The real numbers can be divided into three subsets: negative real numbers, zero, and positive real numbers. Each subset includes fractions, decimals, and irrational numbers according to their algebraic sign (+ or –). In this section we will further define real numbers and use their properties to solve linear equations and inequalities.

The classes of numbers we will explore include:

### Natural numbers

The most familiar numbers are the natural numbers (sometimes called counting numbers): [latex]1, 2, 3[/latex], and so on. The mathematical symbol for the set of all natural numbers is written as [latex]\mathbb{N}[/latex].

### Whole numbers

The set of whole numbers includes all natural numbers as well as [latex]0[/latex].

### Integers

When the set of negative numbers is combined with the set of natural numbers (including 0), the result is defined as the set of integers, [latex]\mathbb{Z}[/latex].