Understanding Mathematics Symbols and Their Uses

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

\[\div\]

Division

12 \[\div\] 2 = 6

<

Greater Than

11 > 9

>

Lesser Than

9 < 19

\[\times\]

Multiplication

6 \[\times\] 4 = 24

\[\neq\]

Not Equals To

6 + 1\[\neq\]8

\[\geq\]

Greater Than or Equals To

a + b\[\geq\]c

\[\leq\]

Lesser Than or Equals To

a + b\[\leq\]c

%

Percentage

60% = \[\frac{60}{100}\]

.

Decimal Point 

\[\frac{1}{3}\]= 0.333

-

Vinculum

Both numerator and denominator are separated by vinculum

\[\frac{4}{5}\]

\[\sqrt{}\]

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 \[\div\]{ 3 \[\times\] ( 2 + (4 - 2)) + 2}

14 \[\div\] {3 \[\times\] (2 + 2)} + 2}

14 \[\div\] {3\[\times\] 4  + 2}

14\[\div\] {14}

= 1

\[\left [  \right ]\]

Square Bracket

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

7 \[\times\] \[\left [3 +  3 + 2\right ]\]

7 \[\times\] 6 + 2

44

\[\epsilon\]

Belongs To

0 \[\epsilon\] 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)

\[\infty\]

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

\[\forall\]

For all

\[\forall\] 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 \[\neq\]b⇔ ¬ (a= b)

| Or :

Such that 

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

y'

Not - negation

y'

\[\overline{y}\]

Not - negation

\[\overline{y}\]

!

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

\[(x+\alpha)^{2}=x^{2}+\alpha^{2}+2x\alpha\]

\[\neq\]

Not equals to

a + 4 = b + 3 \[\Rightarrow\] a\[\equiv\]b

=

Equals to

x = 5

\[\propto\]

Proportional To

a \[\propto\] b \[\Leftrightarrow\] 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

\[\left [(3 + 4)*(1+ 6)\right ]\] = 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 \[ \times ( n - 1) \times(n - 2) \times( n - 3)\times….\times3\times 1\]

\[nC_{r}\]

Or

\[\binom{n}{r}\]

Combination

\[\frac{n!}{r!(n-r)!}\]

\[6C_{3}=\frac{6!}{4!(6!-4!)}\] =  20

\[nP_{r}\]

Permutation

\[nP_{r}= (n) \times(n - 1)\times(n - 2)\times...\times ( n - r -1)\times\](n - r -2)

\[7P_{r}= 7 \times 6 \times5 \times4 \times3\] = 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.

\[\Delta\]

Delta

Discriminant Symbol

\[\lambda\]

Lambda

Represents constant

\[\pi\]

Pi

\[\pi = 3.14 or \frac{22}{7}\]

\[\epsilon\]

Epsilon

Used to denote Universal set

\[\Theta\]

Theta

Denotes angles

\[\rho\]

Rho

Statistical Constant

\[\Sigma\]

Sigma

Denotes the sum

\[\phi\]

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

\[\angle\]

Angle

\[\angle\]XYZ

\[\triangle\]

Triangle symbol

\[\triangle\]XYZ

\[\cong\]

Congruent to

\[\triangle XYZ\cong \triangle ABC\]

\[\sim\]

Similar to

\[\triangle XYZ\sim \triangle ABC\]

\[\perp\]

Is perpendicular with

AB \[\perp\] XY

\[\parallel\]

Is parallel with

AB \[\parallel\] XY

\[^{\circ}\]

Degree

\[\bar{XY}\]

Line segment XY

A line starting from point X to point Y

\[\vec{XY}\]

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: \[\varnothing\] = { }

\[\epsilon\]

Is a element of

3\[\epsilon\mathbb{N}\]

\[\notin\]

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