Mathematical Symbols

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Mathematical Symbols

What Are Math Symbols?

Math symbols are concise marks, signs, or notations representing mathematical operations, quantities, relations, and functions. These symbols help to represent mathematical concepts and equations concisely. 

Math symbols turn a lengthy explanation into a quick, easy calculation, helping you easily find the answer.

Example: Imagine you’re planning to find the area of a garden. Instead of writing “length times width” every time, math symbols let you simply jot down “l × w.” So, if your garden is 10 meters long and 4 meters wide, instead of saying “ten meters multiplied by four meters,” you can quickly see that 10 × 4 = 40 square meters.

 

Mathematical Symbols

Maths symbols are used to perform mathematical operations and make it easier to solve mathematical problems for students. Mathematical symbols are the basic building blocks for solving huge mathematical problems. Without using mathematical symbols, we can’t think of doing math or solving problems.

Each symbol has a special meaning along with the role it plays in solving any equation or problem. There are many symbols in mathematics, from basic ones to complex ones. But, in order to understand complex symbols and solve equations using those symbols, you must know about the basic symbols and their meanings. In this article, let us discuss the basic math symbols and how to use them. Scroll down to find out more.

 

Basic Mathematical Symbols

In Mathematics, it’s all about numbers, symbols and formulas. Here we’re discussing the foundation of Mathematics. In simple words, without symbols, we cannot do arithmetic. Mathematical symbols and symbols are considered to represent a value.

Basic mathematical symbols are used to express mathematical ideas. The relationship between the symbol and the value refers to the basic mathematical requirement. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with words and meanings. Also, an example is given to understand the use of mathematical symbols.

SymbolNameDescription and MeaningExample
+Additionplus4 + 3 = 7
Subtractionminus11 – 5 = 6
×Multiplicationtimes× 4 = 8
.Multiplication dottimes6 ∙ 2 = 12
*Asterisktimes3 * 5 = 15
÷Divisiondivided by8 ÷ 4 = 2
/Divisiondivided by9 ⁄ 3 = 3
horizontal linedivision / fraction8/2 = 4
=Equalityis equal to2 + 6 = 8
< Comparisonis less than17 < 45
> Comparisonis greater than19 > 6
minus – plusminus or plus5 ∓ 9 = -4 and 14
±plus – minusplus or minus5 ± 9 = 14 and -4
.decimal pointperiod12.05 = 12 +(5/100)
modmodulomod of16 mod 5 = 1
abexponentpower73 = 343
√asquare root√a · √a = a√16 = ±4
3√acube root3√a ·3√a · 3√a = a3√81 = 3
4√afourth root4√a ·4√a · 4√a · 4√a = a4√625 = ± 5
n√an-th root (radical)n√a · n√a · · · n times = afor n = 5, n√32 = 2
%percent1 % = 1/10025% × 60
= 25 /100 × 60
= 15
per-mille1 ‰ = 1/1000 = 0.1%

10 ‰ × 50
= 10/1000 × 50
= 0.5

ppmper-million1 ppm = 1/100000010 ppm × 50
= 10/1000000 × 50
= 0.0005
ppbper – billion1 ppb = 10-910 ppb × 50
= 10 × 10-9 × 50
= 5 × 10-7
pptper – trillion1 ppt = 10-1210 ppt × 50
= 10 × 10-12 × 50
= 5 × 10-10

 

Algebra Symbols

Algebra is a mathematical component of symbols and rules to deceive those symbols. In algebra, those symbols represent non-fixed values, called variables. How sentences describe the relationship between certain words, in algebra, mathematics describes the relationship between variables.

SymbolNameDescriptionExample
x, yVariablesunknown value3x = 9 ⇒ x = 3
1, 2, 3….Numeral constantsnumbersx + 5 = 10, here 5 and 10 are constant
In equationis not equal to3 ≠ 5
Approximately equalis approximately equal to√2≈1.41
Definitionequal by definition(a+b)2 ≡ a2+ 2ab + b2
:=Definitionequal by definition(a-b)2 := a2-2ab + b2
Definitionequal by definitiona2-b2 (a-b).(a+b)
< Strict Inequalityis less than17 < 45
> Strict Inequalityis greater than19 > 6
<< Strict Inequalityis much less than1 << 999999999
>> Strict Inequalityis much greater than999999999 >> 1
Inequalityis less than or equal to3 ≤ 5 and 3 ≤ 3
Inequalityis greater than or equal to4 ≥ 1 and 4 ≥ 4
[ ]BracketsSquare brackets[ 1 + 2 ] – [2 +4] + 4 × 5
= 3 – 6 + 4 × 5
= 3 – 6 + 20
= 23 – 6 = 17
( )Bracketsparentheses (round brackets)(15 / 5) × 2 + (2 + 8)
= 3 × 2 + 10
= 6 + 10
= 16
Proportionproportional tox ∝ y⟹ x = ky, where k is constant.
f(x)Functionf(x) = x, is used to maps values of x to f(x)f(x) = 2x + 5
!Factorialfactorial6! = 1 × 2 × 3 × 4 × 5 × 6 = 720
Material implicationimpliesx = 2 ⇒x= 4, but x2= 4 ⇒ x = 2 is false, because x could also be -2.
Material equivalenceif and only ifx = y + 4 ⇔ x-4 = y
|….|Absolute valueabsolute value of|5| = 5 and |-5| = 5

 

Geometry Symbols Used in Maths

There are geometry symbols which are used in mathematics. Here we’re mentioning each and every geometry symbols which are necessary for students to know.

SymbolNameMeaningExample
AngleIt is used to mention an angle formed by two rays∠PQR = 30°
Right angleIt determines the angle formed is right angle i.e. 90°∟XYZ = 90°
.PointIt describes a location in space.(a,b,c) it is represented as a coordinate in space by a point.
RayIt shows the line has a fixed starting point but no end point.\overrightarrow{\rm AB} is a ray.
_Line SegmentIt shows the line has a fixed starting point and a fixed end point.\overline{\rm AB} is a line segment.
LineIt shows the line neither has a starting point nor an end point.\overleftrightarrow{\rm AB} is a line.
\frownArcIt determines the degree of an arc from a point A to point B.\frown\over{\rm AB} = 45°
ParallelIt shows that lines are parallel to each other.AB ∥ CD
Not parallelIt shows the lines are not parallel.AB ∦ CD
PerpendicularIt shows that two lines are perpendicular i.e. they intersect each other at 90°AB ⟂ CD
\not\perpNot perpendicularIt shows lines are not perpendicular to each other.AB\not\perp CD
CongruentIt shows congruency between two shapes, i.e. two shapes are equivalent in shape and size.△ABC ≅ △XYZ
~SimilarityIt shows two shapes are similar to each other i.e. two shapes are similar in shape but not in size.△ABC ~ △XYZ
TriangleIt is used to determine a triangular shape.△ABC, represents ABC is a triangle.
°DegreeIt is a unit that is used to determine the measurement of an angle.a = 30°
rad or cRadians360° = 2πc
grad or gGradians360° = 400g
|x-y|DistanceIt is used to determine distance between two points.| x-y | = 5
πpi constantIt is a predefined constant with value 22/7 or 3.1415926…2π= 2 × 22/7 = 44/7

 

Set Theory Symbols

Some of the most common symbols in Set Theory are listed in the following table:

SymbolNameMeaningExample
{ }SetIt is used to determine the elements in a set.{1, 2, a, b}
|Such thatIt is used to determine the condition of the set.{ a | a > 5}
:{ x : x > 0}
belongs toIt determines that an element belongs to a set.A = {1, 5, 7, c, a}
7 ∈ A
not belongs toIt indicates that an element does not belong to a set.A = {1, 5, 7, c, a}
0 ∉ A
=Equality RelationIt determines that two sets are exactly same.A = {1, 2, 3}
B = {1, 2, 3} then
A = B
SubsetIt represents all of the elements of set A are present in set B or set A is equals to set B

A = {1, 3, a}

B = {a, b, 1, 2, 3, 4, 5}

A ⊆ B

Proper SubsetIt represents all of the elements of set A are present in set B and set A is not equal to set B.

A = {1, 2, a}

B = {a, b, c, 2, 4, 5, 1}

A ⊂ B

Not a SubsetIt determines A is not a subset of set B.

A = {1, 2, 3}

B = {a, b, c}

A ⊄ B

SupersetIt represents all of the elements of set B are present in set A or set A is equals to set B

A = {1, 2, a, b, c}

B = {1, a}

A ⊇ B

Proper SupersetIt determines A is a superset of B but set A is not equal to set BA = {1, 2, 3, a, b}
B = {1, 2, a}
A ⊃ B
ØEmpty SetIt determines that there is no element in a set.{ } = Ø
UUniversal SetIt is set that contains elements of all other relevant sets.A = {a, b, c}
B = {1, 2, 3}, then
U = {1, 2, 3, a, b, c}
|A| or n{A}Cardinality of a SetIt represents the number of items in a set.A= {1, 3, 4, 5, 2}, then |A|=5.
P(X)Power SetIt is the set that contains all possible subsets of a set A, including the set itself and the null set.

If A = {a, b}

P(A) = {{ }, {a}, {b}, {a, b}}

Union of SetsIt is a set that contains all the elements of the provided sets.

A = {a, b, c}

B = {p, q}

A ∪ B = {a, b, c, p, q}

Intersection of SetsIt shows the common elements of both sets.

A = { a, b}

B= {1, 2, a}

A ∩ B = {a}

XC OR X’Complement of a setComplement of a set includes all other elements that does not belongs to that set.

A = {1, 2, 3, 4, 5}

B = {1, 2, 3} then

X′ = A – B

X′ = {4, 5}

Set DifferenceIt shows the difference of elements between two sets.

A = {1, 2, 3, 4, a, b, c}

B = {1, 2, a, b}

A – B = {3, 4, c}

×Cartesian Product of SetsIt is the product of the ordered components of the sets.

A = {1, 2} and B = {a}

A × B ={(1, a), (2, a)}

 

Calculus and Analysis Symbols

In calculus, we have come across different math symbols. All mathematical symbols with names and meanings are provided here. Go through the all mathematical symbols used in calculus.

SymbolSymbol Name in MathsMath Symbols MeaningExample
εepsilonrepresents a very small number, near-zeroε → 0
ee Constant/Euler’s Numbere = 2.718281828…e = lim (1+1/x)x , x→∞
limx→alimitlimit value of a functionlimx→2(2x + 2) = 2×2 + 2 = 6
y‘derivativederivative – Lagrange’s notation(4x2)’ = 8x
y”Second derivativederivative of derivative(4x2)” = 8
y(n)nth derivativen times derivationnth derivative of xn xn {yn(xn)} = n (n-1)(n-2)….(2)(1) = n!
dy/dxderivativederivative – Leibniz’s notationd(6x4)/dx = 24x3
dy/dxderivativederivative – Leibniz’s notationd2(6x4)/dx2 = 72x2
dny/dxnnth derivativen times derivationnth derivative of xn xn {dn(xn)/dxn} = n (n-1)(n-2)….(2)(1) = n!
DxSingle derivative of timeDerivative-Euler’s Notation d(6x4)/dx = 24x3
D2xsecond derivativeSecond Derivative-Euler’s Notationd(6×4)/dx = 24×3
Dnxderivativenth derivative-Euler’s Notationnth derivative of xn {Dn(xn)} = n (n-1)(n-2)….(2)(1) = n!
∂/∂xpartial derivativeDifferentiating a function with respect to one variable considering the other variables as constant∂(x5 + yz)/∂x = 5x4
integralopposite to derivation∫xn dx = xn + 1/n + 1  +  C
double integralintegration of the function of 2 variables∬(x + y) dx.dy
triple integralintegration of the function of 3 variables∫∫∫(x + y + z) dx.dy.dz
closed contour / line integralLine integral over closed curve∮C 2p dp
closed surface integralDouble integral over a closed surface∭V (⛛.F)dV = ∯S (F.n̂) dS
closed volume integralVolume integral over a closed three-dimensional domain∰ (x2 + y2 + z2) dx dy dz
[a,b]closed interval[a,b] = {x | a ≤ x ≤ b}cos x ∈ [ – 1, 1]
(a,b)open interval(a,b) = {x | a < x < b}f is continuous within (-1, 1)
z*complex conjugatez = a+bi → z*=a-biIf z = a + bi then z* = a – bi
iimaginary uniti ≡ √-1z = a + bi
nabla/delgradient / divergence operator∇f (x,y,z)
x * yconvolutionModification in a function due to the other function.y(t) = x(t) * h(t)
lemniscateinfinity symbolx ≥ 0; x ∈ (0, ∞)

 

Combinatorics Symbols Used in Maths

Combinatorics symbols used in maths to study combination of finite discrete structures. Various important combinatorics symbols used in maths are added in table as follows:

SymbolSymbol NameMeaning or DefinitionExample
n!Factorialn! = 1×2×3×…×n4! = 1×2×3×4 = 24
nPkPermutationnPk = n!/(n – k)!4P2 = 4!/(4 – 2)! = 12
nCkCombinationnCk = n!/(n – k)!.k!4C2 = 4!/2!(4 – 2)! = 6

 

Numeral Symbols in Maths

There are various types of numbers used in mathematics by mathematician of various region and some of the most prominent number symbols such as Europeean Numbers and Roman Numbers in maths are,

NameEuropeanRoman
zero0n/a
one1I
two2II
three3III
four4IV
five5V
six6VI
seven7VII
eight8VIII
nine9IX
ten10X
eleven11XI
twelve12XII
thirteen13XIII
fourteen14XIV
fifteen15XV
sixteen16XVI
seventeen17XVII
eighteen18XVIII
nineteen19XIX
twenty20XX
thirty30XXX
forty40XL
fifty50L
sixty60LX
seventy70LXX
eighty80LXXX
ninety90XC
one hundred100C
Two hundred200CC
Three hundred300CCC
Five hundred500D
One Thousand1,000M

 

Symbols used in Maths

List of complete alphabets is provided in the following table:

Greek SymbolGreek Letter NameEnglish Equivalent
Lower CaseUpper Case
ΑαAlphaa
ΒβBetab
ΔδDeltad
ΓγGammag
ΖζZetaz
ΕεEpsilone
ΘθThetath
ΗηEtah
ΚκKappak
ΙιIotai
ΜμMum
ΛλLambdal
ΞξXix
ΝνNun
ΟοOmicrono
ΠπPip
ΣσSigmas
ΡρRhor
ΥυUpsilonu
ΤτTaut
ΧχChich
ΦφPhiph
ΨψPsips
ΩωOmegao

 

Logic Symbols Used in Maths

Some of the common logic symbols are listed in the following table:

SymbolNameMeaningExample
¬Negation (NOT)It is not the case that¬P (Not P)
Conjunction (AND)Both are trueP ∧ Q (P and Q)
Disjunction (OR)At least one is trueP ∨ Q (P or Q)
Implication (IF…THEN)If the first is true, then the second is trueP → Q (If P then Q)
Bi-implication (IF AND ONLY IF)Both are true or both are falseP ↔ Q (P if and only if Q)
Universal quantifier (for all)Everything in the specified set∀x P(x) (For all x, P(x))
Existential quantifier (there exists)There is at least one in the specified set∃x P(x) (There exists an x such that P(x))

 

Discrete Mathematics Symbols

Some symbols related to Discrete Mathematics are:

SymbolNameMeaningExample
Set of natural numbersPositive integers (including zero)0, 1, 2, 3, …
Set of integersWhole numbers (positive, negative, and zero)-3, -2, -1, 0, 1, 2, 3, …
Set of rational numbersNumbers expressible as a fraction1/2, 3/4, 5, -2, 0.75, …
Set of real numbersAll rational and irrational numbersπ, e, √2, 3/2, …
Set of complex numbersNumbers with real and imaginary parts3 + 4i, -2 – 5i, …
n!Factorial of nProduct of all positive integers up to n5! = 5 × 4 × 3 × 2 × 1
nCk or C(n, k)Binomial coefficientNumber of ways to choose k elements from n items5C3 = 10
G, H, …Names for graphsVariables representing graphsGraph G, Graph H, …
V(G)Set of vertices of graph GAll the vertices (nodes) in graph GIf G is a triangle, V(G) = {A, B, C}
E(G)Set of edges of graph GAll the edges in graph GIf G is a triangle, E(G) = {AB, BC, CA}
|V(G)|Number of vertices in graph GTotal count of vertices in graph GIf G is a triangle, |V(G)| = 3
|E(G)|Number of edges in graph GTotal count of edges in graph GIf G is a triangle, |E(G)| = 3
SummationSum over a range of values∑_{i=1}^{n} i = 1 + 2 + … + n
Product notationProduct over a range of values∏_{i=1}^{n} i = 1 × 2 × … × n

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