Symbol

Meaning / definition

Example

 

x variable

unknown value to find

when 2x = 4, then x = 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

f(x) ∝ g(x)

∞

lemniscate

infinity symbol

≪

much less than

much less than

1 ≪ 1000000

≫

much greater than

much greater than

1000000 ≫ 1

( )

parentheses

calculate expression inside first

2 * (3+5) = 16

[ ]

brackets

calculate expression inside first

[(1+2)*(1+5)] = 18

{ }

braces

set

⌊x⌋

floor brackets

rounds number to lower integer

⌊4.3⌋= 4

⌈x⌉

ceiling brackets

rounds number to upper integer

⌈4.3⌉= 5

x!

exclamation mark

factorial

4! = 1*2*3*4 = 24

| x |

single vertical bar

absolute value

| -5 | = 5

f (x)

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 ∈ [2,6]

∆

delta

change / difference

∆t = t₀

∆

discriminant

Δ = b² – 4ac

∑

sigma

summation – sum of all values in range of series

∑ x_i= x₁+x₂+…+x_n

∑∑

sigma

double summation

∏

capital pi

product – product of all values in range of series

∏ x_i=x₁∙x₂∙…∙x_n

e constant / Euler’s number

e = 2.718281828…

e = lim (1+1/x)^x , x→∞

γ

Euler-Mascheroni constant

γ = 0.527721566…

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