The Real Number System

1. The Real Number System Section 1.4 (30)

2. Objectives(30) Identify set of numbers Know the structure of real numbers

3. 1.4.1 The Real Number System(30) Frequently you will see a set is represented by a collection of elements located within braces ( { } ) Examples: Natural numbers { 1, 2, 3, 4, . . . } Whole numbers { 0, 1, 2, 3, 4, . . . } Integers { . . . -3, -2, -1, 0 , 1, 2, 3, 4, . . . } -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 negative numbers positive numbers

4. Rational Numbers Rational numbers are all numbers that can be written as the quotient of two integers (the divisor [denominator] cannot be equal to 0. Examples: You can divide the numerator by the denominator and write a rational number as a decimal. If a number is a terminating decimal ( at some point (only 0s) or if the decimal begins repeating the same digits over and over, it is a rational.

5. Repeating Decimals What is a repeating decimal? The simplest example would be 1/3. As a decimal it would be written as: 0.33333333333333333333333333333333 It would repeat 3s forever. Mathematicians are not patient. They would simply write it as 0.3 . The repeating value(s) would be identified by a line above the repeating value. Example: 292/105 = 2.7809523809523 . . . 2.7809523

6. Irrational Numbers Actually there are a lot more irrational numbers than rational numbers, but we don’t really use them very much. Examples of irrational numbers are:

7. 1.4.2 Know the Structure of the Real Numbers(32) Real Numbers Rational Numbers Irrational Numbers Non-Integers Integers Negative integers Whole Numbers 0 Natural Numbers

8. Example For the set { 2, 4/5, -4.1, 0, Π, , -6, - } Irrational numbers: Π , Rational numbers: 2, 4/5, -4.1, 0, -6, - Integers: 2, 0, -6, - Whole numbers: 2 Note that a square root sign, does not make the number irrational.

9. Objectives(30) Identify set of numbers Know the structure of real numbers

10. The Real Number System Section 1.4 (30)