Mathematical symbols list (+,-,x,º,=,<,>,...)

Mathematical Symbols

List of all mathematical symbols and signs - meaning and examples.

Basic math symbols

Geometry symbols

Algebra symbols

Probability & statistics symbols

Set theory symbols

Logic symbols

Calculus & analysis symbols

Number symbols

Greek symbols

Roman numerals

Basic math symbols

Symbol Symbol Name Meaning / definition Example

= equals sign equality 5 = 2+3

≠ not equal sign inequality 5 ≠ 4

> strict inequality greater than 5 > 4

< strict inequality less than 4 < 5

≥ inequality greater than or equal to 5 ≥ 4

≤ inequality less than or equal to 4 ≤ 5

( ) parentheses calculate expression inside first 2 × (3+5) = 16

[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18

+ plus sign addition 1 + 1 = 2

− minus sign subtraction 2 − 1 = 1

± plus - minus both plus and minus operations 3 ± 5 = 8 and -2

∓ minus - plus both minus and plus operations 3 ∓ 5 = -2 and 8

* asterisk multiplication 2 * 3 = 6

× times sign multiplication 2 × 3 = 6

∙ multiplication dot multiplication 2 ∙ 3 = 6

º division sign / obelus division 6 º 2 = 3

/ division slash division 6 / 2 = 3

– horizontal line division / fraction $\frac{6}{2}=3$

mod modulo remainder calculation 7 mod 2 = 1

. period decimal point, decimal separator 2.56 = 2+56/100

a^b power exponent 2³= 8

a^b caret exponent 2 ^ 3= 8

√a square root
√a · √a = a
√9 = ±3

³√a cube root ³√8 = 2

⁴√a forth root ⁴√16 = ±2

ⁿ√a n-th root (radical) for n=3, ⁿ√8 = 2

% percent 1% = 1/100 10% × 30 = 3

‰ per-mille 1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3

ppm per-million 1ppm = 1/1000000 10ppm × 30 = 0.0003

ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10^-7

ppt per-trillion 1ppb = 10^-12 10ppb × 30 = 3×10^-10

Geometry symbols

Symbol Symbol Name Meaning / definition Example

∠ angle formed by two rays ∠ABC = 30º

measured angle ABC = 30º

spherical angle AOB = 30º

∟ right angle = 90º α = 90º

º degree 1 turn = 360º α = 60º

´ arcminute 1º = 60´ α = 60º59'

´´ arcsecond 1´ = 60´´ α = 60º59'59''

line infinite line

AB line segment line from point A to point B

ray line that start from point A

arc arc from point A to point B = 60º

| perpendicular perpendicular lines (90º angle) AC | BC

|| parallel parallel lines AB || CD

≅ congruent to equivalence of geometric shapes and size ∆ABC ≅ ∆XYZ

~ similarity same shapes, not same size ∆ABC ~ ∆XYZ

Δ triangle triangle shape ΔABC ≅ ΔBCD

|x-y| distance distance between points x and y | x-y | = 5

π pi constant π = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = π·d = 2·π·r

rad radians radians angle unit 360º = 2π rad

grad grads grads angle unit 360º = 400 grad

Algebra symbols

Symbol Symbol Name Meaning / definition Example

x x variable unknown value to find when 2x = 4, then x = 2

≡ equivalence identical to

≜ equal by definition equal by definition

:= equal by definition equal by definition

~ approximately equal weak approximation 11 ~ 10

≈ approximately equal approximation sin(0.01) ≈ 0.01

∝ proportional to proportional to
f(x) ∝ g(x)

∞ lemniscate infinity symbol

≪ much less than much less than 1 ≪ 1000000

≫ much greater than much greater than 1000000 ≫ 1

( ) parentheses calculate expression inside first 2 * (3+5) = 16

[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18

{ } braces set

⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋= 4

⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉= 5

x! exclamation mark factorial 4! = 1*2*3*4 = 24

| x | single vertical bar absolute value | -5 | = 5

f (x) function of x maps values of x to f(x) f (x) = 3x+5

(f ∘g) function composition
(f ∘g) (x) = f (g(x))
f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1)

(a,b) open interval (a,b) = {x | a < x < b} x ∈ (2,6)

[a,b] closed interval [a,b] = {x | a ≤ x ≤ b} x ∈ [2,6]

∆ delta change / difference ∆t = t₁- t₀

∆ discriminant Δ = b² - 4ac

∑ sigma summation - sum of all values in range of series ∑ x_i= x₁+x₂+...+x_n

∑∑ sigma double summation

∏ capital pi product - product of all values in range of series ∏ x_i=x₁∙x₂∙...∙x_n

e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)^x , x→∞

γ Euler-Mascheroni constant γ = 0.527721566...

φ golden ratio golden ratio constant

π pi constant π = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = π·d = 2·π·r

Linear Algebra Symbols

Symbol Symbol Name Meaning / definition Example

∙ dot scalar product a ∙ b

× cross vector product a × b

A⊗B tensor product tensor product of A and B A ⊗ B

$\langle x,y \rangle$ inner product

[ ] brackets matrix of numbers

( ) parentheses matrix of numbers

| A | determinant determinant of matrix A

det(A) determinant determinant of matrix A

|| x || double vertical bars norm

A^T transpose matrix transpose
(A^T)_ij = (A)_ji

A^† Hermitian matrix matrix conjugate transpose
(A^†)_ij = (A)_ji

A^* Hermitian matrix matrix conjugate transpose
(A^*)_ij = (A)_ji

A^-1 inverse matrix A A^-1 = I

rank(A) matrix rank rank of matrix A
rank(A) = 3

dim(U) dimension dimension of matrix A
rank(U) = 3

Probability and statistics symbols

Symbol Symbol Name Meaning / definition Example

P(A) probability function probability of event A P(A) = 0.5

P(A ∩ B) probability of events intersection probability that of events A and B P(A∩B) = 0.5

P(A ∪ B) probability of events union probability that of events A or B P(A∪B) = 0.5

P(A | B) conditional probability function probability of event A given event B occured P(A | B) = 0.3

f (x) probability density function (pdf) P(a ≤ x ≤ b) = ∫ f (x) dx

F(x) cumulative distribution function (cdf) F(x) = P(X ≤ x)

μ population mean mean of population values μ = 10

E(X) expectation value expected value of random variable X E(X) = 10

E(X | Y) conditional expectation expected value of random variable X given Y E(X | Y=2) = 5

var(X) variance variance of random variable X var(X) = 4

σ² variance variance of population values σ² = 4

std(X) standard deviation standard deviation of random variable X std(X) = 2

σ_X standard deviation standard deviation value of random variable X σ_X = 2

median middle value of random variable x

cov(X,Y) covariance covariance of random variables X and Y cov(X,Y) = 4

corr(X,Y) correlation correlation of random variables X and Y corr(X,Y) = 0.6

ρ_X,Y correlation correlation of random variables X and Y ρ_X,Y = 0.6

∑ summation summation - sum of all values in range of series

∑∑ double summation double summation

Mo mode value that occurs most frequently in population

MR mid-range
MR = (x_max+x_min)/2

Md sample median half the population is below this value

Q₁ lower / first quartile 25% of population are below this value

Q₂ median / second quartile 50% of population are below this value = median of samples

Q₃ upper / third quartile 75% of population are below this value

x sample mean average / arithmetic mean x = (2+5+9) / 3 = 5.333

s ² sample variance population samples variance estimator s² = 4

s sample standard deviation population samples standard deviation estimator s = 2

z_x standard score
z_x = (x-x) / s_x

X ~ distribution of X distribution of random variable X X ~ N(0,3)

N(μ,σ²) normal distribution gaussian distribution X ~ N(0,3)

U(a,b) uniform distribution equal probability in range a,b X ~ U(0,3)

exp(λ) exponential distribution f (x) = λe^-λx , x≥0

gamma(c, λ) gamma distribution
f (x) = λ c x^c-1e^-λx / Γ(c), x≥0

χ²(k) chi-square distribution
f (x) = x^k^/2-1e^-x/2 / ( 2^k/2Γ(k/2) )

F (k₁, k₂) F distribution

Bin(n,p) binomial distribution
f (k) = _nC_k p^k(1-p)^n-k

Poisson(λ) Poisson distribution
f (k) = λ^ke^-λ / k!

Geom(p) geometric distribution
f (k) = p(1-p)^k

HG(N,K,n) hyper-geometric distribution

Bern(p) Bernoulli distribution

Combinatorics Symbols

Symbol Symbol Name Meaning / definition Example

n! factorial n! = 1·2·3·...·n 5! = 1·2·3·4·5 = 120

_nP_k permutation $_{n}P_{k}=\frac{n!}{(n-k)!}$ ₅P₃ = 5! / (5-3)! = 60

_nC_k

combination $_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}$ ₅C₃ = 5!/[3!(5-3)!]=10

Set theory symbols

Symbol Symbol Name Meaning / definition Example

{ } set a collection of elements A = {3,7,9,14},
B = {9,14,28}

A ∩ B intersection objects that belong to set A and set B A ∩ B = {9,14}

A ∪ B union objects that belong to set A or set B A ∪ B = {3,7,9,14,28}

A ⊆ B subset subset has fewer elements or equal to the set {9,14,28} ⊆ {9,14,28}

A ⊂ B proper subset / strict subset subset has fewer elements than the set {9,14} ⊂ {9,14,28}

A ⊄ B not subset left set not a subset of right set {9,66} ⊄ {9,14,28}

A ⊇ B superset set A has more elements or equal to the set B {9,14,28} ⊇ {9,14,28}

A ⊃ B proper superset / strict superset set A has more elements than set B {9,14,28} ⊃ {9,14}

A ⊅ B not superset set A is not a superset of set B {9,14,28} ⊅ {9,66}

2^A power set all subsets of A

$\mathcal{P}(A)$ power set all subsets of A

A = B equality both sets have the same members A={3,9,14},
B={3,9,14},
A=B

A^c complement all the objects that do not belong to set A

A \ B relative complement objects that belong to A and not to B A = {3,9,14},
B = {1,2,3},
A-B = {9,14}

A - B relative complement objects that belong to A and not to B A = {3,9,14},
B = {1,2,3},
A-B = {9,14}

A ∆ B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}

A ⊖ B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}

a∈A element of set membership A={3,9,14}, 3 ∈ A

x∉A not element of no set membership A={3,9,14}, 1 ∉ A

(a,b) ordered pair collection of 2 elements

A×B cartesian product set of all ordered pairs from A and B

|A| cardinality the number of elements of set A A={3,9,14}, |A|=3

#A cardinality the number of elements of set A A={3,9,14}, #A=3

aleph-null infinite cardinality of natural numbers set

aleph-one cardinality of countable ordinal numbers set

Ø empty set Ø = { } C = {Ø}

$\mathbb{U}$ universal set set of all possible values

$\mathbb{N}$ ₀ natural numbers / whole numbers set (with zero) $\mathbb{N}$ ₀ = {0,1,2,3,4,...} 0 ∈ $\mathbb{N}$ ₀

$\mathbb{N}$ ₁ natural numbers / whole numbers set (without zero) $\mathbb{N}$ ₁ = {1,2,3,4,5,...} 6 ∈ $\mathbb{N}$ ₁

$\mathbb{Z}$ integer numbers set $\mathbb{Z}$ = {...-3,-2,-1,0,1,2,3,...} -6 ∈ $\mathbb{Z}$

$\mathbb{Q}$ rational numbers set $\mathbb{Q}$ = {x | x=a/b, a,b∈ $\mathbb{N}$ } 2/6 ∈ $\mathbb{Q}$

$\mathbb{R}$ real numbers set $\mathbb{R}$ = {x | -∞ < x <∞} 6.343434 ∈ $\mathbb{R}$

$\mathbb{C}$ complex numbers set $\mathbb{C}$ = {z | z=a+bi, -∞<a<∞, -∞<b<∞} 6+2i ∈ $\mathbb{C}$

Logic symbols

Symbol Symbol Name Meaning / definition Example

· and and x · y

^ caret / circumflex and x ^ y

& ampersand and x & y

+ plus or x + y

∨ reversed caret or x ∨ y

| vertical line or x | y

x' single quote not - negation x'

x bar not - negation x

¬ not not - negation ¬ x

! exclamation mark not - negation ! x

⊕ circled plus / oplus exclusive or - xor x ⊕ y

~ tilde negation ~ x

⇒ implies

⇔ equivalent if and only if

∀ for all

∃ there exists

∄ there does not exists

∴ therefore

∵ because / since

Calculus & analysis symbols

Symbol Symbol Name Meaning / definition Example

$\lim_{x\to x0}f(x)$ limit limit value of a function

ε epsilon represents a very small number, near zero ε → 0

e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)^x , x→∞

y ' derivative derivative - Leibniz's notation (3x³)' = 9x²

y '' second derivative derivative of derivative (3x³)'' = 18x

y⁽ⁿ⁾ nth derivative n times derivation (3x³)⁽³⁾ = 18

$\frac{dy}{dx}$ derivative derivative - Lagrange's notation d(3x³)/dx = 9x²

$\frac{d^2y}{dx^2}$ second derivative derivative of derivative d²(3x³)/dx² = 18x

$\frac{d^ny}{dx^n}$ nth derivative n times derivation

$\dot{y}$ time derivative derivative by time - Newton notation

time second derivative derivative of derivative

$\frac{\partial f(x,y)}{\partial x}$ partial derivative ∂(x²+y²)/∂x = 2x

∫ integral opposite to derivation

∬ double integral integration of function of 2 variables

∭ triple integral integration of function of 3 variables

∮ closed contour / line integral

∯ closed surface integral

∰ closed volume integral

[a,b] closed interval [a,b] = {x | a ≤ x ≤ b}

(a,b) open interval (a,b) = {x | a < x < b}

i imaginary unit i ≡ √-1 z = 3 + 2i

z* complex conjugate z = a+bi → z*=a-bi z* = 3 + 2i

z complex conjugate z = a+bi → z = a-bi z = 3 + 2i

∇ nabla / del gradient / divergence operator ∇f (x,y,z)

vector

unit vector

x * y convolution y(t) = x(t) * h(t)

Laplace transform F(s) = {f (t)}

Fourier transform X(ω) = {f (t)}

δ delta function

∞ lemniscate infinity symbol

Numeral symbols

Name European Roman Hindu Arabic Hebrew

zero 0 ٠

one 1 I ١ א

two 2 II ٢ ב

three 3 III ٣ ג

four 4 IV ٤ ד

five 5 V ٥ ה

six 6 VI ٦ ו

seven 7 VII ٧ ז

eight 8 VIII ٨ ח

nine 9 IX ٩ ט

ten 10 X ١٠ י

eleven 11 XI ١١ יא

twelve 12 XII ١٢ יב

thirteen 13 XIII ١٣ יג

fourteen 14 XIV ١٤ יד

fifteen 15 XV ١٥ טו

sixteen 16 XVI ١٦ טז

seventeen 17 XVII ١٧ יז

eighteen 18 XVIII ١٨ יח

nineteen 19 XIX ١٩ יט

twenty 20 XX ٢٠ כ

thirty 30 XXX ٣٠ ל

fourty 40 XL ٤٠ מ

fifty 50 L ٥٠ נ

sixty 60 LX ٦٠ ס

seventy 70 LXX ٧٠ ע

eighty 80 LXXX ٨٠ פ

ninety 90 XC ٩٠ צ

one hundred 100 C ١٠٠ ק

Greek alphabet letters

Greek Symbol Greek Letter Name English Equivalent Pronunciation

Upper Case Lower Case

Α α Alpha a al-fa

Β β Beta b be-ta

Γ γ Gamma g ga-ma

Δ δ Delta d del-ta

Ε ε Epsilon e ep-si-lon

Ζ ζ Zeta z ze-ta

Η η Eta h eh-ta

Θ θ Theta th te-ta

Ι ι Iota i io-ta

Κ κ Kappa k ka-pa

Λ λ Lambda l lam-da

Μ μ Mu m m-yoo

Ν ν Nu n noo

Ξ ξ Xi x x-ee

Ο ο Omicron o o-mee-c-ron

Π π Pi p pa-yee

Ρ ρ Rho r row

Σ σ Sigma s sig-ma

Τ τ Tau t ta-oo

Υ υ Upsilon u oo-psi-lon

Φ φ Phi ph f-ee

Χ χ Chi ch kh-ee

Ψ ψ Psi ps p-see

Ω ω Omega o o-me-ga

Roman numerals

Number Roman numeral

0 not defined

1 I

2 II

3 III

4 IV

5 V

6 VI

7 VII

8 VIII

9 IX

10 X

11 XI

12 XII

13 XIII

14 XIV

15 XV

16 XVI

17 XVII

18 XVIII

19 XIX

20 XX

30 XXX

40 XL

50 L

60 LX

70 LXX

80 LXXX

90 XC

100 C

200 CC

300 CCC

400 CD

500 D

600 DC

700 DCC

800 DCCC

900 CM

1000 M

5000 V

10000 X

50000 L

100000 C

500000 D

1000000 M

See also

Algebra symbols

Geometry symbols

Statistical symbols

Logic symbols

Set theory symbols

Calculus & analysis symbols

Number symbols

Greek alphabet symbols

Roman numerals

Infinity symbol

Math calculators

Symbol	Symbol Name	Meaning / definition	Example
=	equals sign	equality	5 = 2+3
≠	not equal sign	inequality	5 ≠ 4
>	strict inequality	greater than	5 > 4
<	strict inequality	less than	4 < 5
≥	inequality	greater than or equal to	5 ≥ 4
≤	inequality	less than or equal to	4 ≤ 5
( )	parentheses	calculate expression inside first	2 × (3+5) = 16
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
+	plus sign	addition	1 + 1 = 2
−	minus sign	subtraction	2 − 1 = 1
±	plus - minus	both plus and minus operations	3 ± 5 = 8 and -2
∓	minus - plus	both minus and plus operations	3 ∓ 5 = -2 and 8
*	asterisk	multiplication	2 * 3 = 6
×	times sign	multiplication	2 × 3 = 6
∙	multiplication dot	multiplication	2 ∙ 3 = 6
º	division sign / obelus	division	6 º 2 = 3
/	division slash	division	6 / 2 = 3
–	horizontal line	division / fraction	$\frac{6}{2}=3$
mod	modulo	remainder calculation	7 mod 2 = 1
.	period	decimal point, decimal separator	2.56 = 2+56/100
a^b	power	exponent	2³= 8
a^b	caret	exponent	2 ^ 3= 8
√a	square root	√a · √a = a	√9 = ±3
³√a	cube root		³√8 = 2
⁴√a	forth root		⁴√16 = ±2
ⁿ√a	n-th root (radical)		for n=3, ⁿ√8 = 2
%	percent	1% = 1/100	10% × 30 = 3
‰	per-mille	1‰ = 1/1000 = 0.1%	10‰ × 30 = 0.3
ppm	per-million	1ppm = 1/1000000	10ppm × 30 = 0.0003
ppb	per-billion	1ppb = 1/1000000000	10ppb × 30 = 3×10^-7
ppt	per-trillion	1ppb = 10^-12	10ppb × 30 = 3×10^-10

Symbol	Symbol Name	Meaning / definition	Example
∠	angle	formed by two rays	∠ABC = 30º
	measured angle		ABC = 30º
	spherical angle		AOB = 30º
∟	right angle	= 90º	α = 90º
º	degree	1 turn = 360º	α = 60º
´	arcminute	1º = 60´	α = 60º59'
´´	arcsecond	1´ = 60´´	α = 60º59'59''
	line	infinite line
AB	line segment	line from point A to point B
	ray	line that start from point A
	arc	arc from point A to point B	= 60º
\|	perpendicular	perpendicular lines (90º angle)	AC \| BC
\|\|	parallel	parallel lines	AB \|\| CD
≅	congruent to	equivalence of geometric shapes and size	∆ABC ≅ ∆XYZ
~	similarity	same shapes, not same size	∆ABC ~ ∆XYZ
Δ	triangle	triangle shape	ΔABC ≅ ΔBCD
\|x-y\|	distance	distance between points x and y	\| x-y \| = 5
π	pi constant	π = 3.141592654... is the ratio between the circumference and diameter of a circle	c = π·d = 2·π·r
rad	radians	radians angle unit	360º = 2π rad
grad	grads	grads angle unit	360º = 400 grad

Symbol	Symbol Name	Meaning / definition	Example
x	x variable	unknown value to find	when 2x = 4, then x = 2
≡	equivalence	identical to
≜	equal by definition	equal by definition
:=	equal by definition	equal by definition
~	approximately equal	weak approximation	11 ~ 10
≈	approximately equal	approximation	sin(0.01) ≈ 0.01
∝	proportional to	proportional to	f(x) ∝ g(x)
∞	lemniscate	infinity symbol
≪	much less than	much less than	1 ≪ 1000000
≫	much greater than	much greater than	1000000 ≫ 1
( )	parentheses	calculate expression inside first	2 * (3+5) = 16
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
{ }	braces	set
⌊x⌋	floor brackets	rounds number to lower integer	⌊4.3⌋= 4
⌈x⌉	ceiling brackets	rounds number to upper integer	⌈4.3⌉= 5
x!	exclamation mark	factorial	4! = 123*4 = 24
\| x \|	single vertical bar	absolute value	\| -5 \| = 5
f (x)	function of x	maps values of x to f(x)	f (x) = 3x+5
(f ∘g)	function composition	(f ∘g) (x) = f (g(x))	f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1)
(a,b)	open interval	(a,b) = {x \| a < x < b}	x ∈ (2,6)
[a,b]	closed interval	[a,b] = {x \| a ≤ x ≤ b}	x ∈ [2,6]
∆	delta	change / difference	∆t = t₁- t₀
∆	discriminant	Δ = b² - 4ac
∑	sigma	summation - sum of all values in range of series	∑ x_i= x₁+x₂+...+x_n
∑∑	sigma	double summation
∏	capital pi	product - product of all values in range of series	∏ x_i=x₁∙x₂∙...∙x_n
e	e constant / Euler's number	e = 2.718281828...	e = lim (1+1/x)^x , x→∞
γ	Euler-Mascheroni constant	γ = 0.527721566...
φ	golden ratio	golden ratio constant
π	pi constant	π = 3.141592654... is the ratio between the circumference and diameter of a circle	c = π·d = 2·π·r

Symbol	Symbol Name	Meaning / definition	Example
∙	dot	scalar product	a ∙ b
×	cross	vector product	a × b
A⊗B	tensor product	tensor product of A and B	A ⊗ B
$\langle x,y \rangle$	inner product
[ ]	brackets	matrix of numbers
( )	parentheses	matrix of numbers
\| A \|	determinant	determinant of matrix A
det(A)	determinant	determinant of matrix A
\|\| x \|\|	double vertical bars	norm
A^T	transpose	matrix transpose	(A^T)_ij = (A)_ji
A^†	Hermitian matrix	matrix conjugate transpose	(A^†)_ij = (A)_ji
A^*	Hermitian matrix	matrix conjugate transpose	(A^)_ij* = (A)_ji
A^-1	inverse matrix	A A^-1 = I
rank(A)	matrix rank	rank of matrix A	rank(A) = 3
dim(U)	dimension	dimension of matrix A	rank(U) = 3

Symbol	Symbol Name	Meaning / definition	Example
P(A)	probability function	probability of event A	P(A) = 0.5
P(A ∩ B)	probability of events intersection	probability that of events A and B	P(A∩B) = 0.5
P(A ∪ B)	probability of events union	probability that of events A or B	P(A∪B) = 0.5
P(A \| B)	conditional probability function	probability of event A given event B occured	P(A \| B) = 0.3
f (x)	probability density function (pdf)	P(a ≤ x ≤ b) = ∫ f (x) dx
F(x)	cumulative distribution function (cdf)	F(x) = P(X ≤ x)
μ	population mean	mean of population values	μ = 10
E(X)	expectation value	expected value of random variable X	E(X) = 10
E(X \| Y)	conditional expectation	expected value of random variable X given Y	E(X \| Y=2) = 5
var(X)	variance	variance of random variable X	var(X) = 4
σ²	variance	variance of population values	σ² = 4
std(X)	standard deviation	standard deviation of random variable X	std(X) = 2
σ_X	standard deviation	standard deviation value of random variable X	σ_X = 2
	median	middle value of random variable x
cov(X,Y)	covariance	covariance of random variables X and Y	cov(X,Y) = 4
corr(X,Y)	correlation	correlation of random variables X and Y	corr(X,Y) = 0.6
ρ_X,Y	correlation	correlation of random variables X and Y	ρ_X,Y = 0.6
∑	summation	summation - sum of all values in range of series
∑∑	double summation	double summation
Mo	mode	value that occurs most frequently in population
MR	mid-range	MR = (x_max+x_min)/2
Md	sample median	half the population is below this value
Q₁	lower / first quartile	25% of population are below this value
Q₂	median / second quartile	50% of population are below this value = median of samples
Q₃	upper / third quartile	75% of population are below this value
x	sample mean	average / arithmetic mean	x = (2+5+9) / 3 = 5.333
s ²	sample variance	population samples variance estimator	s² = 4
s	sample standard deviation	population samples standard deviation estimator	s = 2
z_x	standard score	z_x = (x-x) / s_x
X ~	distribution of X	distribution of random variable X	X ~ N(0,3)
N(μ,σ²)	normal distribution	gaussian distribution	X ~ N(0,3)
U(a,b)	uniform distribution	equal probability in range a,b	X ~ U(0,3)
exp(λ)	exponential distribution	f (x) = λe^-λx , x≥0
gamma(c, λ)	gamma distribution	f (x) = λ c x^c-1e^-λx / Γ(c), x≥0
χ²(k)	chi-square distribution	f (x) = x^k^/2-1e^-x/2 / ( 2^k/2Γ(k/2) )
F (k₁, k₂)	F distribution
Bin(n,p)	binomial distribution	f (k) = _nC_k p^k(1-p)^n-k
Poisson(λ)	Poisson distribution	f (k) = λ^ke^-λ / k!
Geom(p)	geometric distribution	f (k) = p(1-p)^k
HG(N,K,n)	hyper-geometric distribution
Bern(p)	Bernoulli distribution

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A = {3,7,9,14}, B = {9,14,28}
A ∩ B	intersection	objects that belong to set A and set B	A ∩ B = {9,14}
A ∪ B	union	objects that belong to set A or set B	A ∪ B = {3,7,9,14,28}
A ⊆ B	subset	subset has fewer elements or equal to the set	{9,14,28} ⊆ {9,14,28}
A ⊂ B	proper subset / strict subset	subset has fewer elements than the set	{9,14} ⊂ {9,14,28}
A ⊄ B	not subset	left set not a subset of right set	{9,66} ⊄ {9,14,28}
A ⊇ B	superset	set A has more elements or equal to the set B	{9,14,28} ⊇ {9,14,28}
A ⊃ B	proper superset / strict superset	set A has more elements than set B	{9,14,28} ⊃ {9,14}
A ⊅ B	not superset	set A is not a superset of set B	{9,14,28} ⊅ {9,66}
2^A	power set	all subsets of A
$\mathcal{P}(A)$	power set	all subsets of A
A = B	equality	both sets have the same members	A={3,9,14}, B={3,9,14}, A=B
A^c	complement	all the objects that do not belong to set A
A \ B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A-B = {9,14}
A - B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A-B = {9,14}
A ∆ B	symmetric difference	objects that belong to A or B but not to their intersection	A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14}
A ⊖ B	symmetric difference	objects that belong to A or B but not to their intersection	A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14}
a∈A	element of	set membership	A={3,9,14}, 3 ∈ A
x∉A	not element of	no set membership	A={3,9,14}, 1 ∉ A
(a,b)	ordered pair	collection of 2 elements
A×B	cartesian product	set of all ordered pairs from A and B
\|A\|	cardinality	the number of elements of set A	A={3,9,14}, \|A\|=3
#A	cardinality	the number of elements of set A	A={3,9,14}, #A=3
	aleph-null	infinite cardinality of natural numbers set
	aleph-one	cardinality of countable ordinal numbers set
Ø	empty set	Ø = { }	C = {Ø}
$\mathbb{U}$	universal set	set of all possible values
$\mathbb{N}$ ₀	natural numbers / whole numbers set (with zero)	$\mathbb{N}$ ₀ = {0,1,2,3,4,...}	0 ∈ $\mathbb{N}$ ₀
$\mathbb{N}$ ₁	natural numbers / whole numbers set (without zero)	$\mathbb{N}$ ₁ = {1,2,3,4,5,...}	6 ∈ $\mathbb{N}$ ₁
$\mathbb{Z}$	integer numbers set	$\mathbb{Z}$ = {...-3,-2,-1,0,1,2,3,...}	-6 ∈ $\mathbb{Z}$
$\mathbb{Q}$	rational numbers set	$\mathbb{Q}$ = {x \| x=a/b, a,b∈ $\mathbb{N}$ }	2/6 ∈ $\mathbb{Q}$
$\mathbb{R}$	real numbers set	$\mathbb{R}$ = {x \| -∞ < x <∞}	6.343434 ∈ $\mathbb{R}$
$\mathbb{C}$	complex numbers set	$\mathbb{C}$ = {z \| z=a+bi, -∞<a<∞, -∞<b<∞}	6+2i ∈ $\mathbb{C}$

Symbol	Symbol Name	Meaning / definition	Example
·	and	and	x · y
^	caret / circumflex	and	x ^ y
&	ampersand	and	x & y
+	plus	or	x + y
∨	reversed caret	or	x ∨ y
\|	vertical line	or	x \| y
x'	single quote	not - negation	x'
x	bar	not - negation	x
¬	not	not - negation	¬ x
!	exclamation mark	not - negation	! x
⊕	circled plus / oplus	exclusive or - xor	x ⊕ y
~	tilde	negation	~ x
⇒	implies
⇔	equivalent	if and only if
∀	for all
∃	there exists
∄	there does not exists
∴	therefore
∵	because / since

Symbol	Symbol Name	Meaning / definition	Example
$\lim_{x\to x0}f(x)$	limit	limit value of a function
ε	epsilon	represents a very small number, near zero	ε → 0
e	e constant / Euler's number	e = 2.718281828...	e = lim (1+1/x)^x , x→∞
y '	derivative	derivative - Leibniz's notation	(3x³)' = 9x²
y ''	second derivative	derivative of derivative	(3x³)'' = 18x
y⁽ⁿ⁾	nth derivative	n times derivation	(3x³)⁽³⁾ = 18
$\frac{dy}{dx}$	derivative	derivative - Lagrange's notation	d(3x³)/dx = 9x²
$\frac{d^2y}{dx^2}$	second derivative	derivative of derivative	d²(3x³)/dx² = 18x
$\frac{d^ny}{dx^n}$	nth derivative	n times derivation
$\dot{y}$	time derivative	derivative by time - Newton notation
	time second derivative	derivative of derivative
$\frac{\partial f(x,y)}{\partial x}$	partial derivative		∂(x²+y²)/∂x = 2x
∫	integral	opposite to derivation
∬	double integral	integration of function of 2 variables
∭	triple integral	integration of function of 3 variables
∮	closed contour / line integral
∯	closed surface integral
∰	closed volume integral
[a,b]	closed interval	[a,b] = {x \| a ≤ x ≤ b}
(a,b)	open interval	(a,b) = {x \| a < x < b}
i	imaginary unit	i ≡ √-1	z = 3 + 2i
z*	complex conjugate	z = a+bi → z*=a-bi	z* = 3 + 2i
z	complex conjugate	z = a+bi → z = a-bi	z = 3 + 2i
∇	nabla / del	gradient / divergence operator	∇f (x,y,z)
	vector
	unit vector
x * y	convolution	y(t) = x(t) * h(t)
	Laplace transform	F(s) = {f (t)}
	Fourier transform	X(ω) = {f (t)}
δ	delta function
∞	lemniscate	infinity symbol

Name	European	Roman	Hindu Arabic	Hebrew
zero	0		٠
one	1	I	١	א
two	2	II	٢	ב
three	3	III	٣	ג
four	4	IV	٤	ד
five	5	V	٥	ה
six	6	VI	٦	ו
seven	7	VII	٧	ז
eight	8	VIII	٨	ח
nine	9	IX	٩	ט
ten	10	X	١٠	י
eleven	11	XI	١١	יא
twelve	12	XII	١٢	יב
thirteen	13	XIII	١٣	יג
fourteen	14	XIV	١٤	יד
fifteen	15	XV	١٥	טו
sixteen	16	XVI	١٦	טז
seventeen	17	XVII	١٧	יז
eighteen	18	XVIII	١٨	יח
nineteen	19	XIX	١٩	יט
twenty	20	XX	٢٠	כ
thirty	30	XXX	٣٠	ל
fourty	40	XL	٤٠	מ
fifty	50	L	٥٠	נ
sixty	60	LX	٦٠	ס
seventy	70	LXX	٧٠	ע
eighty	80	LXXX	٨٠	פ
ninety	90	XC	٩٠	צ
one hundred	100	C	١٠٠	ק

Greek Symbol		Greek Letter Name	English Equivalent	Pronunciation
Upper Case	Lower Case	Greek Letter Name	English Equivalent	Pronunciation
Α	α	Alpha	a	al-fa
Β	β	Beta	b	be-ta
Γ	γ	Gamma	g	ga-ma
Δ	δ	Delta	d	del-ta
Ε	ε	Epsilon	e	ep-si-lon
Ζ	ζ	Zeta	z	ze-ta
Η	η	Eta	h	eh-ta
Θ	θ	Theta	th	te-ta
Ι	ι	Iota	i	io-ta
Κ	κ	Kappa	k	ka-pa
Λ	λ	Lambda	l	lam-da
Μ	μ	Mu	m	m-yoo
Ν	ν	Nu	n	noo
Ξ	ξ	Xi	x	x-ee
Ο	ο	Omicron	o	o-mee-c-ron
Π	π	Pi	p	pa-yee
Ρ	ρ	Rho	r	row
Σ	σ	Sigma	s	sig-ma
Τ	τ	Tau	t	ta-oo
Υ	υ	Upsilon	u	oo-psi-lon
Φ	φ	Phi	ph	f-ee
Χ	χ	Chi	ch	kh-ee
Ψ	ψ	Psi	ps	p-see
Ω	ω	Omega	o	o-me-ga

Number	Roman numeral
0	not defined
1	I
2	II
3	III
4	IV
5	V
6	VI
7	VII
8	VIII
9	IX
10	X
11	XI
12	XII
13	XIII
14	XIV
15	XV
16	XVI
17	XVII
18	XVIII
19	XIX
20	XX
30	XXX
40	XL
50	L
60	LX
70	LXX
80	LXXX
90	XC
100	C
200	CC
300	CCC
400	CD
500	D
600	DC
700	DCC
800	DCCC
900	CM
1000	M
5000	V
10000	X
50000	L
100000	C
500000	D
1000000	M

Mathematical Symbols

Basic math symbols

Geometry symbols

Algebra symbols

Linear Algebra Symbols

Probability and statistics symbols

Combinatorics Symbols

Set theory symbols

Logic symbols

Calculus & analysis symbols

Numeral symbols

Greek alphabet letters

Roman numerals

See also

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