The Real Number System Section 1.4 (30)

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

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

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.

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

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:

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

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.

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

The Real Number System Section 1.4 (30)