Mathematics Symbols

Symbols 

Meaning

Mathematics Symbols Examples

+

Add

6 + 4 = 10

-

Subtract

7 - 3 = 4

=

Equals To

2 + 2 = 4

$$\equiv$$

Identically equals to

The identity $$(\alpha +\beta {)}^2={\alpha }^2+{\beta }^2+2\alpha$$

$$\approx$$

Approximately equals to

$$\pi \approx$$3.14

$$÷$$

Division

12 $$÷$$ 2 = 6

<

Greater Than

11 > 9

>

Lesser Than

9 < 19

$$\times$$

Multiplication

6 $$\times$$ 4 = 24

$$\ne$$

Not Equals To

6 + 1$$\ne$$8

$$\ge$$

Greater Than or Equals To

a + b$$\ge$$c

$$\le$$

Lesser Than or Equals To

a + b$$\le$$c

%

Percentage

60% = $$\frac{60}{100}$$

.

Decimal Point 

$$\frac{1}{3}$$= 0.333

-

Vinculum

Both numerator and denominator are separated by vinculum

$$\frac{4}{5}$$

Square Root

$$\sqrt{9}$$ = 3

$$\sqrt[3]{y}$$

Cube Root of y

$$\sqrt[3]{64}$$ = 4

$$\sqrt[n]{y}$$

Nth root of y

$$\sqrt[4]{81}$$ = 3

()

Parenthesis

9 + ( 8 - 2) = 9 + 6 = 15

{ }

Flower Bracket

14 $$÷$${ 3 $$\times$$ ( 2 + (4 - 2)) + 2}

14 $$÷$$ {3 $$\times$$ (2 + 2)} + 2}

14 $$÷$$ {3$$\times$$ 4  + 2}

14$$÷$$ {14}

= 1

$$\left[\right]$$

Square Bracket

7 $$\times$$ $$[3+(5-2)]$$ + 2

7 $$\times$$ $$[3+3+2]$$

7 $$\times$$ 6 + 2

44

$$ϵ$$

Belongs To

0 $$ϵ$$ whole number 

$$\notin$$

Not belongs to

$$\frac{1}{3}\notin$$ natural number 

∴

Therefore

$$\alpha$$+ 1 = 2 ∴ $$\alpha$$= 1

∵

Because

$$\frac{1}{3}$$0.33 = 1 ( ∵$$\frac{1}{3}$$= 0.33)

$$\mathrm{\infty }$$

Infinity

Infinity means countless

$$\frac{1}{4}$$when expressed in decimal form,

 is endless 0.4444

!

Factorial

6! = 6$$\times$$ 5$$\times$$4$$\times$$3$$\times$$2$$\times$$1

Symbols

Meaning

Mathematics Logic Symbols Examples

∃

There exist at least one element

∃ y : P(y) ∃ y: F(y)

There exist at least one element of p(y), y,

such that F(y) is true

∃!

There exist at least one and only element

∃! Y: F(y)

It implies that there is exactly one y 

Such that F(y) is true

$$\mathrm{\forall }$$

For all

$$\mathrm{\forall }$$ n > 1; n² > 1

$$\vee$$

Logical or

The statement X$$\vee$$Y is true

If X or Y is true

If Both are false

The statement is false

$$\wedge$$

Logical And

The statement X$$\wedge$$Y is true

If X and Y are both true

Else it is False

$$\Rightarrow$$

Implies

y = 2

$$\Rightarrow$$ y² = 4

⇔

If and only if

Example: a + $$\theta$$ = b + $$\theta$$ ⇔ a = b 

¬

Logical Not

Statement K is true 

If ¬ is false

a $$\ne$$b⇔ ¬ (a= b)

| Or :

Such that 

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

y'

Not - negation

y'

$$\bar{y}$$

Not - negation

$$\bar{y}$$

!

Not - negation

!y

Algebraic Symbols

Name

Examples

p,q

Variables

p = 5 , q = 2

+

Add

3x + 4x = 7x

-

Subtract

4x - 2x = 2x

.

Product

3x.4x = 12x

−

Division

$$\frac{2x}{3x}$$

$$\equiv$$

Identically equals to

$$(x+\alpha {)}^2=x^2+{\alpha }^2+2x\alpha$$

$$\ne$$

Not equals to

a + 4 = b + 3 $$\Rightarrow$$ a$$\equiv$$b

=

Equals to

x = 5

$$\propto$$

Proportional To

a $$\propto$$ b $$\iff$$ a = kb

F(y)

Function maps values of y to f(y)

f(y) = y + 4

$$\gg$$

Much Greater Than

1 > 1000000

$$\ll$$

Much Less than

1 < 1000000

$$\left[\right]$$

Brackets

$$[(3+4)\ast (1+6)]$$ = 49

( )

Parenthesis

4 * ( 7 + 5) = 48

$$\approx$$

Approximately Equals

sin(0.01) $$\approx$$  0.01

$$\sim$$

Approximately Equals

7 $$\sim$$ 8

Combiantric Symbols

Meaning

Examples

n!

n Factorial

n! = n $$\times (n-1)\times (n-2)\times (n-3)\times \dots .\times 3\times 1$$

$$n{C}_r$$

Or

$$(\genfrac{}{}{0ex}{}{n}{r})$$

Combination

$$\frac{n!}{r!(n-r)!}$$

$$6C_3=\frac{6!}{4!(6!-4!)}$$ =  20

$$n{P}_r$$

Permutation

$$n{P}_r=(n)\times (n-1)\times (n-2)\times ...\times (n-r-1)\times$$(n - r -2)

$$7P_r=7\times 6\times 5\times 4\times 3$$ = 2520

Greek Symbols

Meaning

Examples

$$\alpha$$

Alpha

Used to represent angles, coefficients.

$$\beta$$

Beta

Used to represent angles, coefficients.

$$\gamma$$

Gamma

Used to represent angles, coefficients.

$$\mathrm{\Delta }$$

Delta

Discriminant Symbol

$$\lambda$$

Lambda

Represents constant

$$\pi$$

Pi

$$\pi =3.14or\frac{22}{7}$$

$$ϵ$$

Epsilon

Used to denote Universal set

$$\mathrm{\Theta }$$

Theta

Denotes angles

$$\rho$$

Rho

Statistical Constant

$$\mathrm{\Sigma }$$

Sigma

Denotes the sum

$$\varphi$$

Phi

Diameter symbol

$$\iota$$

Iota

Used to denote imaginary numbers

Roman Numerals

Meaning

Examples

I

Value in numbers = 1

I = 1

V

Value in numbers = 5

VIII = (5 + 1 + 1) = 6, VIII = (5 + 1 + 1) = 8

X

Value in numbers = 10

XI = (10 + 1)

L

Value in numbers = 50

LI = ( 50 + 1)

C

Value in numbers = 100

CC = ( 100 +100)

D

Value in numbers = 500

DCI = ( 500 + 100 + 1) = 601

M

Value in numbers = 1000

MM = ( 1000 + 1000) = 2000

R or $$\mathbb{R}$$

Real number

$$\frac{1}{5},\frac{1}{6},0.7,\sqrt{5},\sqrt{6}$$

N or $$\mathbb{N}$$

Natural number

1,2,3,4,,5,...100

Z or $$\mathbb{Z}$$

Integers

1, 2, 3 ,6,-7,-9

Q or $$\mathbb{Q}$$

Rational Numbers

$$-\frac{1}{2},\frac{1}{4}$$,0.5

P or P

Irrational numbers

$$\sqrt{2},\sqrt{3},\sqrt{4}$$,

C or C

Complex numbers 

6 + 2i

Geometric Symbols

Meaning

Examples

$$\mathrm{\angle }$$

Angle

$$\mathrm{\angle }$$XYZ

$$\mathrm{△}$$

Triangle symbol

$$\mathrm{△}$$XYZ

$$\cong$$

Congruent to

$$\mathrm{△}XYZ\cong \mathrm{△}ABC$$

$$\sim$$

Similar to

$$\mathrm{△}XYZ\sim \mathrm{△}ABC$$

$$\perp$$

Is perpendicular with

AB $$\perp$$ XY

$$\parallel$$

Is parallel with

AB $$\parallel$$ XY

$${}^{\circ }$$

Degree

$$\overline{XY}$$

Line segment XY

A line starting from point X to point Y

$$\overrightarrow{XY}$$

Ray XY

A line starting from point R extends through Y

$$\overline{XY}$$

Line XY

An infinite line passing through points X and Y

$${}^c$$

Radian symbols

$${360}^{\circ }=2{\pi }^c$$

|A- B| 

Distance between  points A and B

| A- B| = 6

$$\sphericalangle$$

Spherical angle

XOY = 30°

´

1° = 60´

$$\alpha$$ = 60º59′

´´

1’ = 60´´ 

$$\alpha$$ = 60º59’59”

Symbols

Meaning

Examples

$$\cup$$

Union

X = { 2, 3, 4}

Y = { 4, 5, 6}

X $$\cup$$Y = {2, 3,4, 5, 6}

$$\cap$$ 

Intersection

X = { 2, 3, 4}

Y = { 4, 5, 6}

X $$\cap$$Y = {4}

$$\varnothing$$

Empty Set

A set with no elements: $$\varnothing$$ = { }

$$ϵ$$

Is a element of

3$$ϵ\mathbb{N}$$

$$\notin$$

Is not an element of

0$$\notin \mathbb{N}$$

$$\subset$$

Is a subset of 

$$\mathbb{N}\subset$$|

$$\supset$$

Is a superset of

R$$\supset$$W

P(X)

The power set of P

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

X = Y

Equality

(Same element in set X and set Y)

X = {4,5}; Y = { 4,5}

$$\Rightarrow$$X = Y

|X|

Cardinality is the number of element in set X

|{1, 2, 3, 4, 5}| = 5