Algebra Reference Sheet | AuthorJonathanDavid.com

Algebra

General Symbols and Notations

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Symbol	Meaning	Example
=	Equal	0 = 0
≠	Not equal	1 ≠ 0
±	Plus or Minus	x = ±a ⇒ x = a or x = −a
∓	Minus or Plus	x = ∓a ⇒ x = −a or x = a
iff, ⇔	If and only if	p ⇒ q and q ⇒ p then p ⇔ q
⇒	Implies	p ⇒ q
<	Less than	x − a < 0 ⇒ x < a
≤	Less than equal	x − a ≤ 0 ⇒ x ≤ a
≥	Greater than equal	x − a ≥ 0 ⇒ x ≥ a
>	Greater than	x − a > 0 ⇒ x > a
×	Times	2 × 3 = 6
* or ·	Multiplication	2 * 3 = 6 or 2 · 3 = 6
( )( )	Multiplication	(2)(3) = 6
= 6
[ ][ ]	Multiplication	[2][3] = 6
[( )( )]^( )( )	Exponential Multiplication	[(2)(3)]³⁻²(3 − 2) = 6
∞	Infinity	Never ends
Δ	Displacement or change of	Δx = x − x₀
Σ	Summation	Σₙ₌₁³ aₙxⁿ = a₁x¹ + a₂x² + a₃x³
θ	Theta reserved for angles	θ = π/4 = 45°
f(x)	Function of x	f(x) = xⁿ + …
f(x, y)	Function of x and y	f(x, y) = (xy)ⁿ + …
∈	In or element of	x ∈ [a, b) means a ≤ x < b
∀	For all	∀x (for all x)
∴	Therefore	x − a = 0 ⇔ x = a ∴ x = a
∵	Because	∵ x − a = 0, x = a
≡	Equivalent	(−2, 3) ≡ −2 < x < 3
( , )	Open interval	(−2, 3) = −2 < x < 3
[ , ]	Closed interval	[2, 3] = 2 ≤ x ≤ 3
⊂	Proper subset	A ⊂ B ⇒ B ⊄ A
⊆	Subset (equal)	A ⊆ B ⇒ A = B
[ , )	Half-open interval	[1, 4) = 1 ≤ x < 4
{ … }	Set of numbers	{1, 3, 5, 7}
∪	Union	{1,2,3} ∪ {3,4,5} = {1,2,3,4,5}
∩	Intersection	{1,2,3} ∩ {3,4,5} = {3}
ℝ	Real numbers	(−∞, ∞)
P(x₀, y₀)	Point	(1, f(1))

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