Symbol Symbol Name Meaning / definition Example

x x variable unknown value to find when 2 x = 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

f ( x ) function of x maps values of x to f(x) f ( x ) = 3 x +5

( f ∘ g) function composition ( f ∘ g) ( x ) = f ( g( x )) f ( x )=3 x , 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 – t

∆ discriminant Δ = b – 4 ac

∑ sigma summation – sum of all values in range of series ∑ x = x +x +…+x

∑∑ sigma double summation

∏ capital pi product – product of all values in range of series ∏ x =x ∙x ∙…∙x

e e constant / Euler’s number e = 2.718281828… e = lim (1+1/ 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

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