Mathematical Notation Numbers Notation Meaning Example N ...

Mathematical Notation Numbers Notation N

Meaning Natural numbers

Z R |x| a a/b or b a|b   m m Cn or n n! b X xi

Integers Real numbers modulus a over b

Example 1, 2, 3, . . . (some people include 0) . . .√ , −2, −1, 0, 1, 2, . . . 1 , 2, π, . . . 2 |2| = 2, |−3| = 3 12/3 = 4, 2/4 = 0.5

a divides b

4 | 12

m choose n

5

n factorial

5! = 120 3 X i2 = 12 + 22 + 32 = 14

xa + xa+1 + · · · + xb

i=a

C2 = 10

i=1

Sets Notation {. . .}

Meaning a set

x∈A {x : . . .} or {x | . . .} |A|

x is an element of the set A the set of all x such that . . . cardinality of A (number of elements in A) A union B (set of elements in either A or B) A intersection B (set of elements in both A and B) set difference (set of elements in A but not B) A is a subset of B (or equal) complement of A empty set (no elements) ordered pair Cartesian product (set of all ordered pairs)

A∪B A∩B A\B A⊆B A0 ∅ (x, y) A×B

1

Example {1, 2, 3} NOTE: {1, 2} = {2, 1} 2 ∈ {1, 2, 3} {x : x2 = 4} = {−2, 2} |{1, 2, 3}| = 3 {1, 2, 3} ∪ {2, 4} = {1, 2, 3, 4} {1, 2, 3} ∩ {2, 4} = {2} {1, 2, 3} \ {2, 4} = {1, 3} {1, 3} ⊆ {1, 2, 3} everything not in A {1, 2} ∩ {3, 4} = ∅ NOTE: (1, 2) 6= (2, 1) {1, 2} × {1, 3} = {(1, 1), (2, 1), (1, 3), (2, 3)}

The Greek alphabet

You don’t need to learn this; keep it for reference. Apologies to Greek students: you may not recognise this, but it is the Greek alphabet that mathematicians use!

Name Capital alpha A beta B gamma Γ delta ∆ epsilon E zeta Z eta H theta Θ iota I kappa K lambda Λ mu M nu N xi Ξ omicron O pi Π rho P sigma Σ tau T upsilon Υ phi Φ chi X psi Ψ omega Ω

2

Lowercase α β γ δ  ζ η θ ι κ λ µ ν ξ o π ρ σ τ υ φ χ ψ ω