# Math Symbols

You will encounter many mathematical symbols during your math courses. The table below provides you with a list of all the common symbols, and how to read them. The following page has a series of examples of these symbols in use.

## Basic Math Symbols

This is a list of commonly used Basic Maths Symbols in the stream of mathematics.

##### 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 vice-versa does not holds true.
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  $\frac{8}{2} = 4$
/ division slash division 6 / 2 = 3
mod modulo remainder calculation 7 mod 3 = 1
ab power exponent $2^{4} = 16$
. 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
$\sqrt[4]{a}$ fourth root $\sqrt[4]{a} .\sqrt[4]{a} .\sqrt[4]{a} .\sqrt[4]{a} = a$ $\sqrt[4]{16} = \pm 2$
$\sqrt[3]{a}$ cube root $\sqrt[3]{a} .\sqrt[3]{a} .\sqrt[3]{a} = a$ $\sqrt[3]{343} = 7$
% percent 1% = 1/100 10% × 30 = 3
$\sqrt[n]{a}$ n-th root (radical) for n=3, $\sqrt[n]{8}$ = 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

##### 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
$\ddot{y}= \frac{d^{2} y}{dt^{2}}$ Second derivative of time derivative of derivative
$\dot{y}$ Single derivative of time derivative by time – Newton’s notation
$D^{2}x$ second derivative derivative of derivative
Dx derivative derivative – Euler’s notation
integral opposite to derivation
$\frac{\ af(x,y)}{ax}$ partial derivative ∂(x2+y2)/∂x = 2x
triple integral integration of function of 3 variables
double integral integration of function of 2 variables
closed surface integral
closed contour / line integral
[a,b] closed interval [a,b] = {x | a ≤ x ≤ b}
closed volume integral
(a,b) open interval (a,b) = {x | a < x < b}
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+biz = abi z = 3 + 2i
$\vec{x}$ vector $\vec{V} = x \hat{i} + y \hat{j} + z \hat{k}$
x * y convolution y(t) = x(t) * h(t)
lemniscate infinity symbol
δ delta function

### Combinatorics Symbols

Combinatorics is a stream of mathematics that concerns the study of finite discrete structures.

##### 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

##### 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

### Logic symbols

##### 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 xy
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 xy
equivalent if and only if (iff)
implies
for all
equivalent if and only if (iff)
there does not exists
there exists
because / since
therefore

### Numeral symbols

##### Hebrew
zero 0 ٠
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