# Algebra symbols

Symbol
Meaning / definition
Example

x
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 | axb}
x ∈ [2,6]
delta
change / difference
t = t0
discriminant
Δ = b2 – 4ac
sigma
summation – sum of all values in range of series
xi= x1+x2+…+xn
∑∑
sigma
double summation capital pi
product – product of all values in range of series
xi=x1∙x2∙…∙xn
e
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