Maths

Math Symbols: A Comprehensive Collection & Guide!

Math Symbols: A Comprehensive Collection & Guide!
There are tons of symbols in the language of Mathematics - some are easy, while some are complex. Mathematical symbols are used for different purposes in the subject. Using these math symbols, you can form phrases, words, and sentences and represent the relationship between numbers and quantities. Also, mathematical symbols are the only thing that helps us perform mathematical operations.

I hope you already know what mathematics is, right? It is the science and study of measuring, calculating, structure, shape, and quantity. It involves shapes, numerical calculations, and logical thinking. We have dimensions like trigonometry, algebra, and geometry that are solely based on Mathematical symbols and numbers.

For example, we use the pi math symbol (π) to represent the numbers and value 3.17. Also, we use Euler's constant math symbol (e) to represent the value 2.71828... Therefore, understanding the math symbols and their uses is highly essential if you want to ace and build a higher foundation in the subject.

We have compiled this post to help you understand and know about the math symbols in detail! Below, we will share a complete list of all mathematical symbols, from basic to logic to calculus to more. Also, we will be giving solved examples at the end to help you practice and understand the math symbols more efficiently. Keep Reading, and remember to stick till the end!

Basic & Common Math Symbols

Let's start our lesson with some commonly used mathematical symbols. These common symbols are the key mathematical objects, honestly, and we can't do mathematics without them. Imagine, without symbols; math would be like; adding 5 to 10 gives 15. Annoying and complicated, right? But with mathematical symbols, it's just: 5 + 10 = 15. Here, we saved a lot of time, space, and effort. Here is our list of some common and basic symbols:

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

Constants Used As Math Symbols

We use the mathematical constants symbols to represent the numbers that don't vary and stay the same. Key mathematical infinities, key mathematical sets, key mathematical objects, and key numbers are included in constants symbols. Here is a list of all the most commonly used constants and their explanation:

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.


Logic Math Symbols
Here is a list of all logical-mathematical symbols along with their meaning and examples:

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,...}

Math Symbols for Venn Diagram and Set Theory

Here is a list of symbols used in the Venn Diagram and Set Theory:

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

Common Numeral Math Symbols

These Roman numerals are commonly used in our day-to-day lives. Here are some common numeral symbols and their Hindu, Arabic, and Roman versions:

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

Geometry Math Symbols

Below, we are sharing a list of mathematical symbols used in geometry, along with their explanation and examples:

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

Mathematical symbols are a lifesaver when they include in Algebra. Algebra itself is a complex dimension, and it would have been a nightmare without math symbols. Here is a list of all algebraic math symbols with their meaning and examples:

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

Greek Alphabets and Combinatorics Symbols

The table below includes all the commonly used mathematical symbols for Greek Alphabets and Combinatorics symbols. You will also see their examples and usage in the table.

Greek Alphabets as Mathematics Symbols:


Math Symbols

Meaning 

Math Symbol Examples

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


Combinatorics Mathematics Symbols:

Math Symbols

Meaning

Math Symbols Examples

n!

n factorial

n! = n × (n−1) × (n−2) ×.....× 2×1

(n/c)

or

nCr

Combination


nPr

Permutation


Calculus & Analysis Math Symbols

Calculus is full of different math symbols that help us solve and understand the concept. Here is a list of all mathematical symbols used in calculus, along with their names and meanings:

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


Notational Mathematical Symbols in Probability and Statistics
Here is the list of all the math symbols used in the dimension of probability and statistics:

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


Frequently Asked Questions

What is the pi symbol?
Pi is a constant in Maathematics, and its value is equal to approximately 3.14. It is represented by the π, and it defines the ratio of circle circumference to its diameter.

What are the symbols for basic arithmetic operations?
The symbols for basic arithmetic operations are as follows:
+ for Addition
- for Subtraction
x for Multiplication
÷ for Division

Why do we use Math Symbols?
We use Math symbols because they have played a great role in making Mathematics an universal language. Also, it has made the concepts and dimensions of mathematics easy to understand and time-saving!

Final Words

We hope that this post helped you understand the importance of Math symbols and their usage. If you still have questions, you can request the help of a professional tutor from our website. You first tutoring session is just a click away!

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With over 3 years of experience in teaching, Chloe is very deeply connected with the topics that talk about the educational and general aspects of a student's life. Her writing has been very helpful for students to gain a better understanding of their academics and personal well-being. I’m also open to any suggestions that you might have! Please reach out to me at chloedaniel402 [at] gmail.com

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