mathematical symbols list

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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

SymbolSymbol

NameMeaning / definition Example

= equals sign equality 5 = 2+3

not equalsign inequality 5 4

>strict

inequalitygreater than 5 > 4

< strictinequality 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

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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

multiplicationdot

multiplication 2 3 = 6

division sign

/ obelusdivision 6 2 = 3

/ divisionslash

division 6 / 2 = 3

horizontal

linedivision / fraction

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

3a cube root 3a 3a 3a = a 38 = 2

4a fourth root 4a 4a 4a 4a = a 416 = 2

nan-th root

(radical) for n=3, n8 = 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 = 310-7

ppt per-trillion 1ppb = 10-12 10ppb 30 = 310-10

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Geometry symbols

Symbol Symbol Name Meaning / definition Example

angle formed by two rays ABC = 30

measured angle ABC = 30

spherical angle AOB = 30

right angle = 90 = 90

degree 1 turn = 360 = 60

arcminute 1 = 60 = 6059'

arcsecond 1 = 60 = 6059'59''

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 = 60

| perpendicular perpendicular lines (90 angle) AC | BC

|| parallel parallel lines AB || CD

congruent to equivalence of geometric shapes andsize ABC XYZ

~ similarity same shapes, not same size ABC ~ XYZ

triangle triangle shape ABC BCD

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

pi constant = 3.141592654...

is the ratio between the circumference and

diameter of a circle

c = d = 2r

rad radians radians angle unit 360 = 2 rad

grad grads grads angle unit 360 = 400 grad



Algebra symbols


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

equivalence identical to

equal bydefinition

equal by definition

:= equal bydefinition equal by definition

~approximately

equalweak approximation 11 ~ 10

approximately

equalapproximation 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 greaterthan

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 lowerinteger

4.3= 4

x ceiling brackets rounds number to upperinteger 4.3= 5

x! exclamationmark factorial 4! = 1*2*3*4 = 24

| x |single vertical

barabsolute 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)

http://www.rapidtables.com/math/symbols/Infinity_Symbol.htmhttp://www.rapidtables.com/math/symbols/Infinity_Symbol.htmhttp://www.rapidtables.com/math/algebra/Factorial.htm



(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 = b2 - 4ac

sigma summation - sum of all valuesin range of series xi= x1+x2+...+xn

sigma double summation

capital pi product - product of all valuesin range of series xi=x1x2...xn

ee constant /

Euler's numbere = 2.718281828... e = lim (1+1/x)x , x

Euler-

Mascheroni

constant

= 0.527721566...

golden ratio golden ratio constant

pi constant

= 3.141592654...

is the ratio between the

circumference and diameter of a

circle

c = d = 2r

Linear Algebra Symbols


dot scalar product a b

cross vector product a b

AB tensor product tensor product of Aand B

A B

inner product

[ ] brackets matrix of numbers

( ) parentheses matrix of numbers

determinant of matrix

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



| A | determinant A

det(A) determinantdeterminant of matrix

A

|| x || double vertical bars norm

A T transpose matrix transpose (AT)ij = (A)ji

A Hermitian matrixmatrix conjugate

transpose (A)ij = (A)ji

A * Hermitian matrixmatrix 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


P(A) probabilityfunction

probability of event A P(A) = 0.5

P(A B)probability of

events

intersection

probability that of

events A and BP(AB) = 0.5

P(A B)probability of

events union

probability that of

events A or BP(AB) = 0.5

P(A | B)conditional

probability

function

probability of event A

given event B occuredP(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)

population meanmean of population

values = 10

expectation expected value of

http://www.rapidtables.com/math/probability/Expectation.htm



E(X) value random variable X E(X) = 10

E(X | Y) conditionalexpectation

expected value of

random variable X

given Y

E(X | Y=2) = 5

var(X) variancevariance of random

variable Xvar(X) = 4

2 variance variance of populationvalues

2 = 4

std(X)standard

deviation

standard deviation of

random variable Xstd(X) = 2

Xstandard

deviation

standard deviation

value of random

variable X

X = 2

medianmiddle value of

random variable x

cov(X,Y) covariance covariance of randomvariables X and Y

cov(X,Y) = 4

corr(X,Y) correlationcorrelation of random

variables X and Ycorr(X,Y) = 0.6

X,Y correlationcorrelation of random

variables X and YX,Y = 0.6

summationsummation - sum of all

values in range of

series

doublesummation

double summation

Mo modevalue that occurs most

frequently in

population

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

Md sample median half the population isbelow this value

Q1lower / first

quartile

25% of population are

below this value

Q2median / second

quartile


below this value =

median of samples

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Q3upper / third

quartile


below this value

x sample meanaverage / arithmetic

meanx = (2+5+9) / 3 = 5.333

s 2 sample variance

population samples

variance estimator s 2 = 4

ssample standard

deviation

population samples

standard deviation

estimator

s = 2

zx standard score zx = (x-x) / sx

X ~ distribution of Xdistribution of random

variable XX ~ N(0,3)

N(,2)normal

distributiongaussian distribution X ~ N(0,3)

U(a,b)uniform

distribution

equal probability in

range a,b X ~ U(0,3)

exp()exponential

distributionf (x) = e-x , x0

gamma(c, )gamma

distribution

f (x) = c xc-1e-x /

(c), x0

2(k)chi-square

distribution

f (x) = xk/2-1e-x/2 / (

2k/2 (k/2) )

F (k1, k2) F distribution

Bin(n,p)binomial

distribution

f (k) = nCk pk(1-p)n-

k

Poisson()Poisson

distribution f (k) = ke- / k!

Geom(p)geometric

distributionf (k) = p (1-p) k

HG(N,K,n)hyper-geometric

distribution

Bern(p)Bernoulli

distribution

Combinatorics Symbols

http://www.rapidtables.com/math/probability/distribution.htmhttp://www.rapidtables.com/math/probability/normal_distribution.htm



Symbol Symbol

NameMeaning / definition Example

n! factorial n! = 123...n 5! = 12345 = 120

nPk permutation 5P3 = 5! / (5-3)! = 60

nCk

combination 5C3 = 5!/[3!(5-3)!]=10

Set theory symbols


{ } set a collection of elementsA = {3,7,9,14},

B = {9,14,28}

A B intersectionobjects that belong to set

A and set BA B = {9,14}

A B union objects that belong to setA or set B

A B = {3,7,9,14,28}

A B subsetsubset has fewer

elements or equal to the

set

{9,14,28} {9,14,28}

A Bproper subset /

strict subset

subset has fewer

elements than the set{9,14} {9,14,28}

A B not subsetleft set not a subset of

right set{9,66} {9,14,28}

A B superset set A has more elementsor equal to the set B

{9,14,28} {9,14,28}

A Bproper 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 ofset B

{9,14,28} {9,66}

2A power set all subsets of A

power set all subsets of A

A={3,9,14},

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



A = B equality both sets have the samemembers

B={3,9,14},

A=B

Ac complementall the objects that do not

belong to set A

A \ Brelative

complement

objects that belong to A

and not to B

A = {3,9,14},

B = {1,2,3},

A-B = {9,14}

A - B relativecomplement

objects that belong to A

and not to B

A = {3,9,14},

B = {1,2,3},

A-B = {9,14}

A Bsymmetric

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 Bsymmetric

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}

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

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

(a,b) ordered pair collection of 2 elements

AB cartesian productset of all ordered pairs

from A and B

|A| cardinality the number of elements ofset A

A={3,9,14}, |A|=3

#A cardinalitythe number of elements of

set AA={3,9,14}, #A=3

aleph-nullinfinite cardinality of

natural numbers set

aleph-onecardinality of countable

ordinal numbers set

empty set = { } C = {}

universal set set of all possible values

0

natural numbers

/ whole numbers

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



1

natural numbers

/ whole numbers

set (without zero)1 = {1,2,3,4,5,...} 6 1

integer numbers

set

=

{...-3,-2,-1,0,1,2,3,...}-6

rational numbers

set = {x | x=a/b, a,b

}2/6

real numbers set = {x | - < x



for all

there exists

there does not exists

therefore

because / since



limit limit value of a function

epsilon represents a very smallnumber, near zero

0

ee constant / Euler's

numbere = 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

derivative derivative - Lagrange's notation d(3x3)/dx = 9x2

second derivative derivative of derivative d2(3x3)/dx2 = 18x

nth derivative n times derivation

time derivativederivative by time - Newton

notation

time second

derivativederivative of derivative

partial derivative (x2+y2)/x = 2x

integral opposite to derivation

http://www.rapidtables.com/math/number/e_constant.htmhttp://www.rapidtables.com/math/calculus/derivative.htmhttp://www.rapidtables.com/math/calculus/derivative.htmhttp://www.rapidtables.com/math/calculus/integral.htm



double integralintegration of function of 2

variables

triple integral integration of function of 3variables

closed contour /line integral

closed surfaceintegral

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() = {f (t)}

delta function

lemniscate infinity symbol

Numeral symbols

Name European Roman Hindu Arabic Hebrew

zero 0

one 1 I

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two 2 II

three 3 III

four 4 IV

five 5 V

six 6 VI

seven 7 VII

eight 8 VIII

nine 9 IX

ten 10 X

eleven 11 XI

twelve 12 XII

thirteen 13 XIII

fourteen 14 XIV

fifteen 15 XV

sixteen 16 XVI

seventeen 17 XVII

eighteen 18 XVIII

nineteen 19 XIX

twenty 20 XX

thirty 30 XXX

fourty 40 XL

fifty 50 L

sixty 60 LX

seventy 70 LXX

eighty 80 LXXX

ninety 90 XC

one hundred 100 C



Greek alphabet letters

Greek SymbolGreek Letter Name English Equivalent Pronunciation

Upper Case Lower Case

Alpha a al-fa

Beta b be-ta

Gamma g ga-ma

Delta d del-ta

Epsilon e ep-si-lon

Zeta z ze-ta

Eta h eh-ta

Theta th te-ta

Iota i io-ta

Kappa k ka-pa

Lambda l lam-da

Mu m m-yoo

Nu n noo

Xi x x-ee

Omicron o o-mee-c-ron

Pi p pa-yee

Rho r row

Sigma s sig-ma

Tau t ta-oo

Upsilon u oo-psi-lon

Phi ph f-ee



Chi ch kh-ee

Psi ps p-see

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

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




Number symbols

Greek alphabet symbols

Roman numerals

Infinity symbol

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MATH SYMBOLS

Basic math symbols

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