What is a letter or symbol in algebra?

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 x ∈ (2,6)

[a, b] closed interval [a, b] = 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