Math Symbols

Symbols

Meaning

How to use

+

Add

2 + 2 = 4

-

Subtract

3 - 2 = 1

=

Equal to

2 + 1 = 3

\(\equiv\)

Identically equal to

(a - b)²  \(\equiv\) a²- 2ab + b²

≈

Approximately equal to  ()

e ≈ 2.71828

\(\neq\)

Not equal to

3 + 1 \(\neq\) 6

×

Multiply

5 × 2 = 10

÷

Divide

9 ÷ 3 = 3

<

Less than

3 < 6

>

Greater than

6 > 3

\(\leq\)

Less than or equal to

5 - 2 \(\leq\) 3

\(\geq\)

Greater than or equal to

8 - 1 \(\geq\) 4

%

Percentage

20% = 20/100 = 0.20

.

Decimal point or period

13 = 0.333… Here, the dot after 0 is the decimal point.

–

Vinculum (—, it separates the numerator and denominator)

\(3 \over 5\)

\(\sqrt {}\)

Square root

\(\sqrt 9 = \pm 3\)

\(\sqrt [3] {{}}\)

Cube root 

\(\sqrt [3] {64} = 4\)

\(\sqrt [n] {}\)

n^th root

\(\sqrt [2]{25} = 5\)

( )

Parentheses

1 + (3 - 2) = 1 + 1 = 2 

[ ]

Square brackets

2 × [3 + (2 - 1)] + 2

2 × [3 +1] + 2

2 × 4 + 2 = 10

{ }

Curly braces

20 ÷ {2 × [3 + (2 - 1)] + 2}

20 ÷ {2 × [3 +1] + 2}

20 ÷ {2 × 4 + 2}

20 ÷ 10 = 2

\(\in \)

Belongs to

1 \(\in \) whole number

∉

Does not belong to

1/3 ∉ natural numbers

∴

Therefore

x + 3 = 5
∴ x = 2

∵

Because

14/0.25 = 1 (∵  1/4 = 0.25) 

∞

Infinity

1,2,3,4,.... ∞

!

Factorial 

4! = 4 × 3 × 2 × 1 = 24

∑

Summation (sum of a series)

∑(i=1 to n) i

∏

Product (multiplying a series)

ϕ (phi)

Golden Ratio

1.61803…

Used in geometry, art, and architecture.

γ

Euler–Mascheroni Constant

~0.57721

Used in number theory and analysis.

ℵ₀

Aleph-null (Aleph-zero)

—

It represents the cardinality of the set of natural numbers.

∞

Infinity

—

Not a number; used to represent an unbounded quantity. Infinity cannot be a fixed value.

Symbol

Meaning

Example

¬

Not (negation)

¬ P means "not P"

∧

And (conjunction)

P ∧ Q means "P and Q"

∨

Or (disjunction)

P ∨ Q means "P or Q"

⇒

Implies (if...then)

P ⇒ Q means "if P then Q"

⇔

If and only if (biconditional)

P ⇔ Q means "P if and only if Q"

∀

For all (universal quantifier)

∀ x ∈ A, P(x) means "for all x in A, P(x) is true"

∃

There exists (existential quantifier)

∃ x ∈ A such that P(x)

∃!

Unique existence

∃! (5x = 10) can be read as “there exists a unique x such that 5x = 10".

⊤

True (tautology)

P ∨ ¬ P is always ⊤

⊥

False (contradiction)

P ∧ ¬ P is ⊥

⊢

Provable

P ⊢ Q means, in a proof, Q is logically derived from P. 

⊨

Satisfies (semantic entailment)

P ⊨ Q means if P is true, then Q is also true.

Roman Numeral

Value

Math Symbols Examples

I

1

I = 1, II = 2, III =3

V

5

IV = 4 (5-1)

VI = 6 (5+1)

X

10

IX = 9 (10-1)

XI = 11 (10+1)

L

50

XLIX = 49(50-1)

C

100

CC = 100+100 = 200

D

500

DCL = 500+100+50 = 650

M

1000

MCLI = 1000+100+50+1 = 1151

R

Real

numbers

5, -4.2, 0, 2,

Z

Integer

-99, -15, 8, 10,....

N

Natural numbers

1, 2, 3,...

Q

Rational numbers

45, 0.6

P

Irrational numbers

5, 7

C

Complex numbers

3+7i

Symbol

Meaning

Example

∠

Angle

∠ABC means angle ABC

°

Degree (unit of angle measure)

90° is a right angle

‖

Parallel

AB ‖ CD means AB is parallel to CD

⊥

Perpendicular

AB ⊥ CD, means AB is perpendicular to CD

≅

Congruent (same size and shape)

∆ABC ≅ ∆DEF (triangles are congruent)

≈

Approximately equal

∠A ≈ 90° means angle A is about 90 degrees

∼

Similar (same shape, different size)

∆ABC ∼ ∆DEF

△

Triangle

△ABC means triangle ABC

□

Square

□ABCD means square ABCD

∥

Parallel lines (alternative symbol)

l ∥ m means line l is parallel to m

m∠

Measure of an angle

m∠ABC = 45°

π

Pi (ratio of circumference to diameter)

π ≈ 3.1416

r

Radius (of a circle)

r = 5 cm

d

Diameter (of a circle)

d = 2r

C

Circumference

C = πd

A

Area

A = lw for a rectangle, A = πr² for a circle

P

Perimeter

P = sum of side lengths

Symbol

Meaning

Example

⊆

Subset

A ⊆ B

∅

Empty set

X = { } (null set or void set)

∩

Intersection

A ∩ B

∪

Union

A ∪ B

⊂

Proper subset

A ⊂ B

ℕ

Natural numbers

{0, 1, 2, 3, …} or {1, 2, 3, …}

ℤ

Integers

{…, −2, −1, 0, 1, 2, …}

ℚ

Rational numbers

Numbers expressible as p/q

ℝ

Real numbers

All rational + irrational numbers

ℂ

Complex numbers

Numbers in the form a + bi

ℙ

Prime numbers

{2, 3, 5, 7, 11, …} (sometimes used)

Symbol

Meaning

Example

n!

Factorial of n (product of all positive integers up to n)

5! = 5 × 4 × 3 × 2 × 1 = 120

C(n, k) 

Combination

C(5,2​) = 10

P(n, k)

Permutation: arranging k items from n in order

P(5, 2) = 5 × 4 = 20

∑

Summation (adding a series of terms)

\(\sum _{i =1 } ^n = 1+2+3+4 +......+n\) 

∏

Product (multiplying a series of terms)

\(\prod _{i=1} ^n = 1\times 2 \times 3 \times .... \times n\)

∈

Element of a set

a ∈ A means "a belongs to A"

⊆

Subset

A ⊆ B is read as "A is a subset of B"

∅

Empty set

A = ∅ means A has zero elements in the set

∩

Intersection of sets

A ∩ B means the elements in A ∩ B are present in both A and B

∪

Union of sets

A ∪ B means elements in A or B or both

Symbol

Name (Lowercase)

Symbol

Name (Uppercase)

Common Use

α

alpha

Α

Alpha

Used to represent angles in geometry

β

beta

Β

Beta

In linear regression equations, β represents coefficients 

γ

gamma

Γ

Gamma

In physics, γ represents gamma rays, a form of electromagnetic radiation

δ

delta

Δ

Delta

The lowercase δ represents a small change in a variable. The uppercase Δ means difference between values

ε

epsilon

Ε

Epsilon

Epsilon represents a very small positive integer in calculus

ζ

zeta

Ζ

Zeta

In math, zeta is used in the Riemann Zeta Function

η

eta

Η

Eta

Used to represent efficiency in fields like engineering and physics.

θ

theta

Θ

Theta

Commonly used to represent angles in geometry

ι

iota

Ι

Iota

Iota is sometimes used to indicate an infinitesimally small quantity

κ

kappa

Κ

Kappa

Used to represent curvature in geometry

λ

lambda

Λ

Lambda

Wavelength of a wave is often represented by lambda

μ

mu

Μ

Mu

Used to represent the average of a set of numbers

ν

nu

Ν

Nu

In physics, it is used to represent frequency

ξ

xi

Ξ

Xi

Used to denote a random variable

ο

omicron

Ο

Omicron

Typically used for naming variants

π

pi

Π

Pi

It is an important mathematical constant

ρ

rho

Ρ

Rho

Used to represent density

σ

sigma

Σ

Sigma

While Σ is used to represent summation, σ is used to represent the standard deviation

τ

tau

Τ

Tau

It is a constant which equals 2π

υ

upsilon

Υ

Upsilon

In particle physics, it represents a type of meson 

φ

phi

Φ

Phi

It represents golden ratio, a mathematical constant

χ

chi

Χ

Chi

In probability theory and set theory, chi is used to represent the characteristic function

ψ

psi

Ψ

Psi

Wave function of a particle is represented by psi in quantum mechanics

ω

omega

Ω

Omega

ω is used to represent angular velocity in rotational motion