# Mathematical Symbols

Mathematical symbols are used to perform various 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 math symbols not only refer to different quantities but also represent the relationship between two quantities.

## Basic Maths Symbols Names With Meaning and Examples

This is a list of commonly used symbols in the stream of mathematics.

Symbol Symbol Name Meaning or Definition Example
= 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

## 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 exists 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 combination of finite discrete structures. Some of the most important symbols are:

### 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

### 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