Maths Symbols – Basic Mathematics Symbols

Maths symbols are figures or combinations of figures that represent mathematical objects, actions, or relations. They are used to solve mathematical problems quickly and easily.

Foundation of mathematics lies in its symbols and numbers. The symbols in mathematics are used to perform various mathematical operations. The symbols help us to define a relationship between two or more quantities. This article will cover some basic Math symbols along with their descriptions and examples.

Symbols in Maths

Symbols are the basic necessity to perform distinct operations in maths. There is a wide range of symbols used in maths with distinct meanings and uses. Some of the symbols used in mathematics even have pre-defined values or meanings. For example ‘Z’ is a symbol used to determine integers, similarly pi or π is a predefined symbol whose value is 22/7 or 3.14.

Symbols serve as the relation between distinct quantities. Symbols help to understand a topic in a better and more efficient way. The range of symbols in mathematics is huge, ranging from a simple addition ‘+’ to complex differentiation ‘dy/dx’ ones. Symbols are also used as a short form for various commonly used phrases or words, like “∵” is used for “because or since”.

Basic Symbols of Maths

Here are some basic math symbols:

• Plus symbol (+): Signifies addition
• Minus symbol (-): Signifies subtraction
• Equals symbol (=)
• Does not equal symbol (≠)
• Multiplication symbol (×)
• Division symbol (÷)
• Greater than/less than symbols
• Greater than or equal to/less than or equal to symbols (≥ ≤)

Other math symbols include:

• Asterisk sign (*) or times sign (×)
• Multiplication dot (⋅)
• Division slash (/)
• Inequality (≥, ≤)
• Parentheses ( )
• Brackets ()

List of All Maths Symbols

Symbols make our calculations easier and faster. For example, the ‘+’ symbol indicates that we are adding something. There are more than 10,000 symbols in mathematics, out of these few symbols are rarely used and few are used very frequently. The common and basic maths symbols along with their description and meaning are described in the table below:

Symbol	Name	Description	Meaning	Example
+	Addition	plus	a + b is the sum of a and b	2 + 7 = 9
–	Subtraction	minus	a – b is the difference of a and b	14 – 6 = 8
×	Multiplication	times	a × b is the multiplication of a and b.	2 × 5 = 10
.			a . b is the multiplication of a and b.	7 ∙ 2 = 14
*	Asterisk		a * b is the multiplication of a and b.	4 * 5 = 20
÷	Division	divided by	a ÷ b is the division of a by b	5 ÷ 5 = 1
/			a / b is the division of a by b	16 ⁄ 8 = 2
=	Equality	is equal to	If a = b, a and b represent the same number.	2 + 6 = 8
<	Comparison	is less than	If a < b, a is less than b	17 < 45
>		is greater than	If a > b, a is greater than b	19 > 6
∓	minus – plus	minus or plus	a ± b means both a + b and a – b	5 ∓ 9 = -4 and 14
±	plus – minus	plus or minus	a ± b means both a – b and a + b	5 ± 9 = 14 and -4
.	decimal point	period	used to show a decimal number	12.05 = 12 +(5/100)
mod	modulo	mod of	used for remainder calculation	16 mod 5 = 1
ab	exponent	power	used to calculate the product of a number ‘a’, b times.	73 = 343
√a	square root	√a · √a = a	√a is a nonnegative number whose square is ‘a’	√16 = ±4
3√a	cube root	3√a ·3√a · 3√a = a	3√a is a number whose cube is ‘a’	3√81 = 3
4√a	fourth root	4√a ·4√a · 4√a · 4√a = a	4√a is a non negative number whose fourth power is ‘a’	4√625 = ± 5
n√a	n-th root (radical)	n√a · n√a · · · n times = a	n√a is a number whose nth power is ‘a’	for n = 5, n√32 = 2
%	percent	1 % = 1/100	used to calculate the percentage of a given number	25% × 60 = 25 /100 × 60 = 15
‰	per-mille	1 ‰ = 1/1000 = 0.1%	used to calculate one tenth of a percentage of a given number	10 ‰ × 50 = 10/1000 × 50 = 0.5
ppm	per-million	1 ppm = 1/1000000	used to calculate one millionth of a given number	10 ppm × 50 = 10/1000000 × 50 = 0.0005
ppb	per – billion	1 ppb = 10-9	used to calculate one billionth of a given number	10 ppb × 50 = 10 × 10-9 × 50 = 5 × 10-7
ppt	per – trillion	1 ppt = 10-12	used to calculate one trillionth of a given number	10 ppt × 50 = 10 × 10-12 × 50 = 5 × 10-10

Algebra Symbols in Maths

Algebra is that branch of mathematics that helps us to find the value of unknown. The unknown value is represented by variables. Various operations are carried out to find the value of this unknown variable. Algebraic Symbols are used to represent the operations required for the calculation. Symbols used in Algebra are illustrated below:

Symbol	Name	Description	Meaning	Example
x, y	Variables	unknown value	x = 2, represents the value of x is 2.	3x = 9 ⇒ x = 3
1, 2, 3….	Numeral constants	numbers	In x + 2, 2 is the numeral constant.	x + 5 = 10, here 5 and 10 are constant
≠	Inequation	is not equal to	If a ≠ b, a and b does not represent the same number.	3 ≠ 5
≈	Approximately equal	is approximately equal to	If a ≈ b, a and b are almost equal.	√2≈1.41
≡	Definition	is defined as ‘or’ is equal by definition	If a ≡ b, a is defined as another name of b	(a+b)2 ≡ a2+ 2ab + b2
:=			If a := b, a is defined by b	(a-b)2 := a2-2ab + b2
≜			If a ≜ b, a is definition of b.	a2-b2≜ (a-b).(a+b)
<	Strict Inequality	is less than	If a < b, a is less than b	17 < 45
>		is greater than	If a > b, a is greater than b	19 > 6
<<		is much less than	If a < b, a is much less than b	1 << 999999999
>>		is much greater than	If a > b, a is much greater than b	999999999 >> 1
≤	Inequality	is less than or equal to	If a ≤ b, a is less than or equal to b	3 ≤ 5 and 3 ≤ 3
≥		is greater than or equal to	If a ≥ b, a is greater than or equal to b	4 ≥ 1 and 4 ≥ 4
[ ]	Brackets	Square brackets	calculate expression inside [ ] first, it has least precedence of all brackets	[ 1 + 2 ] – [2 +4] + 4 × 5 = 3 – 6 + 4 × 5 = 3 – 6 + 20 = 23 – 6 = 17
( )		parentheses (round brackets)	calculate expression inside ( ) first, it has highest precedence of all brackets	(15 / 5) × 2 + (2 + 8) = 3 × 2 + 10 = 6 + 10 = 16
∝	Proportion	proportional to	If a ∝ b , it is used to show relation/ proportion between a and b	x ∝ y⟹ x = ky, where k is constant.
f(x)	Function	f(x) = x, is used to maps values of x to f(x)		f(x) = 2x + 5
!	Factorial	factorial	n! is the product 1×2×3…×n	6! = 1 × 2 × 3 × 4 × 5 × 6 = 720
⇒	Material implication	implies	A ⇒ B means that if A is true, B must also be true, but if A is false, B is unknown.	x = 2 ⇒x2 = 4, but x2= 4 ⇒ x = 2 is false, because x could also be -2.
⇔	Material equivalence	if and only if	If A is true, B is true and if A is false, B is also false.	x = y + 4 ⇔ x-4 = y
|….|	Absolute value	absolute value of	|a| always returns the absolute or positive value	|5| = 5 and |-5| = 5

Geometry Symbols in Maths

In geometry, various symbols are used as a shorthand of some commonly used word. For example ‘⊥’ is used to determine that the lines are perpendicular to each other. Symbols used in geometry are illustrated below:

Symbol	Name	Meaning	Example
∠	Angle	It is used to mention an angle formed by two rays	∠PQR = 30°
∟	Right angle	It determines the angle formed is right angle i.e. 90°	∟XYZ = 90°
.	Point	It describes a location in space.	(a,b,c) it is represented as a coordinate in space by a point.
→	Ray	It shows the line has a fixed starting point but no end point.	[Tex]\overrightarrow{\rm AB} [/Tex] is a ray.
_	Line Segment	It shows the line has a fixed starting point and a fixed end point.	[Tex]\overline{\rm AB} [/Tex] is a line segment.
↔	Line	It shows the line neither has a starting point nor an end point.	[Tex]\overleftrightarrow{\rm AB} [/Tex] is a line.
[Tex]\frown [/Tex]	Arc	It determines the degree of an arc from a point A to point B.	[Tex]\frown\over{\rm AB} [/Tex] = 45°
∥	Parallel	It shows that lines are parallel to each other.	AB ∥ CD
∦	Not parallel	It shows the lines are not parallel.	AB ∦ CD
⟂	Perpendicular	It shows that two lines are perpendicular i.e. they intersect each other at 90°	AB ⟂ CD
[Tex]\not\perp [/Tex]	Not perpendicular	It shows lines are not perpendicular to each other.	[Tex]AB\not\perp CD [/Tex]
≅	Congruent	It shows congruency between two shapes, i.e. two shapes are equivalent in shape and size.	△ABC ≅ △XYZ
~	Similarity	It shows two shapes are similar to each other i.e. two shapes are similar in shape but not in size.	△ABC ~ △XYZ
△	Triangle	It is used to determine a triangular shape.	△ABC, represents ABC is a triangle.
°	Degree	It is a unit that is used to determine the measurement of an angle.	a = 30°
rad or c	Radians		360° = 2πc
grad or g	Gradians		360° = 400g
|x-y|	Distance	It is used to determine distance between two points.	| x-y | = 5
π	pi constant	It is a predefined constant with value 22/7 or 3.1415926…	2π= 2 × 22/7 = 44/7

Set Theory Symbol in Maths

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

Symbol	Name	Meaning	Example
{ }	Set	It is used to determine the elements in a set.	{1, 2, a, b}
|	Such that	It is used to determine the condition of the set.	{ a | a > 5}
:			{ x : x > 0}
∈	belongs to	It determines that an element belongs to a set.	A = {1, 5, 7, c, a} 7 ∈ A
∉	not belongs to	It indicates that an element does not belong to a set.	A = {1, 5, 7, c, a} 0 ∉ A
=	Equality Relation	It determines that two sets are exactly same.	A = {1, 2, 3}  B = {1, 2, 3} then A = B
⊆	Subset	It 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 Subset	It 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 Subset	It determines A is not a subset of set B.	A = {1, 2, 3} B = {a, b, c} A ⊄ B
⊇	Superset	It 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 Superset	It determines A is a superset of B but set A is not equal to set B	A = {1, 2, 3, a, b} B = {1, 2, a} A ⊃ B
Ø	Empty Set	It determines that there is no element in a set.	{ } = Ø
U	Universal Set	It 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 Set	It represents the number of items in a set.	A= {1, 3, 4, 5, 2}, then |A|=5.
P(X)	Power Set	It 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 Sets	It 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 Sets	It shows the common elements of both sets.	A = { a, b} B= {1, 2, a} A ∩ B = {a}
Xc OR X’	Complement of a set	Complement 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 Difference	It 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 Sets	It 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 Maths

Calculus is a branch of maths that deal with rate of change of function and sum of infinitelously small values using the concept of limits. There are various symbol used in calculs learn all the symbols used in Calculus through the table added below,

Symbol	Symbol Name in Maths	Math Symbols Meaning	Example
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→∞
limx→a	limit	limit value of a function	limx→2(2x + 2) = 2×2 + 2 = 6
y‘	derivative	derivative – Lagrange’s notation	(4x2)’ = 8x
y”	Second derivative	derivative of derivative	(4x2)” = 8
y(n)	nth derivative	n times derivation	nth derivative of xn xn {yn(xn)} = n (n-1)(n-2)….(2)(1) = n!
dy/dx	derivative	derivative – Leibniz’s notation	d(6x4)/dx = 24x3
dy/dx	derivative	derivative – Leibniz’s notation	d2(6x4)/dx2 = 72x2
dny/dxn	nth derivative	n times derivation	nth derivative of xn xn {dn(xn)/dxn} = n (n-1)(n-2)….(2)(1) = n!
Dx	Single derivative of time	Derivative-Euler’s Notation	d(6x4)/dx = 24x3
D2x	second derivative	Second Derivative-Euler’s Notation	d(6×4)/dx = 24×3
Dnx	derivative	nth derivative-Euler’s Notation	nth derivative of xn {Dn(xn)} = n (n-1)(n-2)….(2)(1) = n!
∂/∂x	partial derivative	Differentiating a function with respect to one variable considering the other variables as constant	∂(x5 + yz)/∂x = 5x4
∫	integral	opposite to derivation	∫xn dx = xn + 1/n + 1  +  C
∬	double integral	integration of the function of 2 variables	∬(x + y) dx.dy
∭	triple integral	integration of the function of 3 variables	∫∫∫(x + y + z) dx.dy.dz
∮	closed contour / line integral	Line integral over closed curve	∮C 2p dp
∯	closed surface integral	Double integral over a closed surface	∭V (⛛.F)dV = ∯S (F.n̂) dS
∰	closed volume integral	Volume 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 conjugate	z = a+bi → z*=a-bi	If z = a + bi then z* = a – bi
i	imaginary unit	i ≡ √-1	z = a + bi
∇	nabla/del	gradient / divergence operator	∇f (x,y,z)
x * y	convolution	Modification in a function due to the other function.	y(t) = x(t) * h(t)
∞	lemniscate	infinity symbol	x ≥ 0; x ∈ (0, ∞)

Combinatorics Symbols 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:

Symbol	Symbol Name	Meaning or Definition	Example
n!	Factorial	n! = 1×2×3×…×n	4! = 1×2×3×4 = 24
nPk	Permutation	nPk = n!/(n – k)!	4P2 = 4!/(4 – 2)! = 12
nCk	Combination	nCk = 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,

Name	European	Roman
zero	0	n/a
one	1	I
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
forty	40	XL
fifty	50	L
sixty	60	LX
seventy	70	LXX
eighty	80	LXXX
ninety	90	XC
one hundred	100	C

Greek Symbols in Maths

List of complete Greek alphabets is provided in the following table:

Greek Symbol		Greek Letter Name	English Equivalent
Lower Case	Upper Case
Α	α	Alpha	a
Β	β	Beta	b
Δ	δ	Delta	d
Γ	γ	Gamma	g
Ζ	ζ	Zeta	z
Ε	ε	Epsilon	e
Θ	θ	Theta	th
Η	η	Eta	h
Κ	κ	Kappa	k
Ι	ι	Iota	i
Μ	μ	Mu	m
Λ	λ	Lambda	l
Ξ	ξ	Xi	x
Ν	ν	Nu	n
Ο	ο	Omicron	o
Π	π	Pi	p
Σ	σ	Sigma	s
Ρ	ρ	Rho	r
Υ	υ	Upsilon	u
Τ	τ	Tau	t
Χ	χ	Chi	ch
Φ	φ	Phi	ph
Ψ	ψ	Psi	ps
Ω	ω	Omega	o

Logic Symbols in Maths

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

Symbol	Name	Meaning	Example
¬	Negation (NOT)	It is not the case that	¬P (Not P)
∧	Conjunction (AND)	Both are true	P ∧ Q (P and Q)
∨	Disjunction (OR)	At least one is true	P ∨ Q (P or Q)
→	Implication (IF…THEN)	If the first is true, then the second is true	P → Q (If P then Q)
↔	Bi-implication (IF AND ONLY IF)	Both are true or both are false	P ↔ 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:

Symbol	Name	Meaning	Example
ℕ	Set of natural numbers	Positive integers (including zero)	0, 1, 2, 3, …
ℤ	Set of integers	Whole numbers (positive, negative, and zero)	-3, -2, -1, 0, 1, 2, 3, …
ℚ	Set of rational numbers	Numbers expressible as a fraction	1/2, 3/4, 5, -2, 0.75, …
ℝ	Set of real numbers	All rational and irrational numbers	π, e, √2, 3/2, …
ℂ	Set of complex numbers	Numbers with real and imaginary parts	3 + 4i, -2 – 5i, …
n!	Factorial of n	Product of all positive integers up to n	5! = 5 × 4 × 3 × 2 × 1
nCk or C(n, k)	Binomial coefficient	Number of ways to choose k elements from n items	5C3 = 10
G, H, …	Names for graphs	Variables representing graphs	Graph G, Graph H, …
V(G)	Set of vertices of graph G	All the vertices (nodes) in graph G	If G is a triangle, V(G) = {A, B, C}
E(G)	Set of edges of graph G	All the edges in graph G	If G is a triangle, E(G) = {AB, BC, CA}
|V(G)|	Number of vertices in graph G	Total count of vertices in graph G	If G is a triangle, |V(G)| = 3
|E(G)|	Number of edges in graph G	Total count of edges in graph G	If G is a triangle, |E(G)| = 3
∑	Summation	Sum over a range of values	∑_{i=1}^{n} i = 1 + 2 + … + n
∏	Product notation	Product over a range of values	∏_{i=1}^{n} i = 1 × 2 × … × n

FAQs on Maths Symbols

What are Basic Arithmetic Symbols?

Basic Arithmetic Symbols are Addition (+), Subtraction (-), Multiplication (× or ·), and Division (÷ or /).

What is the Meaning of Equal Sign?

Equal Sign means that two expressions on either side are equivalent in value.

What does Pi represents in Maths?

Pi represents the ratio of the circumference of a circle to its diameter, approximately 3.14159.

What is the Symbol for Addition?

Symbol for addition in maths is “+” and it is used to add any two numeric values.

What is e Symbol in Mathematics?

Symbol “e” in maths represents Euler’s number which approximately equals to 2.71828.

Which Symbol represents Infinity?

Infinity is represented by ∞, it is represented by a horizontal eight also known as a lazy-eight.