Mathematical symbols list (+,-,x,_,=,_,_,..

8/17/2019 Mathematical symbols list (+,-,x,_,=,_,_,..

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Mathematical SymbolsList 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

= equals sign equality

≠ not equal sign inequality

> strict inequality greater than

< strict inequality less than

≥ inequality greater than or equal to

≤ inequality less than or equal to

( ) parentheses calculate expression inside first

[ ] brackets calculate expression inside first

+ plus sign addition

− minus sign subtraction

± plus - minus both plus and minus operations

∓ minus - plus both minus and plus operations

* asterisk multiplication

× times sign multiplication

∙ multiplication dot multiplication

÷ division sign / obelus division

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/ division slash division

– horizontal line division / fraction

mod modulo remainder calculation

. period decimal point, decimalseparator

ab power exponent

a^b caret exponent

√a square root √a ∙ √a = a

3√a cube root 3√a ∙ 3√a ∙ 3√a = a

4√a fourth root 4√a ∙ 4√a ∙ 4√a ∙ 4√a = a

n√a n-th root (radical)

% percent 1% = 1/100

‰ per-mille 1‰ = 1/1000 = 0.1% ppm per-million 1ppm = 1/1000000

ppb per-billion 1ppb = 1/1000000000

ppt per-trillion 1ppt = 10-12

Geometry symbols


∠ angle formed by two rays

measured angle

spherical angle

∟ right angle = 90º

º degree 1 turn = 360º

´ arcminute 1º = 60´

´´ arcsecond 1´ = 60´´

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

| perpendicular perpendicular lines (90º angle)

|| parallel parallel lines

≅ congruent to equivalence of geometric

shapes and size

~ similarity same shapes, not same size

Δ triangle triangle shape

| x- y| distance distance between points x andy

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π pi constant

π = 3.141592654...

is the ratio between the

circumference and diameter of a

circle

rad radians radians angle unit

grad grads grads angle unit

Algebra symbols


x x variable unknown value to find

≡ equivalence identical to

≜ equal by defin ition equal by definit ion

:= equal by defin ition equal by definit ion

~ approximately equal weak approximation

≈ approximately equal approximation

∝ proportional to proportional to

∞ lemniscate infinity symbol

≪ much less than much less than

≫ much greater than much greater than

( ) parentheses calculate expression inside first

[ ] brackets calculate expression inside first

{ } braces set

⌊ x⌋ floor brackets rounds number to lower integer

⌈ x⌉ ceiling brackets rounds number to upper integer

x! exclamation mark factorial

| x | single vertical bar absolute value

f ( x) function of x maps values of x to f(x)

( f ∘ g ) function composition ( f ∘ g ) ( x) = f ( g ( x))

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


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e e constant / Euler's number e = 2.718281828...

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

Linear Algebra Symbols


∙ dot scalar product

× cross vector product

A⊗ B tensor product tensor product of Aand B

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 † Hermitian matrix matrix conjugatetranspose

A * Hermitian matrix matrix conjugatetranspose

A -1 inverse matrix A A-1 = I

rank( A) matrix rank rank of matrix A

dim(U ) dimension dimension of matrix A

Probability and statistics symbols


P ( A) probabil ity function probability of event A

P ( A ∩ B) probability of eventsintersectionprobability that of events A andB

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

P ( A | B) conditional probability function probability of event A givenevent B occured

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

E ( X ) expectation value expected value of randomvariable X

http://www.rapidtables.com/math/probability/Expectation.htmhttp://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constanthttp://www.rapidtables.com/math/number/e_constant.htm


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E ( X | Y ) conditional expectation expected value of randomvariable X given Y

var ( X ) variance variance of random variable X

σ2 variance variance of population values

std ( X ) standard deviation standard deviation of randomvariable X

σ X standard deviation standard deviation value of

random variable X

median middle value of random

variable x

cov( X ,Y ) covariance covariance of random variablesX and Y

corr ( X ,Y ) correlation correlation of random variablesX and Y

ρ X ,Y correlation correlation of random variables

X and Y

∑ summation summation - sum of all valuesin range of series

∑∑ double summation double summation

Mo mode value that occurs mostfrequently in population

MR mid-range MR = ( xmax+ xmin)/2

Md sample median half the population is below thisvalue

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

s 2 sample variance population samples variance

estimator

s sample standard deviation population samples standarddeviation estimator

z x standard score z x = ( x- x) / s x

X ~ distribution of X distribution of random variableX

N ( μ,σ 2) normal distribution gaussian distribution

U (a,b) uniform distribution equal probability in range a,b

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

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

χ 2(k ) chi-square distribution f ( x) = xk /2-1e- x/2 / ( 2k/2

Γ(k /2) )

F (k 1 , k 2) F distribution

Bin(n, p) binomial distribution f (k ) =nC

k pk (1-p)n-k

Poisson(λ) Poisson distribution f (k ) = λk e- λ / k !

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

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

Bern( p) Bernoulli distribution

Combinatorics Symbols


n! factorial n! = 1·2·3·...·n

n P k permutation

nC k

combination

Set theory symbols


{ } set a collection of elements

A ∩ B intersection objects that belong to set A and set B

A ∪ B union objects that belong to set A or set B

A ⊆ B subset subset has fewer elements or equal tothe set

A ⊂ B proper subset / strict subset subset has fewer elements than the set

A⊄

B not subset left set not a subset of right set

A ⊇ B superset set A has more elements or equal to theset B

A ⊃ B proper superset / strict superset set A has more elements than set B

A ⊅ B not superset set A is not a superset of set B

2A power set all subsets of A

power set all subsets of A

A = B equality both sets have the same membersAc 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 - B relative complement objects that belong to A and not to B

A ∆ B symmetric difference objects that belong to A or B but not totheir intersection

A ⊖ B symmetric difference objects that belong to A or B but not totheir intersection

a∈A element of set membership

x∉A not element of no set membership

(a,b) ordered pair collection of 2 elements

http://www.rapidtables.com/math/algebra/Factorial.htm


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

|A| cardinality the number of elements of set A

#A cardinality the number of elements of set A

aleph-null infinite cardinality of natural numbers set

aleph-one cardinality of countable ordinal numbers

set

Ø empty set Ø = { }

universal set set of all possible values

0 natural numbers / whole numbers set

(with zero) 0 = {0,1,2,3,4,...}

1 natural numbers / whole numbers set

(without zero) 1 = {1,2,3,4,5,...}

integer numbers set = {...-3,-2,-1,0,1,2,3,...}

rational numbers set = { x | x=a/b, a,b∈ }

real numbers set = { x | -∞


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∴ therefore

∵ because / since



limit limit value of a function

ε epsilon represents a very smallnumber, near zero

e e constant / Euler's number e = 2.718281828...

y ' derivative derivative - Lagrange's notation

y '' second derivative der ivat ive of der ivat ive

y(n) nth derivative n times derivation

derivative derivative - Leibniz's notation

second derivative der ivat ive of der ivat ive

nth derivative n times derivation

time derivative derivative by time - Newton's

notation

time second derivative derivative of derivative

D x y derivative derivative - Euler's notation

D x2

y second derivative der ivat ive of der ivat ive

partial derivative

∫ integral opposite to derivation

∬ double integral integration of function of 2variables

∭ 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


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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 Hebrew

zero 0

one 1 I

two 2 II

three 3 III ג

four 4 IV ד

five 5 V ה

six 6 VI ו

seven 7 VII ז

eight 8 VIII ח

nine 9 IX ט

ten 10 X י

eleven 11 XI יtwelve 12 XII י

thirteen 13 XIII יג

fourteen 14 XIV יד

fifteen 15 XV טו

sixteen 16 XVI טז

seventeen 17 XVII יז

eighteen 18 XVIII יח

nineteen 19 XIX יט

twenty 20 XX כ

thirty 30 XXX ל

fourty 40 XL מ

fifty 50 L נ

sixty 60 LX ס

seventy 70 LXX ע

eighty 80 LXXX פ

ninety 90 XC צ

one hundred 100 C ק

Greek alphabet letters

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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 C500000 D

1000000 M

See also

Algebra symbols

Geometry symbols

Statistical symbolsLogic symbols

Set theory symbols


http://www.rapidtables.com/math/symbols/Calculus_Symbols.htmhttp://www.rapidtables.com/math/symbols/Set_Symbols.htmhttp://www.rapidtables.com/math/symbols/Logic_Symbols.htmhttp://www.rapidtables.com/math/symbols/Statistical_Symbols.htmhttp://www.rapidtables.com/math/symbols/Geometry_Symbols.htmhttp://www.rapidtables.com/math/symbols/Algebra_Symbols.htm


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Number symbols

Greek alphabet symbols

Roman numerals

Infinity symbol

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