An Introduction to Sets

A very useful concept in mathematics is the idea of the set. A set is essentially a collection of items. Here are some examples of sets:

Set $(1)$ is a set of the first three natural numbers, set $(2)$ is a set of fruits, and set $(3)$ is a set of mathematical functions.

Set Operations

It is often useful to perform operations on sets to compare them.

The intersection of two sets is a new set that contains elements that are only in both sets. This is denoted using the $\cap$ symbol. For example,

The union of two sets is a new set that contains elements that are in either set. This is denoted using the $\cup$ symbol. For example,

• set difference
• complement
• set diagrams

Sets and Graphs

• $\mathbb{R}$
• $\mathbb{R}^2$
• $\mathbb{R}^3$

Set Builder Notation