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 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 = t1 - 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
