Mathematical Symbols (original) (raw)

Last Updated : 24 Sep, 2025

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
**· 7 ∙ 2 = 14
* Asterisk 4 * 5 = 20
**÷ Division divided by 5 ÷ 5 = 1
****/** 16 ⁄ 8 = 2
= Equality is equal to 2 + 6 = 8
< Comparison is less than 17 < 45
**> 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
**≥ 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
****( )** 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

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° = 2πc
grad or g Gradians 360° = 400g
|x-y Distance | x-y
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}
: { 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.
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 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} thenX′ = A – BX′ = {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 limx→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
**d n y/dx n 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
**D 2 x second derivative d(6x4)/dx = 24x3
**D n x 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 = xn + 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
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

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
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
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
|E(G) Number of edges in graph G Total count of edges in graph G
∑ 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