Maths Symbols

Maths symbols are used to denote various mathematical quantities and operations. The symbols make it easier to refer the maths quantities and help in easy denotation. It is interesting to note that the whole of maths is completely based on numbers and symbols. The mathematical symbols not only refer to different quantities but also represent the relationship between two quantities. The tables below provide you with a list of all the common symbols in maths and examples on how to read and operate with them.

List of Maths Symbols

Basic Math Symbols

This 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 holds 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

Calculus & Analysis Symbols in Maths

Symbol Symbol Name Meaning or definition Example
ε epsilon represents a very small number, near zero ε → 0
\(\lim \limits_{x \to a}\) limit limit value of a function \(\lim \limits_{x \to a}(3x+1)= 3 \times a + 1 = 3a + 1\)
y derivative derivative – Lagrange’s notation \(\left ( 5x^{3} \right )’ = 15 x^{2}\)
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 \(3x^{n} = 3 n (n-1)(n-2)….(2)(1)= 3n!\)
y second derivative derivative of derivative \((4x^{3})” = 24x\)
\(\frac{d^2 y}{d x^2}\) 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
\(D^{2}x\) 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 finite discrete structures. Some of the most important symbols are:

Symbol Symbol Name Meaning or Definition Example
\(_{n}P _{k}\) permutation \(_{n}P_{k} = \frac{n!}{(n-k)!}\) \(_{5}P _{3}\) = 5! / (5-3)! = 60
n! factorial n! = 1·2·3·…·n 5! = 1·2·3·4·5 = 120
\(_{n}C _{k}\)\(\left ( \frac{n}{k} \right )\) combination \(_{n}C_{k} = \left ( \frac{n}{k} \right ) = \frac{n!}{k! (n-k)!}\) \(_{5}C _{3}\) = 5!/[3!(5-3)!] =10

Greek Alphabet Letters Used in Maths

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

Maths Logic symbols

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 exists n/a n/a
there exists n/a n/a
because / since n/a n/a
therefore n/a n/a

Common Maths 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 were some of the most important and commonly used symbols in mathematics. It is important to get completely acquainted with the all the maths symbols to be able to solve maths problems efficiently. It should be noted that without knowing the maths symbols, it is extremely difficult to grasp certain concepts in 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.

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Practise This Question

 Determine the faces, vertices and edges of the following shape.