruent
˜ \sim similar (same shape) \nsim \nsim not similar
\| \| is parallel with \nparallel \nparallel is not parallel with
\perp \perp is perpendicular to \not\perp \not\perp is not perpendicular to

Delimiters

Delimiters
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
| \, | divides \| \| divides unitarily, is parallel with / \, / slash \backslash \backslash  
( \, ( \, left parenthesis ) \, ) \, right parenthesis [ \, [ \, left [square] bracket ] \, ] \, right [square] bracket
{ \{ left brace } \} right brace \langle \langle left angle bracket \rangle \rangle right angle bracket
\lceil \lceil ceiling (left) \rceil \rceil ceiling (right) \lfloor \lfloor floor (left) \rfloor \rfloor floor (right)
\ulcorner \ulcorner   \urcorner \urcorner   \llcorner \llcorner   \lrcorner \lrcorner  

Arrows

Arrows
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
\rightarrow or \to \rightarrow or \to   \Rightarrow \Rightarrow   \longrightarrow \longrightarrow   \Longrightarrow \Longrightarrow  
\mapsto \mapsto     \longmapsto \longmapsto    
\leftarrow or \gets \leftarrow or \gets   \Leftarrow \Leftarrow   \longleftarrow \longleftarrow   \Longleftarrow \Longleftarrow  
Symbol LaTeX Comment Symbol LaTeX Comment
\uparrow \uparrow Knuth's up-arrow notation \Uparrow \Uparrow  
\downarrow \downarrow   \Downarrow \Downarrow  
\updownarrow \updownarrow   \Updownarrow \Updownarrow  

Other symbols

Other symbols
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
\partial \partial partial derivative \imath \imath   \Re \Re real part \nabla \nabla del (vector calculus)
\eth \eth   \jmath \jmath   \Im \Im imaginary part \Box \Box  
\hbar \hbar reduced Planck's constant \ell \ell   \wp \wp [Weierstrass] powerset \infty \infty infinity

Hebrew lettters
Symbol LaTeX Comment
\aleph \aleph aleph numbers
\beth \beth  
\gimel \gimel  

Trigonometric functions

Circular functions
The prefix arc used for inverse circular trigonometric functions is the abbreviation for arcus.
Symbol LaTeX Symbol LaTeX Symbol LaTeX Symbol LaTeX
sin \sin arcsin \arcsin csc \csc arccsc \arccsc
cos \cos arccos \arccos sec \sec arcsec \arcsec
tan \tan arctan \arctan cot \cot arccot \arccot

Hyperbolic functions
The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands for area.
Symbol LaTeX Symbol LaTeX Symbol LaTeX Symbol LaTeX
sinh \sinh \operatorname{arsinh} \operatorname{arsinh} \operatorname{csch} \operatorname{csch} \operatorname{arcsch} \operatorname{arcsch}
cosh \cosh \operatorname{arcosh} \operatorname{arcosh} \operatorname{sech} \operatorname{sech} \operatorname{arsech} \operatorname{arsech}
tanh \tanh \operatorname{artanh} \operatorname{artanh} coth \coth \operatorname{arcoth} \operatorname{arcoth}

Sections remaining to be done: Table 3 onwards from symbols.pdf [1]


Notes

  1. To do.

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