The set of **real numbers** can be divided into two subsets:

**rational numbers** and **irrational numbers**.

A **rational number** can be written as a fraction $\frac{p}{q}$,

where $p$ and $q$ are integers and $q$ does not equal zero.

Integers, fractions, and repeating or terminating decimals are rational numbers.

An **irrational number** cannot be written as a fraction $\frac{p}{q}$,

where $p$ and $q$ are integers and $q$ does not equal zero.

Non-repeating, non-terminating decimals are irrational numbers.

**Whole numbers** are rational numbers greater than or

equal to zero that do not have a fraction or decimal {0, 1, 2, 3, ...}.

**Integers** are whole numbers and their opposites {..., -3, -2, -1, 0, 1, 2, 3, ...}.

**Natural numbers** are rational numbers greater than

zero that do not have a fraction or decimal.

Rational numbers and irrational numbers are subsets of real numbers.

Integers are a subset of rational numbers, so integers are also real numbers.

Whole numbers are a subset of integers, so whole numbers are also rational numbers and real numbers.

Natural numbers are a subset of whole numbers, so natural numbers are also integers, rational numbers, and real numbers.