# The Real Number System

May 28th, 2015
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•Real numbers consist of all the rational and irrational numbers.•The real number system has many subsets:–Natural Numbers – Whole Numbers – Integers

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The Real Number SystemReal numbers consist of all the rational and irrational numbers.The real number system has many subsets:Natural Numbers Whole Numbers Integers 1. Natural numbers are the set of counting numbers.{1, 2, 3,}2. Whole numbers are the set of numbers that include 0 plus the set of natural numbers.{0, 1, 2, 3, 4, 5,}3. Integers are the set of whole numbers and their opposites.{,-3, -2, -1, 0, 1, 2, 3,}4. Rational numbers are any numbers that can be expressed in the form of , where a and b are integers, and b 0. They can always be expressed by using terminating decimals or repeating decimals. Terminating decimals are decimals that contain a finite number of digits.Examples:a. 36.8b. 0.125c. 4.55. Repeating decimals are decimals that contain a infinite number of digits.Examples:a. 0.333b. 1.9c. 7.6896896. Irrational numbers are any numbers that cannot be expressed as . They are expressed as non-terminating, non-repeating decimals; decimals that go on forever without repeating a pattern.Examples of irrational numbers:a. 0.34334333433334b. 45.86745893c. (pi)d. Other Vocabulary Associated with the Real Number System(ellipsis)continues without end{ } (set)a collection of objects or numbers. Sets are notated by using braces { }.Finitehaving bounds; limitedInfinitehaving no boundaries or limitsVenn diagrama diagram consisting of circles or squares to show rela

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