Mathematical Symbols

Mathematical symbols are used to perform various operations. The symbols make it easier to refer the Maths quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the relationship between two quantities. The mathematical symbols are mainly used to perform mathematical operations under various concepts. As we know, the concept of maths is purely dependent on numbers and symbols. 

There are many symbols in Maths which has some predefined values. To simplify the expressions, we can use those kinds of values instead of those symbols. Some of the examples are the pi (π) symbol which holds the value 22/7 or 3.17, and e-symbol in Maths which holds the value e= 2.718281828….This symbol is known as e-constant or Euler’s constant. The table provided below has a list of all the common symbols in Maths with meaning and examples.

There are so many mathematical symbols which are very important to students. To understand this in an easier way, the list of mathematical symbols are noted here with definition and examples. There are numerous signs and symbols, ranging from simple addition concept sign to the complex integration concept sign. Here, the list of mathematical symbols is provided in a tabular form, and those notations are categorized according to the concept-wise. 

List of Mathematical Symbols

Basic Maths Symbols Names With Meaning and Examples

The basic symbols help us to work with mathematical concepts in a theoretical manner. In simpler words, without symbols, we cannot do maths. The mathematical signs and symbols are considered as the representative of the value. The basic symbols in maths are used to express the mathematical thoughts. The relationship between the sign and the value refers to the fundamental need of mathematics. With the help of symbols, certain concepts and ideas are clearly explained. Here, is a list of commonly used symbols in the stream of mathematics.

Symbol Symbol Name Meaning or Definition Example
not equal sign inequality 10 ≠ 6
= equals 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 = 17
( ) parentheses calculate expression inside first 3 × (3 + 7) = 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

Maths Logic symbols With Meaning

Symbol Symbol Name Meaning or Definition 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
x bar not – negation x
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)
implies n/a n/a
for all n/a n/a
equivalent if and only if (iff) n/a
there does not exist n/a n/a
there exists n/a n/a
because / since n/a n/a
therefore n/a n/a

Calculus and Analysis Symbols in Maths

Symbol Symbol Name Meaning or definition 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
\(\frac{d^2 y}{d x^2}\) second derivative derivative of derivative \(\frac{d^2 }{d x^2}(6x^{3}+x^{2}+3x+1) = 36x + 1\)
dy/dx derivative derivative – Leibniz’s notation \(\frac{d }{d x}(5x) = 5\)
\(\frac{d^n y}{d x^n}\) nth derivative n times derivation n/a
\(\ddot{y}= \frac{d^{2} y}{dt^{2}}\) Second derivative of time derivative of derivative n/a
\(\dot{y}\) Single derivative of time derivative by time – Newton’s notation n/a
D2x second derivative derivative of derivative n/a
Dx derivative derivative – Euler’s notation n/a
integral opposite to derivation n/a
\(\frac{\ af(x,y)}{ax}\) partial derivative ∂(x2+y2)/∂x = 2x n/a
triple integral integration of function of 3 variables n/a
double integral integration of function of 2 variables n/a
closed surface integral n/a n/a
closed contour / line integral n/a n/a
[a,b] closed interval [a,b] = {x | a ≤ x ≤ b} n/a
closed volume integral n/a
(a,b) open interval (a,b) = {x | a < x < b} n/a
z* complex conjugate z = a+bi → z*=a-bi z* = 3 + 2i
i imaginary unit i ≡ √-1 z = 3 + 2i
nabla / del gradient / divergence operator ∇f (x,y,z)
z complex conjugate z = a+bi → z = a-bi z = 3 + 2i
\(\vec{x}\) vector \(\vec{V} = x \hat{i} + y \hat{j} + z \hat{k}\) n/a
x * y convolution y(t) = x(t) * h(t) n/a
lemniscate infinity symbol n/a
δ delta function n/a n/a

 

Combinatorics Symbols in Mathematics

Combinatorics is a stream of mathematics that concerns the study of the combination of finite discrete structures. Some of the most important symbols are:

Permutation and Combiantion Symbols

Greek Alphabet Letters Used in Maths

Mathematicians frequently use Greek alphabets in their work to represent the variables, constants, functions and so on. Some of the commonly used Greek symbols are listed below:

Greek Symbol Greek Letter Name English Equivalent Pronunciation
Upper Case
Lower Case
Β β Beta b be-ta
Α α Alpha a al-fa
Δ δ Delta d del-ta
Γ γ Gamma g ga-ma
Ζ ζ Zeta z ze-ta
Ε ε Epsilon e ep-si-lon
Θ θ Theta th te-ta
Η η Eta h eh-ta
Κ κ Kappa k ka-pa
Ι ι Iota i io-ta
Μ μ Mu m m-yoo
Λ λ Lambda l lam-da
Ξ ξ Xi x x-ee
Ν ν Nu n noo
Ο ο Omicron o o-mee-c-ron
Π π Pi p pa-yee
Σ σ Sigma s sig-ma
Ρ ρ Rho r row
Υ υ Upsilon u oo-psi-lon
Τ τ Tau t ta-oo
Χ χ Chi ch kh-ee
Φ φ Phi ph f-ee
Ω ω Omega o o-me-ga
Ψ ψ Psi ps p-see

Common Numeral Symbols 

Name European Roman Hindu Arabic Hebrew
zero 0 n/a 0 n/a
one 1 I ١ א
two 2 II ٢ ב
three 3 III ٣ ג
four 4 IV ٤ ד
five 5 V ٥ ה
six 6 VI ٦ ו
seven 7 VII ٧ ז
eight 8 VIII ٨ ח
nine 9 IX ٩ ט
ten 10 X ١٠ י
eleven 11 XI ١١ יא
twelve 12 XII ١٢ יב
thirteen 13 XIII ١٣ יג
fourteen 14 XIV ١٤ יד
fifteen 15 XV ١٥ טו
sixteen 16 XVI ١٦ טז
seventeen 17 XVII ١٧ יז
eighteen 18 XVIII ١٨ יח
nineteen 19 XIX ١٩ יט
twenty 20 XX ٢٠ כ
thirty 30 XXX ٣٠ ל
forty 40 XL ٤٠ מ
fifty 50 L ٥٠ נ
sixty 60 LX ٦٠ ס
seventy 70 LXX ٧٠ ע
eighty 80 LXXX ٨٠ פ
ninety 90 XC ٩٠ צ
one hundred 100 C ١٠٠ ק

These are some of the most important and commonly used symbols in mathematics. It is important to get completely acquainted with all the maths symbols to be able to solve maths problems efficiently. It should be noted that without knowing maths symbols, it is extremely difficult to grasp certain concepts on a universal scale. Some of the key importance of maths symbols are summarized below.

Importance of Maths Symbols

  • Helps in denoting quantities
  • Establishes relationships between quantities
  • Helps to identify the type of operation
  • Makes reference easier
  • Maths symbols are universal and break the language barrier


Frequently Asked Questions on Math Symbols

What is the symbol for pi?

The symbol of pi is π. It is a Greek alphabet. The value of pi is approximately equal to 3.14, and it is considered as an irrational number. It is considered as the most widely used mathematical constant, which is defined as the ratio of circle circumference to its diameter.

What is e symbol in mathematics?

The “e” symbol in maths represents the Euler’s number which is approximately equal to 2.71828…It is considered as one of the most important numbers in mathematics. It is an irrational number, and it cannot be represented as a simple fraction

Write down the symbols for basic arithmetic operations.

The symbols for basic arithmetic operations are addition (+), subtraction (-), Multiplication (×), Division(÷).

Why do we use mathematical symbols?

Mathematics is a universal language, and the basics of maths are the same everywhere in the universe. Mathematical symbols play a major role in this. The definition and the value of the symbols are constant. For example, the Roman letter X represents the value 10 everywhere around us.

Mention the logic symbols in maths.

The logic symbols in maths are:
AND (^)
OR (∨)
NOT (¬)
Implies (⇒)
Equivalent (⇔)
For all (∀)
There exists (∃)

Keep visiting BYJU’S – The Learning App to get more such maths topics and concepts. Also, register at BYJU’S and download the app to access various video lessons and practice tests on different maths topics.

4 Comments

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