Operator
Environment
GreekLetter
Symbol
Formula
Logic
SetTheory
Relation
Calculus
Arrow
BigO
Dots
Angle
Function
Trigonometric
For all
∀\forall
\forall
Exists
∃\exists
\exists
Or
∨\lor
\lor
And
∧\land
\land
Xor
⊻\veebar
\veebar
Not
¬\neg
\neg
Proper superset
⊃\supset
\supset
Superset
⊇\supseteq
\supseteq
Proper subset
⊂\subset
\subset
Subset
⊆\subseteq
\subseteq
Member
∈\in
\in
Empty set
∅\emptyset
\emptyset
Set union
∪\cup
\cup
Set intersection
∩\cap
\cap
Set-builder notation
{x∣x∈Z∧0≤x≤10}\{ x|x \in \mathbb{Z} \land 0 \leq x \leq 10 \}
\{ x|x \in \mathbb{Z} \land 0 \leq x \leq 10 \}
Natural numbers
N\mathbb{N}
\mathbb{N}
Real numbers
R\mathbb{R}
\mathbb{R}
Integers
Z\mathbb{Z}
\mathbb{Z}
Rational numbers
Z\mathbb{Z}
\mathbb{Z}
Complex numbers
C\mathbb{C}
\mathbb{C}
Imaginary numbers
I\mathbb{I}
\mathbb{I}
Left arrow
←,⟵,⇐,⟸\leftarrow, \longleftarrow, \Leftarrow, \Longleftarrow
\leftarrow, \longleftarrow, \Leftarrow, \Longleftarrow
Right arrow
→,⟶,⇒,⟹\rightarrow, \longrightarrow, \Rightarrow, \Longrightarrow
\rightarrow, \longrightarrow, \Rightarrow, \Longrightarrow
Up arrow
↑,⇑\uparrow, \Uparrow
\uparrow, \Uparrow
Down arrow
↓,⇓\downarrow, \Downarrow
\downarrow, \Downarrow
Left and right arrow
↔,⟷,⇔,⟺\leftrightarrow, \longleftrightarrow, \Leftrightarrow, \Longleftrightarrow
\leftrightarrow, \longleftrightarrow, \Leftrightarrow, \Longleftrightarrow
Up and down arrow
↕,⇕\updownarrow, \Updownarrow
\updownarrow, \Updownarrow
Maplet arrow / maps to
↦,⟼\mapsto, \longmapsto
\mapsto, \longmapsto
Hook arrow
↩,↪\hookleftarrow, \hookrightarrow
\hookleftarrow, \hookrightarrow
Harpoon arrows
↼,⇀,↽,⇁\leftharpoonup, \rightharpoonup, \leftharpoondown, \rightharpoondown
\leftharpoonup, \rightharpoonup, \leftharpoondown, \rightharpoondown
Ordinal or Intercardinal direction arrows
↗,↘,↙,↖\nearrow, \searrow, \swarrow, \nwarrow
\nearrow, \searrow, \swarrow, \nwarrow
Pythagoras Theorem
a2+b2=c2a^2 + b^2 = c^2
a^2 + b^2 = c^2
Theory of Relativity
E=mc2E = mc^2
E = mc^2
Euler's Identity
eiπ+1=0e^{i\pi} + 1 = 0
e^{i\pi} + 1 = 0
Euler's polyhedron formula
F−E+V=2F - E + V = 2
F - E + V = 2
Newton's law of gravity
F=Gm1m2d2F = G\frac{m_1 m_2}{d^2}
F = G\frac{m_1 m_2}{d^2}
Origin of complex numbers
i2=−1i^2 = -1
i^2 = -1
de Morgan's Laws
(E∪F)′=E′∩F′(E∩F)′=E′∪F′\begin{align} \left ( E \cup F \right )' = E' \cap F' \\ \left ( E \cap F \right )' = E' \cup F' \end{align}
\begin{align} \left ( E \cup F \right )' = E' \cap F' \\ \left ( E \cap F \right )' = E' \cup F' \end{align}
Repeating decimals
0.324‾0.\overline{324}
0.\overline{324}
Fraction
xy\frac{x}{y}
\frac{x}{y}
Exponent
a2,xya^2, x^y
a^2, x^y
Radical
9,xn\sqrt{9}, \sqrt[n]{x}
\sqrt{9}, \sqrt[n]{x}
Square Root
25\sqrt{25}
\sqrt{25}
Logarithm
log⁡x,log⁡2x\log x, \log_{2}x
\log x, \log_{2}x
Factorial
n!n!
n!
Absolute Value
∣x∣\vert{x} \vert
\vert{x} \vert
Calligraphic font
R,Z,D\mathcal{R}, \mathcal{Z}, \mathcal{D}
\mathcal{R}, \mathcal{Z}, \mathcal{D}
Bars over symbols
aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c}
\bar{a}, \bar{b}, \bar{c}
Hats over symbols
a~,b~,c~\tilde{a}, \tilde{b}, \tilde{c}
\tilde{a}, \tilde{b}, \tilde{c}
Arrows over symbols
a→,b→,c→\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}
\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}
Dots over symbols
a˙,b˙,c˙\dot{a}, \dot{b}, \dot{c}
\dot{a}, \dot{b}, \dot{c}
Spacing between symbols
a  b  ca\;b\;c
a\;b\;c
Nabla (gradient)
∇f(x0,y0)\nabla f(x_0, y_0)
\nabla f(x_0, y_0)
Text
Something\text{Something}
\text{Something}
Sums with limits
∑i=1ni2\sum\limits_{i=1}^{n}i^2
\sum\limits_{i=1}^{n}i^2
Products with limits
∏i=1ni2\prod\limits_{i=1}^{n}i^2
\prod\limits_{i=1}^{n}i^2
Integrals with limits
∫−∞∞f(x) dx\int\limits_{-\infty}^{\infty}f(x)\,\mathrm{d}x
\int\limits_{-\infty}^{\infty}f(x)\,\mathrm{d}x
Partial Derivative
∂Q∂t,∂2L∂x∂y\frac{\partial Q}{\partial t}, \frac{\partial^2L}{\partial x \partial y}
\frac{\partial Q}{\partial t}, \frac{\partial^2L}{\partial x \partial y}
Limits
lim⁡x→0(1+x)1x=e\lim_{x\to 0} (1+x)^\frac{1}{x} = e
\lim_{x\to 0} (1+x)^\frac{1}{x} = e
Max
max⁡(1,2,3)\max(1,2,3)
\max(1,2,3)
Min
min⁡(3,4,5)\min(3,4,5)
\min(3,4,5)
vmatrix
∣abcd∣\begin{vmatrix} a & b \\ c & d \end{vmatrix}
\begin{vmatrix} a & b \\ c & d \end{vmatrix}
pmatrix
(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
bmatrix
[abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}
\begin{bmatrix} a & b \\ c & d \end{bmatrix}
Bmatrix
{abcd}\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}
Vmatrix
∥abcd∥\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}
\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}
Infinity
∞\infty
\infty
Partial
∂\partial
\partial
star
⋆\star
\star
asterisk
∗\ast
\ast
dagger
†\dag
\dag
double dagger
‡\ddag
\ddag
oplus
⊕\oplus
\oplus
circ
∘\circ
\circ
bullet
∙\bullet
\bullet
copyright
©\copyright
\copyright
center dots
1,⋯1, \cdots
1, \cdots
diagonal dots
⋱\ddots
\ddots
lower dots
1,…1, \ldots
1, \ldots
vertical dots
⋮\vdots
\vdots
angle
∠\angle
\angle
Measured angle
∡\measuredangle
\measuredangle
Spherical angle
∢\sphericalangle
\sphericalangle
alpha
α\alpha
\alpha
beta
β\beta
\beta
gamma
γ\gamma
\gamma
delta
δ\delta
\delta
epsilon and varepsilon
ϵ,ε\epsilon, \varepsilon
\epsilon, \varepsilon
zeta
ζ\zeta
\zeta
eta
η\eta
\eta
theta and vartheta
θ,ϑ\theta, \vartheta
\theta, \vartheta
iota
ι\iota
\iota
kappa and varkappa
κ,ϰ\kappa, \varkappa
\kappa, \varkappa
lambda
λ\lambda
\lambda
mu
μ\mu
\mu
nu
ν\nu
\nu
xi
ξ\xi
\xi
omicron
oo
o
pi and varpi
π,ϖ\pi, \varpi
\pi, \varpi
rho and varrho
ρ,ϱ\rho, \varrho
\rho, \varrho
sigma and varsigmna
σ,ς\sigma, \varsigma
\sigma, \varsigma
tau
τ\tau
\tau
upsilon
υ\upsilon
\upsilon
phi and varphi
ϕ,φ\phi, \varphi
\phi, \varphi
chi
χ\chi
\chi
psi
ψ\psi
\psi
omega
ω\omega
\omega
Big O
O,O\mathcal{O}, O
\mathcal{O}, O
Big Omega
Ω\Omega
\Omega
Big Theta
Θ\Theta
\Theta
Small O [micron]
oo
o
Small Omega
ω\omega
\omega
On the order of
∼\sim
\sim
Constant Time
O(1)O(1)
O(1)
Logarithmic Time
O(log⁡n)O(\log{}n)
O(\log{}n)
Linear Time
O(n)O(n)
O(n)
Quasilinear Time
O(nlog⁡n)O(n\log{}n)
O(n\log{}n)
Quadratic Time
O(n2)O(n^2)
O(n^2)
Cubic Time
O(n3)O(n^3)
O(n^3)
Factorial Time
O(n!)O(n!)
O(n!)
Times
×\times
\times
Dot
⋅\cdot
\cdot
Division
÷\div
\div
Plus minus
±\pm
\pm
Not equal
≠\neq
\neq
Approximately equal
≈\approx
\approx
Less than
<\lt
\lt
Less than or equal
≤\leq
\leq
Greater than
>\gt
\gt
Greater than or equal
≥\geq
\geq
Much less than
≪\ll
\ll
Much greater than
≫\gg
\gg
sin
sin⁡θ\sin \theta
\sin \theta
cos
cos⁡θ\cos \theta
\cos \theta
tan
tan⁡θ\tan \theta
\tan \theta
cot
cot⁡θ\cot \theta
\cot \theta
sec
sec⁡θ\sec \theta
\sec \theta
csc
csc⁡θ\csc \theta
\csc \theta
arcsin
arcsin⁡θ\arcsin \theta
\arcsin \theta
arccos
arccos⁡θ\arccos \theta
\arccos \theta
arctan
arctan⁡θ\arctan \theta
\arctan \theta