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.
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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 | x ≈ y |
| > | 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.
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″
|
 |
Infinite line | The line extends at both sides infinitely |  |
 |
Line segment | A line from point a to point b | |
 |
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
|
| |x–y|
|
distance | Distance between two points | | x–y | = 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
|
|
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 |
 |
derivative | derivative – Leibniz’s notation | d(3x3)/dx = 9x2 |
 |
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 | |
 |
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+bi → z*=a–bi | z* = 3 – 2i |
| z | complex conjugate | z = a+bi → z = a–bi | 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) |
 |
vector | ||
 |
unit vector | ||
| x * y | convolution | y(t) = x(t) * h(t) | |
 |
Laplace transform | F(s) = {f (t)} | |
 |
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.
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Stick these tables in the classroom or send via Google Classroom so that children can easily get hold of these mathematical symbols.