Set Theory and Notation

In Maths we tend to have to list many numbers, items or objects. An easy way to do this is to use set notation. We will start by looking at all the notation used within set theory.

A set refers to a unique collection of values or items. For example, the odd numbers are a set of values. We notate this using a capital letter such as: $A = {odd \space number}$

The items that fit within the set are called elements or members. For example, 3 is an odd number. Therefore, it is a member of set A.

We use the symbol ∈ to indicate when members are part of a set. Since 3 is an odd number, and part of Set A, we can write 3 ∈ A

When a value is not a member of a set, we use the same notation with a line through it. Since 5 is not an even number, we can write it as 5 ∉ E

The universal set refers to all the possible values for a set.

There are only 5 numbers which are positive, odd integers less than 10. This describes set A, where the number of items in set A is 5. We can notate this as: $n(A) = 5$