Mathematical Symbols

Maths symbols are special notations used to represent numbers, operations, relations, sets, functions, and other mathematical ideas. Instead of writing everything in words, mathematicians use symbols to make expressions shorter, clearer, and more universal.

math_symbols — Some Common Maths Symbols

List of mathematics symbols along with their names, uses, and examples.

Basic Symbols of Maths

Symbol	Name	Description	Example
➕	Addition	plus	2 + 7 = 9
➖	Subtraction	minus	14 - 6 = 8
⨉	Multiplication	times	2 × 5 = 10
·	Multiplication		7 ∙ 2 = 14
*	Asterisk		4 * 5 = 20
÷	Division	divided by	5 ÷ 5 = 1
/	Division	divided by	16 ⁄ 8 = 2
=	Equality	is equal to	2 + 6 = 8
<	Comparison	is less than	17 < 45
>	Comparison	is greater than	19 > 6
∓	minus – plus	minus or plus	5 ∓ 9 = -4 and 14
±	plus – minus	plus or minus	5 ± 9 = 14 and -4
.	decimal point	period	12.05 = 12 +(5/100)
mod	modulo	mod of	16 mod 5 = 1
a^b	exponent	power	7³ = 343
√a	square root	√a · √a = a	√16 = 4
³√a	cube root	³√a ·³√a · ³√a = a	³√27 = 3
⁴√a	fourth root	⁴√a ·⁴√a · ⁴√a · ⁴√a = a	⁴√625 = 5
ⁿ√a	n-th root (radical)	ⁿ√a · ⁿ√a · · · n times = a	for n = 5, ⁿ√32 = 2
%	percent	1 % = 1/100	25% × 60 = 25 /100 × 60 = 15
‰	per-mile	1 ‰ = 1/1000 = 0.1%	10 ‰ × 50 = 10/1000 × 50 = 0.5
ppm	per-million	1 ppm = 1/1000000	10 ppm × 50 = 10/1000000 × 50 = 0.0005
ppb	per-billion	1 ppb = 10^-9	10 ppb × 50 = 10 × 10^-9 × 50 = 5 × 10^-7
ppt	per-trillion	1 ppt = 10^-12	10 ppt × 50 = 10 × 10^-12 × 50 = 5 × 10^-10

Algebraic Symbols

Symbol	Name	Description	Example
x, y	Variables	unknown value	3x = 9 ⇒ x = 3
1, 2, 3....	Numeral constants	numbers	x + 5 = 10, here 5 and 10 are constants
≠	Inequation	is not equal to	3 ≠ 5
≈	Approximately equal	is approximately equal to	√2≈1.41
≡	Definition	is defined as 'or' is equal by definition	(a+b)²≡ a²+ 2ab + b²
:=			(a-b)²:= a²-2ab + b²
≜			a²-b²≜ (a-b).(a+b)
<	Strict Inequality	is less than	17 < 45
>		is greater than	19 > 6
<<		is much less than	1 << 999999999
>>		is much greater than	999999999 >> 1
≤	Inequality	is less than or equal to	3 ≤ 5 and 3 ≤ 3
≥	Inequality	is greater than or equal to	4 ≥ 1 and 4 ≥ 4
[ ]	Brackets	Square brackets	[ 1 + 2 ] - [2 +4] + 4 × 5 = 3 - 6 + 4 × 5 = 3 - 6 + 20 = 23 - 6 = 17
( )	Brackets	Parentheses (round brackets)	(15 / 5) × 2 + (2 + 8) = 3 × 2 + 10 = 6 + 10 = 16
∝	Proportion	proportional to	x ∝ y⟹ x = ky, where k is a constant.
f(x)	Function	f(x) = x, is used to maps values of x to f(x)	f(x) = 2x + 5
!	Factorial	factorial	6! = 1 × 2 × 3 × 4 × 5 × 6 = 720
⇒	Material implication	implies	x = 2 ⇒x²= 4, but x²= 4 ⇒ x = 2 is false, because x could also be -2.
⇔	Material equivalence	if and only if	x = y + 4 ⇔ x-4 = y
\|....\|	Absolute value	Absolute value of	\|5\| = 5 and \|-5\| = 5

Geometry Symbols

Symbol	Name	Example
∠	Angle	∠PQR = 30°
∟	Right angle	∟XYZ = 90°
.	Point	(a,b,c) It is represented as a coordinate in space by a point.
→	Ray	\overrightarrow{\rm AB} is a ray.
_	Line Segment	\overline{\rm AB} is a line segment.
↔	Line	\overleftrightarrow{\rm AB} It is a line.
\frown	Arc	\frown\over{\rm AB} = 45°
∥	Parallel	AB ∥ CD
∦	Not parallel	AB ∦ CD
⟂	Perpendicular	AB ⟂ CD
\not\perp	Not perpendicular	AB\not\perp CD
≅	Congruent	△ABC ≅ △XYZ
~	Similarity	△ABC ~ △XYZ
△	Triangle	△ABC represents ABC as a triangle.
°	Degree	a = 30°
rad or ^c	Radians	360° = 2π^c
grad or ^g	Gradians	360° = 400^g
\|x-y\|	Distance	\| x-y \| = 5
π	pi constant	2π= 2 × 22/7 = 44/7

Set Theory Symbols

Symbol	Name	Meaning	Example
{ }	symbols	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}
:	such that	It is used to determine the condition of the set.	{ 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 the same.	A = {1, 2, 3} B = {1, 2, 3} then A = B
⊆	Subset	It represents that all of the elements of set A are present in set B, or set A is equal 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 that 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 that A is not a subset of set B.	A = {1, 2, 3} B = {a, b, c} A ⊄ B
⊇	Superset	It represents that all of the elements of set B are present in set A, or set A is equal to set B.	A = {1, 2, a, b, c} B = {1, a} A ⊇ B
⊃	Proper Superset	It determines that 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 a 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}
X^c_OR X’	Complement of a Set	t of a set includes all other elements that do not belong 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 in elements between the 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 & Analysis Symbols

Symbol	Symbol Name	Example
ε	epsilon	ε → 0
e	e Constant/Euler’s Number	e = lim (1+1/x)x , x→∞
lim_x→a	limit	lim_x→2(2x + 2) = 2×2 + 2 = 6
y‘	derivative	(4x²)’ = 8x
y”	Second derivative	(4x²)” = 8
y⁽ⁿ⁾	nth derivative	nth derivative of xⁿ xⁿ {yⁿ(xⁿ)} = n (n-1)(n-2)….(2)(1) = n!
dy/dx	derivative	d(6x⁴)/dx = 24x³
dy/dx	derivative	d²(6x⁴)/dx² = 72x²
dⁿy/dxⁿ	nth derivative	nth derivative of xⁿ xⁿ {dⁿ(xⁿ)/dxⁿ} = n (n-1)(n-2)….(2)(1) = n!
Dx	Single derivative of time	d(6x⁴)/dx = 24x³
D²x	second derivative	d(6x4)/dx = 24x3
Dⁿx	derivative	nth derivative of xⁿ {Dⁿ(xⁿ)} = n (n-1)(n-2)….(2)(1) = n!
∂/∂x	partial derivative	∂(x⁵+ yz)/∂x = 5x⁴
∫	integral	∫xⁿ dx = x^{n + 1}/n + 1 + C
∬	double integral	∬(x+ y) dx. dy
∭	triple integral	∫∫∫(x+ y + z) dx.dy.dz
∮	closed contour/line integral	∮_C 2p dp
∯	closed surface integral	∭_V (⛛.F)dV = ∯_S (F.n̂) dS
∰	closed volume integral	∰ (x² + y² + z²) dx dy dz
[a,b]	closed interval	cos x ∈ [ – 1, 1]
(a,b)	open interval	f is continuous within (-1, 1)
z*	complex conjugate	If z = a + bi then z* = a – bi
i	imaginary unit	z = a + bi
∇	nabla/del	∇f (x,y,z)
*x y**	convolution	y(t) = x(t) * h(t)
∞	lemniscate	x ≥ 0; x ∈ (0, ∞)

Combinatorics Symbols

Symbol	Symbol Name	Meaning or Definition	Example
n!	Factorial	n! = 1×2×3×…×n	4! = 1×2×3×4 = 24
ⁿP_k	Permutation	ⁿP_k= n!/(n - k)!	⁴P₂ = 4!/(4 - 2)! = 12
ⁿC_k	Combination	ⁿC_k= n!/(n - k)!.k!	⁴C₂ = 4!/2!(4 - 2)! = 6

Numeral Symbols

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

Greek Symbol		Greek Letter Name	English Equivalent
Lower Case	Upper Case	Greek Letter Name	English Equivalent
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

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

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
ⁿC_k 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