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].