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# Set Theory and Notation

### Set Theory and Notation

Set notation is an easy way to list many numbers, items or objects.

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

Choose the correct notation to describe this: 8 is one of the even numbers (E).

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

Choose the correct notation to describe this: 5 is not one of the even numbers (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:
$n(A) = 5$