## Numbers & Number Sets

We all deal with numbers on a daily basis, such as measuring out three-fourths of a cup of cereal for breakfast. They can be classified into **number sets**, which are just a collection of numbers. The most common number sets, along with the symbols we use to represent each set, are illustrated in the following image:

Let's start with the **natural numbers**, which consist of the counting numbers 1, 2, 3, and so on to infinity; **whole numbers** include all of the natural numbers and 0. We call them whole numbers because they represent the whole, not a fractional portion of the number. Next, we have the **integers**, which consist of all of the whole numbers and their negatives.

**Rational numbers** are those numbers that can be written as a fraction. By comparison, **irrational numbers** can't be written as a fraction and extend indefinitely after their decimal point without assuming a repeating pattern.

**Real numbers** are those that we normally work with on a daily basis. They include all of the sets of numbers described, excluding complex numbers and imaginary numbers. Imaginary numbers contain the number *i* = √-1. Real numbers are complex numbers and can be written as *a* + *bi*.

Number sets follow an order where each set is contained in the one that comes after it, with a few exceptions, as shown in the following diagram:

A given number can belong to more than one number set. We can place a number in a set if it satisfies the definition of that set. For example, the number 3/4 does not satisfy the definition for a natural, a whole, an irrational, or an imaginary number, or an integer. However, it does satisfy the definitions for rational, real, and complex numbers. Thus, we can place it in our diagram as shown: