Section_1.1-Real_Numbers

Section_1.1-Real_Numbers - Section 1.1 Real Numbers Types...

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Unformatted text preview: Section 1.1 Real Numbers Types of Real Numbers 1. Natural numbers ( N ): 1 , 2 , 3 , 4 , 5 , . . . 2. Integer numbers ( Z ): , ± 1 , ± 2 , ± 3 , ± 4 , ± 5 , . . . REMARK: Any natural number is an integer number, but not any integer number is a natural number. 3. Rational numbers ( Q ): r = m n , where m ∈ Z , n ∈ N EXAMPLES: 1 2 7 3- 11 53 2 = 2 1 . 2 = 2 10 = 1 5 . 222 . . . = 0 . 2 = 2 9 . 999 . . . = 0 . 9 = 1 REMARK: Any integer number is a rational number, but not any rational number is an integer. 4. Irrational Numbers . These are numbers that cannot be expressed as a ratio of integers. EXAMPLES: √ 2 √ 3 √ 2 + √ 3 1 + √ 5 2- 3 √ 2 π √ π 2 √ 2 The set of all real numbers is denoted by R . The real numbers can be represented by points on a line which is called a coordinate line , or a real number line , or simply a real line : 1 Every real number has a decimal representation. If the number is rational, then its correspond- ing decimal is repeating. For example, 1 2 = 0 . 500 . . . = 0 . 5 0 = 0 . 4 9 , 2 3 = 0 . 66666 . . . = 0 . 6 157 495 = 0 . 3171717 . . . = 0 . 3 17 , 9 7 = 1 . 285714285714 . . . = 1 . 285714 If the number is irrational, the decimal representation is nonrepeating: √ 2 = 1 . 414213562373095 . . . π = 3 . 141592653589793 . . . Operations on Real Numbers Real numbers can be combined using the familiar operations of addition, subtraction, multi- plication, and division. When evaluating arithmetic expressions that contain several of these operations, we use the following conventions to determine the order in which the operations are performed: 1. Perform operations inside parentheses first, beginning with the innermost pair. In dividing two expressions, the numerator and denominator of the quotient are treated as if they are within parentheses....
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This note was uploaded on 01/23/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.

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Section_1.1-Real_Numbers - Section 1.1 Real Numbers Types...

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