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): , and so on. The mathematical symbol for the set of all natural numbers is written as .Whole numbers
The set of whole numbers includes all natural numbers as well as .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, .Rational numbers
A rational number, , 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 . Real numbers are usually represented by using decimal numerals.