**sets** and their properties. A set is a well-defined collection of non-repeating “things” (which could be numbers, people, places etc) which are known as **elements** of the set.

For example, the set containing the whole numbers between 1 and 4 is: \{1, 2, 3, 4\}

There are many properties used to describe a set and so before going any further it is important to meet

several of the most common ones.

- A finite set is one with a non-infinite number of elements.
- An infinite set is one with an infinite number of elements.
- The empty set is the set without any elements, commonly represented with the symbol \emptyset .}

Many are surprised to learn they have already encountered a few sets during their lifetime. These were most likely not referred to as sets but are nonetheless. Below are a few you may have already met:

- The
**integers**, sometimes referred to as the “whole” numbers. These are positive and negative numbers without a decimal.

Some examples are -2, -15, 1, 6 etc. These are represented with the symbol \mathbb{Z} . - The
**natural numbers**, sometimes referred to as the “counting numbers”. These are the positive integers represented with the symbol \mathbb{N} . There is some debate as to whether zero should be included in the natural numbers. The natural numbers are a**subset**of the integers. - There are many more that you may be familar with, such as the
**rational**and**irrational**numbers, the**real**numbers (all the previous sets are subsets of the real numbers) and some may also be familiar with the**imaginary**and**complex**numbers.