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List Of Math Symbols & Their Meaning [Free Downloadable Chart For Classroom]

Wednesday July 29, 2020

The list of math symbols can be long. You can’t possibly learn all their meanings in one go, can you? You can make use of our tables to get a hold on all the important ones you’ll ever need. This is an introduction to the name of symbols, their use, and meaning.

The Mathematical symbol is used to denote a function or to signify the relationship between numbers and variables. There are many symbols that you might not know the meaning of.

This will help you in improving your algebra skills.

Numbers and symbols form the very basis of mathematics. Math symbols can denote the relationship between two numbers or quantities.

We have ordered the symbols in order of importance for you.

You can also download the ones according to your need.

Table of Content


1. Basic Math Symbols

These are all the mathematical symbols needed to do basic as well as complex algebraic calculations.

list of Math symbols and their meaning:

Symbol
Name
Meaning
Example
= Equal to Equality 1+2=3

X=5

Not Equal to Inequality X≠5

3+1≠6

Approximately equal to To approximate xy
Strict inequality Greater than 7>1
Strict inequality Lesser than 3<8
Inequality greater than or equal to 3 ≥ 1

x ≥ 6

inequality less than or equal to 5 ≤ 5

y≤8

( ) parentheses calculate expression inside first 3 × (9-2) = 21
[ ] brackets calculate expression inside first [(2+3)×(2+6)] = 40
+ plus addition 4+1=5
minus subtraction 4-1=3
± plus – minus both plus and minus operations 4 ± 6 = 10 or -2
± minus – plus both minus and plus operations 5 ∓ 7 = -2 or 10
* asterisk multiplication 3 * 4 = 12
× times sign multiplication 5×1=5
÷ division sign / obelus division 15 ÷ 5 = 3
. multiplication dot multiplication 2 ∙ 3 = 6
horizontal line division / fraction 8/2 = 4
/ division slash division 6 ⁄ 2 = 3
mod modulo remainder calculation 7 mod 3 = 1
ab power exponent 24 = 16
. period decimal point, decimal separator 4.36 = 4 +36/100
√a square root √a · √a = a √9 = ±3
a^b caret exponent 2 ^ 3 = 8
4√a fourth root 4√a ·4√a · 4√a · 4√a = a 4√16= ± 2
% percent 1% = 1/100 10% × 30 = 3
n√a n-th root (radical) n√a · n√a · · · n times = a for n=3, n√8 = 2
% percent 1% = 1/100 10% × 30 = 3
Per mile 1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3
ppt per-trillion 1ppt = 10-12 10ppt × 30 = 3×10-10
ppb per-billion 1 ppb = 1/1000000000 10 ppb × 30 = 3×10-7

2. Geometry

Geometry is the study of shapes and angles. These symbols are used to express shapes in formula mode. You can study the terms all down below.

You might be familiar with shapes and the units of measurements. When starting out with Geometry you should learn how to measure angles and the length of various shapes.

math symbols

You can use this image to put the below math symbols into context

 

Symbol

 

Name

 

Meaning

 

Example

Angle

 

Used to denote a corner of shape ∠ACB of a triangle

 

 

 

Measured Angle Used to express the value of an angle ∡ACB is 45°

 

 

 

Right Angle Symbol used instead of ∠ when the angle is 90° ∟ABC is 90°

 

° Degree symbol Measure of angle 20°, 180°

 

prime

 

arcminute, 1° = 60′

 

α = 60°59′

 

 

double prime

 

arcsecond, 1′ = 60″

 

α = 60°59′59″

 

math symbols Infinite line The line extends at both sides infinitely math symbols
math symbols Line segment A line from point a to point b math symbols
ray A line that starts from a point and keeps on going
Arc Arc from point A to B

 

perpendicular

 

Lines that are 90 degree from a line  ⊥

 

 

parallel

 

Lines that are parallel to each other

 

 ∥

 

 

congruent to

 

Denotes that the shape and size of one is equal to another ∆ABC≅ ∆XYZ

 

~

 

Similar to Similarity by shape but not size ∆ABC~ ∆XYZ

 

Δ

 

Triangle triangle shape

 

ΔABC~ ΔBCD

 

|xy|

 

distance Distance between two points | xy | = 3

 

π

 

pi Ratio between circumference and diameter C=2 . π . r

 

‘Rad’ or ‘c’

 

radians

 

radians angle unit

 

360° = 2π rad or 360° = 2π c

 

 

‘Grad’ or ‘g’

 

gradians / gons

 

grads angle unit

 

360° = 400 grad

Or 360° = 400 g

 

3. Set Theory

A set is a collection of objects or elements. We can use a set function to find out the relationships between sets. These functions are stated in the table below.

Here is the proper set of math symbols and notations. You should pay attention because these symbols are easy to mix up. Especially ones like intersection and union symbols.

Symbol Name Meaning Example
{} set The symbol that encapsulates the numbers of a set A = {3,7,9,14},
B = {9,12,38}

 

intersection objects that are common to two sets

 

A ∩ B = {9,14}

 

 

union Objects of two sets A ∪ B = {3,7,9,14,28}

 

 

subset The contents of one set is derived from another {9,14,28} ⊆ {9,14,28}

 

 

proper subset / strict subset

 

A is a subset of B, but A is not equal to B.

 

{9,14} ⊂ {9,14,28}

 

 

not subset

 

set A is not a subset of set B

 

{9,66} ⊄ {9,14,28}

 

 

superset

 

A is a superset of B. set A includes set B

 

{9,14,28} ⊇ {9,14,28}

 

 

proper superset / strict superset

 

A is a superset of B, but B is not equal to A.

 

{9,14,28} ⊃ {9,14}

 

 

not superset

 

set A is not a superset of set B

 

{9,14,28} ⊅ {9,66}

 

‘2A’

Or ‘P(A)’

power set

 

all subsets of A

 

=

 

equality

 

both sets have the same members

 

A={3,9,14},
B={3,9,14},
A=B
Ac

 

complement

 

all the objects that do not belong to set A

 

‘A \ B’ or ‘A – B’

 

relative complement

 

objects that belong to A and not to B

 

A = {3,9,14},
B = {1,2,3},
A-B = {9,14}
‘A ∆ B’ or ‘A ⊖ B’

 

symmetric difference

 

objects that belong to A or B but not to their intersection

 

A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}
a∈A

 

 

Elements belongs to Element of ‘a’ belong to ‘A’ A={3,9,14}, 3 ∈ A

 

x∉A

 

not element of

 

no set membership

 

A={3,9,14}, 1 ∉ A

 

(a,b)

 

ordered pair

 

collection of 2 elements

 

A×B

 

cartesian product

 

set of all ordered pairs from A and B

 

‘|A|’ or ‘#A’

 

cardinality

 

the number of elements of set A

 

A={3,9,14}, |A|=3

 

|

 

bar Such that A={x|3<x<14}

 

Ø

 

Empty set A without any elements C= Ø

 

U Universal set Set that has all possible elements
N0 and N1 Set of Natural numbers Set of natural numbers starting from 0 or 1  

0 = {0,1,2,3,4,…}

 

1 = {1,2,3,4,5,…}

 

 

Z Integer set Set of integer values  

= {…-3,-2,-1,0,1,2,3,…}

 

Q rational numbers set

 

= {x | x=a/b, a,b∈}

 

2/6 ∈ Q

 

R real numbers set

 

= {x | -∞ < x <∞}

 

6.343434∈ R

 

C complex numbers set

 

= {z | z=a+bi, -∞<a<∞,      -∞<b<∞}
6+2i ∈ C

 

“Download Set Symbols absolutely free”

4. Calculus and Integration

Calculus helps us understand how the values in a function change. It is a very important concept in math.

For example, calculus can be used to predict the rate of which Covid 19 is spreading. The various values like the number of infected, the number of vulnerable people can be applied to calculus.

Calculus can be a nightmare for you if not studied properly. The calculus and precalculus symbols should be studied in order. From integration to derivation.

Symbol Symbol Name Meaning / definition Example
limit limit value of a function
ε epsilon represents a very small number, near zero ε → 0
e e constant / Euler’s number e = 2.718281828… e = lim (1+1/x)x , x→∞
y derivative derivative – Lagrange’s notation (3x3)’ = 9x2
y second derivative derivative of derivative (3x3)” = 18x
y(n) nth derivative n times derivation (3x3)(3) = 18
math symbols derivative derivative – Leibniz’s notation d(3x3)/dx = 9x2
math symbols second derivative derivative of derivative d2(3x3)/dx2 = 18x
nth derivative n times derivation
time derivative derivative by time – Newton’s notation
time second derivative derivative of derivative
Dx y derivative derivative – Euler’s notation
Dx2y second derivative derivative of derivative
math symbols partial derivative ∂(x2+y2)/∂x = 2x
integral opposite to derivation f(x)dx
∫∫ double integral integration of function of 2 variables ∫∫ f(x,y)dxdy
∫∫∫ triple integral integration of function of 3 variables ∫∫∫ f(x,y,z)dxdydz
closed contour / line integral
closed surface integral
closed volume integral
[a,b] closed interval [a,b] = {x | a x b}
(a,b) open interval (a,b) = {x | a < x < b}
i imaginary unit i ≡ √-1 z = 3 + 2i
z* complex conjugate z = a+biz*=abi z* = 3 – 2i
z complex conjugate z = a+biz = abi z = 3 – 2i
Re(z) real part of a complex number z = a+bi → Re(z)=a Re(3 – 2i) = 3
Im(z) imaginary part of a complex number z = a+bi → Im(z)=b Im(3 – 2i) = -2
| z | absolute value/magnitude of a complex number |z| = |a+bi| = √(a2+b2) |3 – 2i| = √13
arg(z) argument of a complex number The angle of the radius in the complex plane arg(3 + 2i) = 33.7°
nabla / del gradient / divergence operator f (x,y,z)
math symbols vector
math symbols unit vector
x * y convolution y(t) = x(t) * h(t)
Laplace transform F(s) = {f (t)}
math symbols Fourier transform X(ω) = {f (t)}
δ delta function
lemniscate infinity symbol

Be sure to print our table to learn the various math symbols and functions easily.

Download Link
Conclusion

Mathematical symbols allow us to save a lot of time because they are abbreviations. Learning new symbols will allow you to learn more theories and concepts simultaneously.

Also Read: Multiplication Charts: 1 -12 & 1-100 [Free Download and Printable]

Stick these tables in the classroom or send via Google Classroom so that children can easily get hold of these mathematical symbols.

 

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