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The Real Number System
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Definitions:
A set is a collection of elements (items) listed within braces {}. A subset is a set whose
members are all contained in another set. The set of positive integers, for example, is a subset
of the set of integers.
Sets of Real Numbers
1. Natural Numbers:
 The set of real numbers that begin with the number one (1) that is,{1, 2, 3, 4, 5, 6 …}
 also known as counting numbers
 the smallest set of real numbers
2. Whole Numbers:
 The set of real numbers that begin with the number zero (0) that is {0, 1, 2, 3, 4, 5, 6…}
 Builds from the set of natural numbers by adding the number zero.
3. Integers:

Builds from the set of whole numbers by adding negative ‘whole’ numbers, i.e., {…,
-3, -2, -1, 0, 1, 2, 3 …}
Note: There are no decimals in the sets of natural numbers, whole numbers, and integers!
4. Rational Numbers:
 The set of real numbers that is a ratio of two integers (fractions)
 This set builds from the set of integers by adding fractions
 This set also consist of terminating decimals and repeating decimals, i.e.,
{.25, .50, .3333…,.6666…}
5. Irrational Numbers:
 This set consist of numbers that are not rational.
 This set consists of non-terminating, non-repeating decimals
6. Real Numbers:
 A set of numbers that consist of rational and irrational numbers
Real Number System