Mathematical Symbols

Mathematics is a universal language and Mathematical symbols play a major role in this. Meaning and value Mathematical symbols are constant.

The symbols of mathematics not only refer to different quantities but also represent the relationship between two quantities. Mathematical symbols are mainly used to conduct mathematical operations under various concepts.

We know that the concept of mathematics is purely dependent on numbers and symbols. The relationship between symbol and value reflects the basic fundamental of mathematics.

List of mathematical symbols

Different types of Mathematical Symbols

List of all mathematical symbols with Meaning.

Basic math symbols

Basic mathematical symbols are used to express mathematical ideas. With the help of basic symbols, some concepts and ideas of mathematics are clearly explained.

SymbolSymbol NameMeaning of Symbol
Not Equal SignInequality
=Equals SignEquality
Approximately EqualApproximation
Strict InequalityLess Than
Strict InequalityGreater Than
InequalityLess Than or Equal To
InequalityGreater Than or Equal To
[ ]BracketsCalculate Expression Inside First
( )ParenthesesCalculate Expression Inside First
Minus SignSubtraction
+Plus SignAddition
Minus – PlusBoth Minus and Plus Operations
±Plus – MinusBoth Plus and Minus Operations
×Times SignMultiplication
÷Division Sign / ObelusDivision
Multiplication DotMultiplication
Horizontal LineDivision or Fraction
/Division SlashDivision
%Percent1% = 1/100 (The amount in every hundred.)
.PeriodDecimal Point, Decimal Separator
modModuloRemainder Calculation
√aSquare Roota ⋅ a  = a
3√aCube Root3√a ·3√a · 3√a = a
4√aFourth Root4√a ·4√a · 4√a · 4√a = a
n√aN-Th Root (Radical)n√a · n√a · · · n times = a
ppmPer-Million1 ppm = 1/1000000
Per-Mille1‰ = 1/1000 = 0.1%
pptPer-Trillion1ppt = 10-12
ppbPer-Billion1 ppb = 1/1000000000

Numeral Symbols 

Symbols and collections of mathematical symbols used to represent numbers based on different types of the ancient system.

NameWestern ArabicRomanEastern ArabicHebrew
zero0 ٠ 
one hundred100C١٠٠ק

Greek Alphabets Symbols

Greek alphabets are generally used to represent the variables, constants, functions and other mathematical objects. Some Greek Alphabets mathematical symbols are mentioned below:

Upper Case LetterLower Case LetterGreek Letter NameEnglish EquivalentLetter Name Pronounce

Geometry Symbols

In mathematics, geometric symbols are used to configure geometric objects – the most basic straight lines, circles, and end points.

SymbolSymbol NameMeaning of Symbol
anglethe figure formed by two rays meeting at a common end
spherical anglespherical anglean angle formed by the intersection of two great circles of a sphere.
right anglea right angle is = 90°
°degreeone full rotation is = 360°
degdegree one full rotation is = 360deg
primearcminute, (1′=1/60)
double primearcsecond, 1″ = 1/3600=1/60′)
linelineinfinite line
ABline segmentline from point A to point B
rayrayline that start from point A
arcarcarc from point A to point B (arc= 60°)
perpendicularperpendicular lines (90° angle)
parallelparallel lines
congruent toequivalence of geometric shapes and size
~similaritysame shapes, not same size
Δtriangletriangle shape
|xy|distancedistance between points x and y
πpi constantπ = 3.141592654…is the ratio between the circumference and diameter of a circle
radradiansradians angle unit (360° = 2π rad)
cradiansradians angle unit (360° = 2π c)
gradgradians / gonsgrads angle unit (360° = 400 grad)
ggradians / gonsgrads angle unit (360° = 400 g)

Algebra symbols

Algebra mathematical symbols are the major component of math that is used to unify mathematics concepts.

Algebra symbols are used to represent variables to find the distance, the perimeter of an area, volume, determining the cost of something, renting something, time relationships, pricing options for something you want to buy, and more.

SymbolSymbol NameMeaning of Symbol
xx variableto find the unknown value
equivalenceidentical to
equal by definitionequal by definition
:=equal by definitionequal by definition
~approximately equalweak approximation
approximately equalapproximation
proportional toproportional to
lemniscatefigure-eight or ∞-shaped curves
much less thanmuch less than
much greater thanmuch greater than
( )parenthesescalculate expression inside first
[ ]bracketscalculate expression inside first
{ }bracesset
xfloor bracketsrounds number to lower integer
xceiling bracketsrounds number to upper integer
x!exclamation markfactorial
x |vertical barsabsolute value
(x)function of xmaps values of x to f(x)
(f ∘ g)function composition(f ∘ g) (x) = (g(x))
(a,b)open interval(a,b) = {x | a < x < b}
[a,b]closed interval[a,b] = {x | a ≤ x ≤ b}
deltachange / difference
discriminantΔ = b2 – 4ac
sigmasummation – sum of all values in range of series
∑∑sigmadouble summation
capital piproduct – product of all values in range of series
ee constant / Euler’s numbere = 2.718281828…
e = lim (1+1/x)x , x→∞
γEuler-Mascheroni constantγ = 0.5772156649…
φgolden ratiogolden ratio constant
πpi constantπ = 3.141592654…is the ratio between the circumference and diameter of a circle

Probability and Statistics Symbols

Probability and statistics correspond to the mathematical study of chance and data, respectively.

Statistics and Probability theory have some commonly used rules, in addition to standard mathematical notation and mathematical symbols.

SymbolSymbol NameMeaning of Symbol
P(A)probability functionprobability of event A
P(A ⋃ B)probability of events unionprobability that of events A or B
P(A ⋂ B)probability of events intersectionprobability that of events A and B
P(A | B)conditional probability functionprobability of event A given event B occurred
(x)probability density function (pdf)P( x  b) = ∫ f (x) dx
F(x)cumulative distribution function (cdf)F(x) = P(X x)
μpopulation meanmean of population values
E(X)expectation valueexpected value of random variable X
E(X | Y)conditional expectationexpected value of random variable X given Y
var(X)variancevariance of random variable X
σ2variancevariance of population values
std(X)standard deviationstandard deviation of random variable X
σXstandard deviationstandard deviation value of random variable X
medianmedianmiddle value of random variable x
cov(X,Y)covariancecovariance of random variables X and Y
corr(X,Y)correlationcorrelation of random variables X and Y
ρX,Ycorrelationcorrelation of random variables X and Y
summationsummation – sum of all values in range of series
∑∑double summationdouble summation
Momodevalue that occurs most frequently in population
Mdsample medianhalf the population is below this value
MRmid-rangeMR = (xmax+xmin)/2
Mdsample medianhalf the population is below this value
Q1lower / first quartile25% of population are below this value
Q2median / second quartile50% of population are below this value = median of samples
Q3upper / third quartile75% of population are below this value
xsample meanaverage / arithmetic mean
ssample standard deviationpopulation samples standard deviation estimator
s2sample variancepopulation samples variance estimator
zxstandard scorezx = (xx) / sx
~distribution of Xdistribution of random variable X
N(μ,σ2)normal distributionGaussian distribution
U(a,b)uniform distributionequal probability in range a,b 
exp(λ)exponential distribution(x) = λeλx , x≥0
gamma(c, λ)gamma distribution(x) = λ c xc-1eλx / Γ(c), x≥0
χ 2(k)chi-square distribution(x) = xk/2-1ex/2 / ( 2k/2 Γ(k/2) )
(k1, k2)F distribution 
Bin(n,p)binomial distribution(k) = nCk pk(1-p)n-k
Poisson(λ)Poisson distribution(k) = λkeλ / k!
Geom(p)geometric distribution(k) =  p(1-p) k
HG(N,K,n)hyper-geometric distribution 
Bern(p)Bernoulli distribution 

Logic Symbols

Logic symbols is commonly used to express logical representation. Some Logic mathematical symbols are mentioned below:

SymbolSymbol NameMeaning of Symbol
^caret / circumflexand
reversed caretor
|vertical lineor
xsingle quotenot – negation
xbarnot – negation
¬notnot – negation
!exclamation marknot – negation
circled plus / oplusexclusive or – xor
~tildenegation (equivalent to)
implies if is true, then is also true
equivalentif and only if (iff)
equivalentif and only if (iff)
for all 
there exists 
there does not exists 
because / since 

Calculus & Analysis Symbols

In mathematics, calculus represents courses of elementary and analysis which are mainly dedicated to the study of function limits.

SymbolSymbol NameMeaning of Symbol
\lim_{x\to x0}f(x)limitlimit value of a function
εepsilonrepresents a very small number, near zero: ε →0
ee constant / Euler’s numbere = 2.718281828…
e = lim (1+1/x)x , x→∞
y ‘derivativederivative – Lagrange’s notation
y ”second derivativederivative of derivative
y(n)nth derivativen times derivation
\frac{dy}{dx}derivativederivative – Leibniz’s notation
\frac{d^2y}{dx^2}second derivativederivative of derivative
\frac{d^ny}{dx^n}nth derivativen times derivation
\dot{y}time derivativederivative by time – Newton’s notation
time drivative IItime second derivativederivative of derivative
Dyderivativederivative – Euler’s notation
Dx2ysecond derivativederivative of derivative
\frac{\partial f(x,y)}{\partial x}partial derivativeExample: ∂(x2+y2)/∂x = 2x
integralopposite to derivation: ∫ f(x)dx
∫∫double integralintegration of function of 2 variables: ∫∫ f(x,y)dxdy
∫∫∫triple integralintegration of function of 3 variables: ∫∫∫ f(x,y,z)dxdydz
closed contour / line integral contour integral
closed surface integralgeneralization of multiple integrals to integration over surfaces
closed volume integralintegral over a 3-dimensional domain
[a,b]closed interval[a,b] = {| a  x  b}
(a,b)open interval(a,b) = {| a < x < b}
iimaginary uniti ≡ √-1
z*complex conjugate= a+bi → z*=abi
zcomplex conjugate= a+bi → = abi
Re(z)real part of a complex numberz = a+bi → Re(z)=a
Im(z)imaginary part of a complex numberz = a+bi → Im(z)=b
z |absolute value/magnitude of a complex number|z| = |a+bi| = √(a2+b2)
arg(z)argument of a complex numberThe angle of the radius in the complex plane
nabla / delgradient / divergence operator
unit%20vectorunit vector Direction Vector
* yconvolutiony(t) = x(t) * h(t)
LLaplace transformF(s) = L{(t)}
FFourier transformX(ω) = F{(t)}
δdelta function 
lemniscateinfinity symbol

Set Theory Symbols

Set theory mathematical symbols are used to define the properties of well-defined collections such as objects or numbers or functions.

SymbolSymbol NameMeaning of Symbol
{ }seta collection of elements
A ∪ BunionElements that belong to set A or set B
A ∩ BintersectionElements that belong to both the sets, A and B
A ⊆ Bsubsetsubset has few or all elements equal to the set
A ⊄ Bnot subsetleft set is not a subset of right set
A ⊂ Bproper subset / strict subsetsubset has fewer elements than the set
A ⊃ Bproper superset / strict supersetset A has more elements than set B
A ⊇ Bsupersetset A has more elements or equal to the set B
Øempty setØ = { }
P (C)power setall subsets of C
A ⊅ Bnot supersetset X is not a superset of set Y
A = Bequalityboth sets have the same members
A \ B or A-Brelative complementobjects that belong to A and not to B
Accomplementall the objects that do not belong to set A
A ∆ Bsymmetric differenceobjects that belong to A or B but not to their intersection
a∈Belement ofset membership
(a,b)ordered paircollection of 2 elements
x∉Anot element ofno set membership
|B|, #Bcardinalitythe number of elements of set B
A×Bcartesian productset of all ordered pairs from A and B
N1natural numbers / whole numbers  set (without zero)N1 = {1, 2, 3, 4, 5,…}
N0natural numbers / whole numbers  set (with zero)N0 = {0, 1, 2, 3, 4,…}
Qrational numbers setQ= {x | x=a/b, a, b∈Z}
Zinteger numbers setZ= {…-3, -2, -1, 0, 1, 2, 3,…}
Ccomplex numbers setC= {z | z=a+bi, -∞<a<∞,                         -∞<b<∞}
Rreal numbers setR= {x | -∞ < x <∞}

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