Chapter 0 - Prelimaries

Question 1

Axiom

Answer 1

mathematical statements we regard as true

Question 2

Proof by induction

Answer 2

If S is a set of natural numbers with
1. S contains 1
2. Also contains n + 1
Then S = N

Base case → Induction hypothesis → induction step
(for n=1) (holds for n) (prove for n+1)

Question 3

Definition - union and intersection

Answer 3

Given 2 sets A and B, the union is AUB, and is defined by x ∈ A U B , provided that x ∈ A or x ∈ B
The intersection A n B is defined by x ∈ A n D provided x ∈ A and x ∈ B.

Question 4

Definition - subset

Answer 4

we say A is a subset of B if every element of A is also in B. x ∈ A → x ∈ B

Two sets A and B are equal if they have the same elements A=B

Question 5

Definition - Function

Answer 5

A function f: A →B between 2 sets A and B is a rule that associates with each element a ∈ A, a unique element f(a) ∈ B, f(a) the image of A under f.
The set A is the domain of f