2. Sets of Numbers

You will almost always have a question asking you to identify which
numbers belong to which number set. All of the following are real
numbers.

The set of natural numbers includes the numbers we use for counting:
{1, 2, 3, 4, 5, 6, 7,. . .}

The set of whole numbers includes the natural numbers along with 0.
{0, 1, 2, 3, 4, 5, 6, 7,. . .}

The set of integers includes both of the sets above along with the
negative numbers.
{. . . -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. . .}

The set of rational numbers includes the above sets along with any
number that can be written in the form of a fraction.

Numbers such as 3/4 or -4/1 are ones that can be written as the ratio of two
integers. When written as decimals, these numbers must terminate or
repeat. For example, 1/4 = 0.25 and 2/3 = 0.666....

The set of irrational numbers are real numbers that are not rational. These include square roots or numbers which do not terminate or repeat like pi. For example:

, , and

We also have non-real numbers which are also called imaginary numbers .
For example, or .

For your practice, you get to decide which numbers belong to which set.

Practice problems and answers.