Math Symbols: A Comprehensive Collection & Guide!

Math Symbols

Meaning

Math Symbol Examples

+

Add

4 + 4 = 8

-

Subtract / Minus 

4 - 4 = 0

= 

Equal to 

2 + 2 = 4

≡

Ideantically equal to

(a+b)2 ≡ a2 + 2ab +b2

≈

Approximately equal to

Π ≈ 3.14

≠

Not equal to

4 + 5 ≠ 10

×

Multiply 

2 × 4 = 8

÷

Division sign

6 ÷ 3 = 2

<

Less than

5 < 7

>

Greater than

10 > 2

≤

Less than or equal to

x +y ≤ z

≥

Greater than or equal to

x +y ≥ z

% 

Percentage 

60% = 60/100

. 

Decimal Point or Period

⅔ = 0.6

_

Vincullum: Separates the numerator and denominator

2

-

3

√

Square Root

√16 = 4

()

Parentheses 

2+(5−3)=2+2=4

[ ]

Square Brackets

6×[3+(5−4)]+1

∞

Infinity

Infinity means countless

Math Symbol Name 

Explanation

0 (Zero)

Additive identity of common numbers

1 (One)

Multiplicative identity of common numbers

√2 (Square root of 2)

A positive number whose square is 2. Approximately equals 1.41421.

e (Euler's constant)

The base of the natural logarithm. Approximately equals 2.71828

π (Pi, Archimedes’ constant)

The ratio of a circle’s circumference to its diameter. Half-circumference of a unit circle. Approximately equals 3.14159

Φ (Phi, golden ratio)

Ratio between a larger number and p smaller number q when (p+q)/p = p/q. Positive solution to the equation y2-y-1 = 0 .

i (Imaginary unit)

The principal root of -1. The foundational component of a complex number.

Symbol

Meaning

Math Symbols Examples

∃

There exists at least one

∃ x: P(x)∃ x: F(x)

There exists at least one element of p(x), 

X, such that F(x) is True.

∃!

There exists one and only one

∃! x: F(x)

means that there is exactly one X such that F(x) is true.

∀

For all

∀n>1 ; n2>1

¬

Logical Not

Statement A is true only if  

 ¬ is false x≠y⟺¬(x=y)

∨

Logical OR

The statement A ∨ B is true

if A or B is true;

if both are false,

the statement is false. 

∧

Logical And

The statement A ∧ B is true

if A and B are both true;

else it is false.

⟹

Implies

x = 2

⟹ x2 = 4

⟺

If and only If

x +1 = y +1 ⟺ x = y

| or :

Such that

{ X | X > 0 } = {1,2,3,...}

Symbol 

Meaning 

Examples

∩

Intersection

A = {2,3,4}

B = {4,5,6}

A∩B = {4}

∪

Union

A = {2,3,4} B = {4,5,6} A∪B = {2,3,4,5,6}

∅

Empty Set

A set with no elements 

∅ = {   }

∈

Is a member of

2 ∈ N

∉

Is not a member of 

0 ∉ N

⊂

Is a subset

N ⊂ I

⊃

Is a super set

R ⊃ W

P(A)

The Power Set of A

P ({1,2}) = { {}, {1}, {2}, {1,2} }

A=B

Equality (Same elements)

A = {1,2}; B = {1,2}

⟹ A = B

A×B

Cartesian Product

A = {5,6}; B = {7,8}

⟹ A×B = 

{(5,7),(5,8),(6,7),(6,8)}

|A|

Cardinality is the number of elements in set A

|{1,2,3,4}| =  4

Name

European

Roman

Hindu Arabic

Hebrew

zero

0

n/a

0

n/a

one

1

I

١

א

two

2

II

٢

ב

three

3

III

٣

ג

four

4

IV

٤

ד

five

5

V

٥

ה

six

6

VI

٦

ו

seven

7

VII

٧

ז

eight

8

VIII

٨

ח

nine

9

IX

٩

ט

ten

10

X

١٠

י

eleven

11

XI

١١

יא

twelve

12

XII

١٢

יב

thirteen

13

XIII

١٣

יג

fourteen

14

XIV

١٤

יד

fifteen

15

XV

١٥

טו

sixteen

16

XVI

١٦

טז

seventeen

17

XVII

١٧

יז

eighteen

18

XVIII

١٨

יח

nineteen

19

XIX

١٩

יט

twenty

20

XX

٢٠

כ

thirty

30

XXX

٣٠

ל

forty

40

XL

٤٠

מ

fifty

50

L

٥٠

נ

sixty

60

LX

٦٠

ס

seventy

70

LXX

٧٠

ע

eighty

80

LXXX

٨٠

פ

ninety

90

XC

٩٠

צ

one hundred

100

C

١٠٠

ק

Symbols 

Meaning

Math Symbol Examples

∠

Mention the angle

∠ABC

Δ

Triangle symbol

ΔPQR

≅

Congruent to

ΔPQR ≅ ΔABC

∼

Similar to

ΔPQR ∼ ΔABC

⊥

Is perpendicular with

AB ⊥PQ

∥

Is parallel with

AB ∥ CD

∘

Degree

90∘

¯¯

AB

Line Segment AB

A line from Point A to Point B

−−→

AB

Ray AB

A line starting from Point A and extends through B

←→

AB

Line AB

An infinite line passing through points A and B

⌢

AB

Arc A to B

⌢

AB=90∘

c

Radians Symbol

360∘=2πc

Algebraic Math Symbols

Meaning

Math Symbol Examples

x,y

Variables 

X = 5, y = 2

+

Add 

2x + 3x = 5x

−

Subtract

3x−x = 2x

.

Product

2x.3x = 6x

−

Division

2x

−

3y

≡

Identically equal to

(a+b)2 ≡ a2 + 2ab + b2

≠

Not equal to

A + 5 = b + 1⟹ a ≠ b

=

Equal to

A = 7

∝

Proportional to 

X ∝ y ⟹ x = ky

f (x)

Function maps values of x to 

f(x)

F (x) = x + 3

α

Alpha

Used to denote angles and coefficients

β

Beta

Used to denote angles and coefficients

γ

Gamma

Used to denote angles and coefficients

Δ

Delta

Discriminant symbol

ε

Epsilon

Used to represent an Universal Set

ι

lota

Represents an imaginary number

λ

Lambda

Represents constant

π

Pi

π ≈ 3.14

Σ

Sigma

Represents the sum

θ

Theta

Represents angles

ρ

Rho

Statistical constant

ϕ

Phi

Diameter symbol

Math Symbols

Meaning

Math Symbols Examples

n!

n factorial

n! = n × (n−1) × (n−2) ×.....× 2×1

(n/c)

or

nCr

Combination

nPr

Permutation

Math Symbol

Symbol Name

Meaning

Math Symbols Example

ε

Epsilon

Represents a very small number

ε → 0

limx→a

limit

Limit value of a function

limx→a(3x+1)= 3 × a + 1 = 3a + 1

y ‘

derivative

Derivative - Lagrange’s notation

(5x3)’ = 15x2

e

e constant / Euler’s number

e = 2.718281828…

e = lim (1+1/x)x , x→∞

y(n)

nth derivative

n times derivation

nth derivative of 3xn = 3 n (n-1)(n-2)….(2)(1)= 3n!

y”

second derivative 

derivative of derivative

(4x3)” = 24x

D2x

second derivative

derivative of derivative

n/a

∫

Integral 

Opposite to derivation

n/a

∭

Triple integral

Integration of function of 3 variables

n/a

∬

Double integral(a,b)

Integration of function of 2 variables

n/a

∯

Closed surface integral

n/a

n/a

∮

Closed contour / Line integral

n/a

n/a

[a,b]

Closed Interval

[a,b] = {x | a ≤ x ≤ b}

n/a

∰

Closed volume integral

n/a

n/a

(a,b)

Open interval

(a,b) = {x | a < x < b}

n/a

i

Imaginary unit

i ≡ √-1

z = 3 + 2i

z

Complex conjugate

z = a+bi → z = a-bi

z = 3 + 2i

Math Symbol

Symbol Name 

Meaning

Math Symbols Example

P(A)

Probability function

probability of event A

P(A) = 0.5

P(A ⋂ B)

probability of events intersection

probability that of events A and B

P(A⋂B) = 0.5

P(A ⋃ B)

probability of events union

probability that of events A or B

P(A⋃B) = 0.5

P(A | B)

conditional probability function

probability of event A given event B occured

P(A | B) = 0.3

f (x)

probability density function (pdf)

P(a ≤ x ≤ b) = ∫ f (x) dx

F(x)

cumulative distribution function (cdf)

F(x) = P(X≤ x)

μ

population mean

mean of population values

μ = 10

E(X)

expectation value

expected value of random variable X

E(X) = 10

E(X | Y)

conditional expectation

expected value of random variable X given Y

E(X | Y=2) = 5

∑

summation

summation - sum of all values in range of series

∑∑

double summation

double summation

Mo

mode

value that occurs most frequently in population