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The Mathematical symbols are used in almost every equation in the field of Mathematics. Not only this, the mathematical symbols finds it usefulness in the Physics domain also. The mathematical symbols are used in performing basic calculations to complex calculations. In other words, it can be summarized that the Mathematics is all about numbers, symbols, and formulas. In this article, we will provide students with a list of all the mathematics symbols used along with their name and examples.
Mathematical Symbols
Mathematical symbols are used to perform a variety of operations on numbers or functions. Math symbols have various functions depending on the area of mathematics. Expressions are simpler to understand when mathematical information is represented by symbols because these symbols illustrate the relationship between quantities. Without these math symbols, the subject of Mathematics cannot show its beautiful color.
The mathematical symbols not only refer to different quantities but also represent the relationship between those two mathematical quantities. All the mathematical symbols are generally used to perform mathematical operations under various concepts.
Maths Symbols Meaning
Maths symbols are used to define relationship between the two quantities. The Maths symbols are used to represent mathematical operations, concepts, relationships, and structures. Each Math symbols have their own meaning which can have different logical implementation under different circumstances. The maths symbols are used in different formulas like algebra formulas, geometry formulas, combinatorics formulas, etc.
Mathematical Symbols Name
Some of the basic mathematical symbols with their name has been given in this section. These basic mathematical symbols are + (Addition), – (Subtraction), % (Percentage), etc. It could get complicated if we write “adding 4 to 2 gives 6” over and over. It also takes longer to write and requires more space for these words. Rather, by employing symbols, we may save both time and space.
Symbol | Symbol Name | Math Symbols Meaning | Example |
≠ | not equal sign | inequality | 10 ≠ 6 |
= | equal sign | equality | 3 = 1 + 2 |
< | strict inequality | less than | 7 < 10 |
> | strict inequality | greater than | 6 > 2 |
≤ | inequality | less than or equal to | x ≤ y, means, y = x or y > x, but not vice-versa. |
≥ | inequality | greater than or equal to | a ≥ b, means, a = b or a > b, but vice-versa does not hold true. |
[ ] | brackets | calculate expression inside first | [ 2×5] + 7 = 10 + 7 = 17 |
( ) | parentheses | calculate expression inside first | 3 × (3 + 7) = 3 × 10 = 30 |
− | minus sign | subtraction | 5 − 2 = 3 |
+ | plus sign | addition | 4 + 5 = 9 |
∓ | minus – plus | both minus and plus operations | 1 ∓ 4 = -3 and 5 |
± | plus – minus | both plus and minus operations | 5 ± 3 = 8 and 2 |
× | times sign | multiplication | 4 × 3 = 12 |
* | asterisk | multiplication | 2 * 3 = 6 |
÷ | 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 |
3√a | cube root | 3√a ·3√a · 3√a = a | 3√343 = 7 |
% | 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 |
ppm | per-million | 1 ppm = 1/1000000 | 10ppm × 30 = 0.0003 |
‰ | per-mille | 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 |
Check: Trigonometry Chart
Maths Symbols Chart For Geometry
Geometry is a branch of mathematics that deal with the concept of points, 1D, 2D, and 3D figures. Geometry being a branch of mathematics use various symbols for the calculation and notation purposes. Like ∠ sign is used for the representation of angles. The chart of the geometry symbols in Mathematics is given below for students.
Symbol | Symbol Name | Meaning | Example |
∠ | formed by two rays | The value of an angle | ∠ABC=30° |
measured angle | ABC=30° | ||
spherical angle | 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 | |
AB | line segment | line from point A to point B | |
→ | ray | line that start from point A | |
⊥ | 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 |
grad | gradians ∕ gons | grads angle unit | 360°;=400 grad |
g | gradians ∕ gons | grads angle unit | 360°=400g |
Maths Symbols for Class 12
As the Class 12 Mathematics board exam 2024 is approaching, students must be fully prepared for this exam by having a thorough knowledge of the maths symbols used in class 12. Students are often given questions in the exam which contains many symbols. Examiners do not define the meaning of these symbols to test the knowledge of board students. For this, students must remember the Maths symbols given below.
Symbol | Symbol Name | Math Symbols Meaning | Example |
---|---|---|---|
ε | epsilon | represents a very small number, near-zero | 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 |
|
second derivative | derivative of derivative |
|
dy/dx | derivative | derivative – Leibniz’s notation |
|
|
nth derivative | n times derivation |
|
|
Second derivative of time | derivative of derivative | If y = 4t2, then
|
|
Single derivative of time | derivative by time – Newton’s notation | y = 5t, then
|
D2x | second derivative | derivative of derivative | y” + 2y + 1 = 0⇒ D2y + 2Dy + 1 = 0 |
Dx | derivative | derivative – Euler’s notation | dy/x – 1 = 0⇒ Dy – 1 = 0 |
∫ | integral | opposite to derivation | ∫xn dx = xn + 1/n + 1 + C |
|
partial derivative | Differentiating a function with respect to one variable considering the other variables as constant | ∂(x2+y2)/∂x = 2x |
∭ | triple integral | integration of the function of 3 variables |
|
∬ | double integral | integration of the function of 2 variables | ∬(x3+y3)dx dy |
∯ | closed surface integral | Double integral over a closed surface | ∭V (⛛.F)dV = ∯S (F.n̂) dS |
∮ | closed contour / line integral | Line integral over closed curve | ∮C 2/z dz |
[a,b] | closed interval | [a,b] = {x | a ≤ x ≤ b} | sin x ∈ [ – 1, 1] |
∰ | closed volume integral | Volume integral over a closed three-dimensional domain | ∰ (x2 + y2 + z2) dx dy dz |
(a,b) | open interval | (a,b) = {x | a < x < b} | f is continuous within (0, 1) |
z* | complex conjugate | z = a+bi → z*=a-bi | If z = 3 + 2i then z* = 3 – 2i |
i | imaginary unit | i ≡ √-1 | z = 3 + 2i |
∇ | nabla / del | gradient / divergence operator | ∇f (x,y,z) |
|
vector | A quantity with magnitude and direction |
|
x * y | convolution | Modification in a function due to the other function. | y(t) = x(t) * h(t) |
∞ | lemniscate | infinity symbol | 3x ≥ 0; x ∈ (0, ∞) |
δ | delta function | Dirac Delta function |
δ(x) = { 0 if x ≠0
{ ∞ if x = 0
|
Constant Mathematical Symbols Name
In mathematics, a lot of symbols are employed with predetermined values. We can substitute those values for those symbols in order to simplify the expressions. Among the instances is the pi sign (π), which represents the numbers 3.14 and 22/7. The ratio of a circle’s diameter to its circumference is known as the pi symbol, which is a mathematical constant.
The pi sign is also known as the Archimedes constant in mathematics. Furthermore, the Mathematical e-symbol, which has the value e= 2.718281828.The term “e-constant” or “Euler’s constant” refers to this symbol. All of the popular constant mathematical symbols are listed in the table below, along with their explanation.
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. Limit of the sequence (1 + (1/n)n ). Approximately equals 2.71828 |
The ratio of a circle’s circumference to its diameter. Half-circumference of a unit circle. Approximately equals 3.14159 | |
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. |
Advanced Maths Symbols
There are many advanced Maths symbols present in Mathematics in the field of combinatorics, linear algebra, etc. The list of all these symbols are given below for the sake of students preparing for the Mathematics subject.
Symbol | Symbol Name | Meaning | Example |
· | dot | scalar product | a·b |
× | cross | vector product | a×b |
A⊗B | tensor product | tensor product of A and B | A ⊗ B |
inner product | |||
[ ] | brackets | matrix of numbers | |
| A | | determinant | determinant of matrix A | |
det(A) | determinant | determinant of matrix A | |
∥ x ∥ | double vertical bars | norm | |
AT | transpose | matrix transpose | (AT ) ij = ( A ) ji |
A† | Hermitian matrix | matrix conjugate transpose | (A† ) ij = ( A ) ji |
A* | Hermitian matrix | matrix conjugate transpose | (A* ) ij = ( A ) ji |
A-1 | inverse matrix | A=1/A^-1 | |
rank(A) | matrix rank | rank of matrix A | rank(A)= 3 |
dim(U) | dimension | dimension of matrix A | dim(U)= 3 |
n! | factorial | n! = 1⋅2⋅3⋅…⋅n | 5! = 1⋅2⋅3⋅4⋅5 = 120 |
nPk | permutation | n!/(n-k)! | 5P3 = 5! / (5-3)! = 60 |
nCk | combination | n!/[k!(n-k)!] | 5C3 = 5!/[3!(5-3)!]=10 |
Algebra Mathematical Symbols With Name and Examples
A mathematical component of algebra consists of symbols and the rules used to trick those symbols. Those symbols stand for variables, or non-fixed values, in algebra. In mathematics, algebra expresses the relationship between variables in a similar way to how sentences describe the relationship between specific words. The chart of the algebra mathematical symbols is given herein.
Symbol | Symbol Name | Meaning | Example |
χ | x variable | unknown value to find | when 2χ=4, then χ=2 |
≡ | equivalence | identical to | |
≜ | equal by definition | equal by definition | |
≔ | equal by definition | equal by definition | |
∽ | 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 | |
≪ | much less than | much less than | 1≪1000000 |
⁽ ⁾ | much grataer than | much grataer than | 1000000 ≫1 |
⁽ ⁾ | parentheses | calculate expression inside first | 2 *(3+5) = 16 |
[ ] | brackets | calculate expression inside first | [ (1+2)*(1+5) ] = 18 |
{ } | braces | set | |
⌊ χ ⌋ | floor brackets | rounds number to lower integer | ⌊4.3⌋ = 4 |
⌈ χ ⌉ | ceiling brackets | rounds number to upper integer | ⌈4.3⌉ = 5 |
χ! | exclamation mark | factorial | 4! =1*2*3*4 = 24 |
|χ| | vertical bars | absolute value | | -5 | = 5 |
Af(χ) | 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&isin[2,6] |
Δ | delta | change / difference | Δ=t1-t0 |
Δ | discriminant | Δ=b²-4ac | |
∑ | sigma | summation – sum of all values in range of series | ∑x1=x1+x2+…+xn |
∑∑ | sigma | double summation | |
∏ | capital pi | product – product of all values in range of series | ∏x1=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… | |
φ | golden ratio | golden ratio constant | |
π | pi constant | π = 3.141592654… is the ratio between the circumference and diameter of a circle | c=π⋅d=2⋅π⋅r |
Math Symbols Meaning for Probability and Statistics
Mathematics also includes statistics and probability. Since you have already studied statistics and probability in your junior classes, you must have encountered several mathematical symbols. The most significant symbols in statistics and probability are listed below.
Symbol | Symbol Name | Meaning | 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 occurred | 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 |
var( X ) | variance | variance of random variable X | var( X )= 4 |
σ2 | variance | variance of population values | σ2= 4 |
std( X ) | standard deviation | standard deviation of random variable X | std( X ) = 2 |
σx | standard deviation | standard deviation value of random variable X | σx = 2 |
median | middle value of random variable x | ||
cov( X,Y ) | covariance | covariance of random variables X and Y | cov( X,Y )= 4 |
corr( X,Y ) | correlation | correlation of random variables X and Y | corr( X,Y )= 0.6 |
cov( X,Y ) | covariance | covariance of random variables X and Y | cov( X,Y )= 4 |
corr( X,Y ) | correlation | correlation of random variables X and Y | corr( X,Y )= 0.6 |
ρ x,y | correlation | correlation of random variables X and Y | ρ x,y= 0.6 |
∑ | summation | summation – sum of all values in range of series | |
∑∑ | double summation | double summation | |
Mo | mode | value that occurs most frequently in population | |
MR | mid-range | MR =( xmax+xmin)/2 | |
Md | sample median | half the population is below this value | |
Q1 | lower / first quartile | 25 % of population are below this value | |
Q2 | median / second quartile | 50% of population are below this value = median of samples | |
Q3 | upper / third quartile | 75% of population are below this value | |
x | sample mean | average / arithmetic mean | x=(2+5+9) /3=5.333 |
s2 | sample variance | population samples variance estimator | s2= 4 |
s | sample standard deviation | population samples standard deviation estimator | s= 2 |
Zx | standard score | Zx=(x-x)/ Sx | |
X ~ | distribution of X | distribution of random variable X | X ~ N (0,3) |
X ~ | distribution of X | distribution of random variable X | X ~ N (0,3) |
N(μσ2) | normal distribution | gaussian distribution | X ~ N (0,3) |
U( a,b ) | uniform distribution | equal probability in range a,b | X ~ U (0,3) |
exp(λ) | exponential distribution | f(x)=λe-λx x≥0 | |
gamma(c, λ) | gamma distribution | f(x)=λ c xc-1 e-λx / Γ ( c ) x≥0 | |
χ2(k) | chi-square distribution | f(x)=xk/2-1 e-x/2 / ( 2k/2Γ )(k/2) ) | |
F (k1,k2) | F distribution | ||
Bin( n,p ) | binomial distribution | F(k) = nCk pk(1-p)n-k | |
Poisson( λ ) | Poisson distribution | F(k) = λke-λ / k ! | |
Geom( p ) | geometric distribution | F(k) = p( 1-p)k | |
HG( N ,K ,n ) | hyper-geometric distribution | ||
Bern( p ) | Bernoulli distribution |
Math Symbols Name: Set Theory
The set theory is an important domain of mathematics that contain many symbols. The list of symbols present in the set theory chapter of mathematics is tabulated hereunder.
Symbol | Symbol Name | Meaning | Example |
{ } | set | a collection of elements | A = {3,7,9,14}, |
B = {9,14,28} | |||
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} |
2A | power set | all subsets of A | |
P(A) | power set | all subsets of A | |
A = B | 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 | 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, | set membership | A={3,9,14}, 3 ∈ A |
belongs to | |||
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×B = {(a,b)|a∈A , b∈B} |
|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 |
| | vertical bar | such that | A={x|3<x<14} |
Φ | empty set | Φ = {} | C = {Φ} |
U | universal set | set of all possible values |
Mathematical Symbols Name for Logic
Logic is an important concepts in Mathematics which deals with the reasoning competence. The list of logic symbols along with their name and example is given below.
Symbol | Math Symbol Name | Math Symbols Meaning | Example |
^ | caret / circumflex | and | x ^ y |
· | and | and | x · y |
+ | plus | or | x + y |
& | ampersand | and | x & y |
| | vertical line | or | x | y |
∨ | reversed caret | or | x ∨ y |
X̄ | bar | not – negation | x̄ |
x’ | single-quote | not – negation | x’ |
! | Exclamation mark | not – negation | ! x |
¬ | not | not – negation | ¬ x |
~ | tilde | negation | ~ x |
⊕ | circled plus / oplus | exclusive or – xor | x ⊕ y |
⇔ | equivalent | if and only if (iff) | p: this year has 366 days |
q: this is a leap year | |||
p ⇔ q | |||
⇒ | implies | Implication | p: a number is a multiple of 4 |
q: the number is even | |||
p ⇒ q | |||
∈ | Belong to/is an element of | Set membership | A = {1, 2, 3} |
2 ∈ A | |||
∉ | Not element of | Negation of set membership | A={1, 2, 3} |
0 ∉ A | |||
∀ | for all | Universal Quantifier | 2n is even ∀ n ∈ N |
where N is a set of Natural Numbers | |||
↔ | equivalent | if and only if (iff) | p: x is an even number |
q: x is divisible by 2 | |||
p ↔ q | |||
∄ | there does not exist | Negation of existential quantifier | b is not divisible by a, then ∄ n ∈ N such that b = na |
∃ | there exists | Existential quantifier | b is divisible by a, then ∃ n ∈ N such that b = na |
∵ | because / since | Because shorthand | a = b, b = c |
⇒ a = c (∵ a = b) | |||
∴ | therefore | Therefore shorthand (Logical consequence) | x + 6 = 10 |
∴ x = 4 |
Greek Symbols Name in Mathematics
Greek alphabets are widely used by mathematicians in their work to represent variables, constants, functions, and other concepts. The following is a list of some of the Greek symbols that are frequently used in math:
Upper Case | Lower Case | Greek Letter Name | English Equivalent | Pronunciation |
Α | α | Alpha | a | al-fa |
Β | β | Beta | b | be-ta |
Γ | γ | Gamma | g | ga-ma |
Δ | δ | Delta | d | del-ta |
Ε | ε | Epsilon | e | ep-si-lon |
Ζ | ζ | Zeta | z | Ze-ta |
Η | η | Eta | h | eh-ta |
Θ | θ | Theta | th | te-ta |
Ι | ι | Iota | i | io-ta |
Κ | κ | Kappa | k | ka-pa |
Λ | λ | Lambda | l | lam-da |
Μ | μ | Mu | m | m-yoo |
Μ | μ | Mu | m | m-yoo |
Ν | ν | Nu | n | noo |
Ν | ν | Nu | n | noo |
Ξ | ξ | Xi | x | x-ee |
Ο | ο | Omicron | o | o-mee-c-ron |
Π | π | Pi | p | pa-yee |
Ρ | ρ | Rho | r | row |
Σ | σ | Sigma | s | sig-ma |
Τ | τ | Tau | t | ta-oo |
Υ | υ | Upsilon | u | oo-psi-lon |
Φ | φ | Phi | ph | f-ee |
Χ | χ | Chi | ch | kh-ee |
Ψ | ψ | Psi | ps | p-see |
Ω | ω | Omega | o | o-me-ga |
Mathematical Symbols PDF
The PDF of the Mathematical symbols have been given below for download. Students can consult to this PDF whenever they want to know about the meaning and examples of the important mathematical symbols. These mathematical symbols are important for every exam, whether board exams or competitive exams.