The concept of mathematics is completely based on the relationship between numbers and symbols. These math symbols are used to perform different mathematical operations and represent various mathematical concepts.
And although students sometimes find it challenging to use complex math symbols to solve math problems, these symbols are used to refer math quantities and help in easy denotation.
There are a lot of math symbols applied in any given mathematical concept ranging from simple addition and subtraction to complicated operations like integration. This is the main reason why students find math symbols confusing to understand and difficult to remember.
Since there are so many notations that are important for students to understand, we have put down a list of common math symbols, their concise definition and how to use them.
(You can also download this chart to use in the classroom and distribute it among the students)
Let’s first divide the types of math symbols you’ll need as per the syllabus:
- Basic math symbols
- Algebra symbols
- Geometry symbols
- Set theory symbols
- Calculus & analysis symbols
1. Basic Math Symbols
Symbol | Symbol Name | Meaning / definition | Example |
= | equals sign | equality | 5 = 2+3
5 is equal to 2+3 |
≠ | not equal sign | inequality | 5 ≠ 4
5 is not equal to 4 |
≈ | approximately equal | approximation | sin(0.01) ≈ 0.01,
x ≈ y means x is approximately equal to y |
> | strict inequality | greater than | 5 > 4
5 is greater than 4 |
< | strict inequality | less than | 4 < 5
4 is less than 5 |
≥ | inequality | greater than or equal to | 5 ≥ 4,
x ≥ y means x is greater than or equal to y |
≤ | inequality | less than or equal to | 4 ≤ 5,
x ≤ y means x is less than or equal to y |
( ) | parentheses | calculate expressions inside first | 2 × (3+5) = 16 |
[ ] | brackets | calculate expressions inside first | [(1+2)×(1+5)] = 18 |
+ | plus sign | addition | 1 + 1 = 2 |
− | minus sign | subtraction | 2 − 1 = 1 |
± | plus – minus | both plus and minus operations | 3 ± 5 = 8 or -2 |
± | minus – plus | both minus and plus operations | 3 ∓ 5 = -2 or 8 |
* | asterisk | multiplication | 2 * 3 = 6 |
× | times sign | multiplication | 2 × 3 = 6 |
⋅ | multiplication dot | multiplication | 2 ⋅ 3 = 6 |
÷ | division sign / obelus | division | 6 ÷ 2 = 3 |
/ | division slash | division | 6 / 2 = 3 |
mod | modulo | remainder calculation | 7 mod 2 = 1 |
. | period | decimal point, decimal separator | 2.56 = 2+56/100 |
ab | power | exponent | 23 = 8 |
a^b | caret | exponent | 2 ^ 3 = 8 |
√a | square root | √a ⋅ √a = a | √9 = ±3 |
3√a | cube root | 3√a ⋅ 3√a ⋅ 3√a = a | 3√8 = 2 |
4√a | fourth root | 4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a = a | 4√16 = ±2 |
n√a | n-th root (radical) | n/a | for n=3, n√8 = 2 |
% | percent | 1% = 1/100 | 10% × 30 = 3 |
‰ | per-mille | 1‰ = 1/1000 = 0.1% | 10‰ × 30 = 0.3 |
ppm | per-million | 1ppm = 1/1000000 | 10ppm × 30 = 0.0003 |
ppb | per-billion | 1ppb = 1/1000000000 | 10ppb × 30 = 3×10-7 |
ppt | per-trillion | 1ppt = 10-12 | 10ppt × 30 = 3×10-10 |
Download the printable chart here- Basic Math Symbols
2. Algebra Symbols
Symbol | Symbol Name | Meaning / definition | Example |
x | x variable | unknown value to find | when 2x = 4, then x = 2 |
≡ | equivalence | identical to | n/a |
≜ | equal by definition | equal by definition | n/a |
:= | equal by definition | equal by definition | n/a |
~ | approximately equal | weak approximation | 11 ~ 10 |
≈ | approximately equal | approximation | sin(0.01) ≈ 0.01 |
∝ | proportional to | proportional to | y ∝ x when y = kx, k constant |
∞ | lemniscate | infinity symbol | n/a |
≪ | much less than | much less than | 1 ≪ 1000000 |
≫ | much greater than | much greater than | 1000000 ≫ 1 |
( ) | parentheses | calculate expression inside first | 2 * (3+5) = 16 |
[ ] | brackets | calculate expression inside first | [(1+2)*(1+5)] = 18 |
{ } | braces | set | n/a |
⌊x⌋ | floor brackets | rounds number to lower integer | ⌊4.3⌋ = 4 |
⌈x⌉ | ceiling brackets | rounds number to upper integer | ⌈4.3⌉ = 5 |
x! | exclamation mark | factorial | 4! = 1*2*3*4 = 24 |
| x | | single vertical bar | absolute value | | -5 | = 5 |
f (x) | function of x | maps values of x to f(x) | f (x) = 3x+5 |
(f ∘ g) | function composition | (f ∘ g) (x) = f (g(x)) | f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1) |
(a,b) | open interval | (a,b) = {x | a < x < b} | x∈ (2,6) |
[a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} | x ∈ [2,6] |
∆ | delta | change / difference | ∆t = t1 – t0 |
∆ | discriminant | Δ = b2 – 4ac | n/a |
∑ | sigma | summation – sum of all values in range of series | ∑ xi= x1+x2+…+xn |
∑∑ | sigma | double summation | |
∏ | capital pi | product – product of all values in range of series | ∏ xi=x1∙x2∙…∙xn |
e | e constant / Euler’s number | e = 2.718281828… | e = lim (1+1/x)x , x→∞ |
γ | Euler-Mascheroni constant | γ = 0.5772156649… | n/a |
φ | golden ratio | golden ratio constant | n/a |
π | pi constant | π = 3.141592654…
is the ratio between the circumference and diameter of a circle |
c = π⋅d = 2⋅π⋅r |
Download the printable chart here- Algebra Symbols
3. Geometry Symbols
Symbol | Symbol Name | Meaning / definition | Example |
∠ | angle | formed by two rays | ∠ABC = 30° |
measured angle | n/a | ABC = 30° | |
spherical angle | n/a | AOB = 30° | |
∟ | right angle | = 90° | α = 90° |
° | degree | 1 turn = 360° | α = 60° |
deg | degree | 1 turn = 360deg | α = 60deg |
′ | prime | arcminute, 1° = 60′ | α = 60°59′ |
″ | double prime | arcsecond, 1′ = 60″ | α = 60°59′59″ |
line | infinite line | n/a | |
AB | line segment | line from point A to point B | n/a |
ray | line that start from point A | n/a | |
arc | arc from point A to point B | = 60° | |
⊥ | perpendicular | perpendicular lines (90° angle) | AC ⊥ BC |
∥ | parallel | parallel lines | AB ∥ CD |
≅ | congruent to | equivalence of geometric shapes and size | ∆ABC ≅ ∆XYZ |
~ | similarity | same shapes, not same size | ∆ABC ~ ∆XYZ |
Δ | triangle | triangle shape | ΔABC ≅ ΔBCD |
|x–y| | distance | distance between points x and y | | x–y | = 5 |
π | pi constant | π = 3.141592654…is the ratio between the circumference and diameter of a circle | c = π⋅d = 2⋅π⋅r |
rad | radians | radians angle unit | 360° = 2π rad |
^{c} | radians | radians angle unit | 360° = 2π ^{c} |
grad | gradians / gons | grads angle unit | 360° = 400 grad |
^{g} | gradians / gons | grads angle unit | 360° = 400 ^{g} |
Download the printable chart here- Geometric Symbol
4. Set Theory Symbols
Symbol | Symbol Name | Meaning / definition | Example |
{ } | set | a collection of elements | A = {3,7,9,14}, B = {9,14,28} |
| | such that | so that | A = {x | x∈, x<0} |
A⋂B | intersection | objects that belong to set A and set B | A ⋂ B = {9,14} |
A⋃B | union | objects that belong to set A or set B | A ⋃ B = {3,7,9,14,28} |
A⊆B | subset | A is a subset of B. set A is included in set B. | {9,14,28} ⊆ {9,14,28} |
A⊂B | proper subset / strict subset | A is a subset of B, but A is not equal to B. | {9,14} ⊂ {9,14,28} |
A⊄B | not subset | set A is not a subset of set B | {9,66} ⊄ {9,14,28} |
A⊇B | superset | A is a superset of B. set A includes set B | {9,14,28} ⊇ {9,14,28} |
A⊃B | proper superset / strict superset | A is a superset of B, but B is not equal to A. | {9,14,28} ⊃ {9,14} |
A⊅B | not superset | set A is not a superset of set B | {9,14,28} ⊅ {9,66} |
2^{A} | power set | all subsets of A | n/a |
power set | all subsets of A | n/a | |
A=B | equality | both sets have the same members | A={3,9,14}, B={3,9,14}, A=B |
A^{c} | complement | all the objects that do not belong to set A | n/a |
A’ | complement | all the objects that do not belong to set A | n/a |
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 | 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 | 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⊖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 | element of, belongs to |
set membership | 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 | n/a |
A×B | cartesian product | set of all ordered pairs from A and B | n/a |
|A| | cardinality | the number of elements of set A | A={3,9,14}, |A|=3 |
#A | cardinality | the number of elements of set A | A={3,9,14}, #A=3 |
aleph-null | infinite cardinality of natural numbers set | n/a | |
aleph-one | cardinality of countable ordinal numbers set | n/a | |
Ø | empty set | Ø = {} | A = Ø |
universal set | set of all possible values | n/a | |
_{0} | natural numbers / whole numbers set (with zero) | _{0} = {0,1,2,3,4,…} | 0 ∈ _{0} |
_{1} | natural numbers / whole numbers set (without zero) | _{1} = {1,2,3,4,5,…} | 6 ∈ _{1} |
integer numbers set | = {…-3,-2,-1,0,1,2,3,…} | -6 ∈ | |
rational numbers set | = {x | x=a/b, a,b∈ and b≠0} | 2/6 ∈ | |
real numbers set | = {x | -∞ < x <∞} | 6.343434 ∈ | |
complex numbers set | = {z | z=a+bi, -∞<a<∞, -∞<b<∞} | 6+2i ∈ |
Download the printable chart here- Set Theory Symbols
5. Calculus & Analysis Symbols
Symbol | Symbol Name | Meaning / definition | Example |
limit | limit value of a function | n/a | |
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 | (3x^{3})’ = 9x^{2} |
y ” | second derivative | derivative of derivative | (3x^{3})” = 18x |
y^{(n)} | nth derivative | n times derivation | (3x^{3})^{(3)} = 18 |
derivative | derivative – Leibniz’s notation | d(3x^{3})/dx = 9x^{2} | |
second derivative | derivative of derivative | d^{2}(3x^{3})/dx^{2} = 18x | |
nth derivative | n times derivation | n/a | |
time derivative | derivative by time – Newton’s notation | n/a | |
time second derivative | derivative of derivative | n/a | |
D_{x }y | derivative | derivative – Euler’s notation | n/a |
D_{x}^{2}y | second derivative | derivative of derivative | n/a |
partial derivative | n/a | ∂(x^{2}+y^{2})/∂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 | n/a | n/a |
∯ | closed surface integral | n/a | n/a |
∰ | closed volume integral | n/a | n/a |
[a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} | 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 |
z | complex conjugate | z = a+bi → z = a–bi | z = 3 + 2i |
∇ | nabla / del | gradient / divergence operator | ∇f (x,y,z) |
vector | n/a | n/a | |
unit vector | n/a | n/a | |
x * y | convolution | y(t) = x(t) * h(t) | n/a |
Laplace transform | F(s) = {f (t)} | n/a | |
Fourier transform | X(ω) = {f (t)} | n/a | |
δ | delta function | n/a | n/a |
∞ | lemniscate | infinity symbol | n/a |
Download the printable chart here- Calculus & Analysis Symbols
These are some of the most commonly used math symbols that your students need to learn in order to solve math questions. To help your students better memorise these symbols, you can download these math symbol charts and distribute them among your students as well as stick it in the classroom.
Use these charts and math symbols in your classroom to help your students clearly understand mathematical concepts and perform tasks. You can also quiz your students on these symbols and hold fun contests in the class.
If you are interested in introducing Prodigy in your class, you can sign up for a free demo here: https://india.prodigygame.com/get-started/