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): $1, 2, 3$ , and so on. The mathematical symbol for the set of all natural numbers is written as $\mathbb{N}$ .

Whole numbers

The set of whole numbers includes all natural numbers as well as $0$ .

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, $\mathbb{Z}$ .

Rational numbers

A rational number,

Q

$\mathbb{Q}$ , 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

R

$\mathbb{R}$ . Real numbers are usually represented by using decimal numerals.

Module 1: Real Numbers and Algebraic Expressions