## Algebra symbols

Symbol Symbol Name 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 y ∝ x when y = kx, k constant
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
(x) function of x maps values of x to f(x) (x) = 3x+5
(f ∘ g) function composition (f ∘ g) (x) = (g(x)) (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 = 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