1. The Real Number System
Section 1.4
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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 { , -2, -1, 0 , 1, 2, 3, 4, }
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: It would repeat 3s forever. Mathematicians are not patient. They would simply write it as The repeating value(s) would be identified by a line above the repeating value. Example: 292/105 =

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
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