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# Mathematical (Maths) Symbols With Name, Examples PDF

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
$\begin{array}{l}\frac{{\mathrm{d²y/dx²}}^{}}{}\end{array}$
second derivative derivative of derivative
$\begin{array}{l}\frac{{d}^{2}}{\mathrm{dx²}{}^{}}\left(6{x}^{3}+{x}^{2}+3x+1\right)=36x+2\end{array}$
dy/dx derivative derivative – Leibniz’s notation
$\begin{array}{l}\frac{d}{\mathrm{dx}}\left(5x\right)=5\end{array}$
nth derivative n times derivation
$\begin{array}{l}\stackrel{¨}{y}=\frac{{d}^{2}y}{\mathrm{dt}{}^{2}}\end{array}$
Second derivative of time derivative of derivative If y = 4t2, then

$\begin{array}{l}\stackrel{¨}{y}=\frac{{d}^{2}y}{{\mathrm{dt}}^{2}}=4\frac{{d}^{2}}{{\mathrm{dt}}^{2}}\left({t}^{2}\right)=8\end{array}$

$\begin{array}{l}\stackrel{˙}{y}\end{array}$
Single derivative of time derivative by time – Newton’s notation y = 5t, then

$\begin{array}{l}\stackrel{˙}{y}=\frac{\mathrm{dy}}{\mathrm{dt}}=5\frac{d}{\mathrm{dt}}\left(t\right)=5\end{array}$

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
$\begin{array}{l}\frac{\mathrm{\partial f}\left(x,y\right)}{\mathrm{dy}}\end{array}$
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
$\begin{array}{l}{\int }_{1}^{2}{\int }_{2}^{3}{\int }_{0}^{1}\left(\mathrm{xyz}\right)\phantom{\rule{0.222em}{0ex}}\mathrm{dx dy dz}\end{array}$
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)
$\begin{array}{l}\stackrel{\to }{x}\end{array}$
vector A quantity with magnitude and direction
$\begin{array}{l}\stackrel{\to }{x}=\stackrel{^}{\mathrm{xi}}+\stackrel{^}{\mathrm{yj}}+\stackrel{^}{\mathrm{zk}}\end{array}$
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

Check: CBSE Class 12 Mathematics Previous Year Question Paper with Solutions

## 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 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.

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

## 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.

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## FAQs

### What is the importance of mathematical symbols?

The Mathematical symbols provide the following advantages:
aids in quantity indication
demonstrates the connections between quantity
aids in determining the kind of operation
simplifies referencing
Mathematical symbols are universal and transcend linguistic boundaries.

### Does Geometry contains mathematical symbols.

Yes, the Geometry branch of mathematics is full with different types of symbols. For example: ° (Degree) symbol, ∠ (angle) symbol, etc.

### Name some logical symbols.

Some of the logical symbols are listed below.
AND (^)
OR (∨)
NOT (¬)
For all (∀)
There exists (∃)
Implies (⇒)
Equivalent (⇔)

### Name some constant symbols with their values.

Some of the constant symbols with their values are given below:
π - PI, value = 22/7 or 3.14...
e - Euler's constant, value = 2.71828