Introduction to Classifying and Defining Properties of Real Numbers

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].


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].

Rational numbers

A rational number, [latex]\mathbb{Q}[/latex], is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator.

Real numbers

The real numbers include all the measuring numbers. The symbol for the real numbers is [latex]\mathbb{R}[/latex]. Real numbers are usually represented by using decimal numerals.