We call any collection of things a set. These things can be objects, or they can be numbers, or anything else. The things that belong to the set are called members of the set.

The order in a set is not important. So {3,2,1} = {1,2,3}

We can describe a set or we can list its members. So a set could be {All whole numbers from one to ten} or it could be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

If there are too many numbers to list, we sometimes use …, e.g. {2, 4, 6, 8, 10, …, 96, 98, 100}

Worked Example

• Use words to describe the following sets:
  • {Alice, Ann, Alison, Anya}
  • {35, 42, 49, 56, 63}

Exercise 1

Membership

We say that something is a member of a set using the symbol ϵ

So 2 ∈ {2, 4, 6, 8} and 2 ∉ {1, 3, 5, 7}.

The empty set ∅ has no members, so {people with 7 heads} = ∅ (I think).

Exercise 2

Answers to both exercises