lesson01 - THE UNIVERSITY OF AKRON Mathematics and Computer...

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~ w mptii menu THE UNIVERSITY OF AKRON Mathematics and Computer Science Lesson 1: Setting Up the Environment Directory Table of Contents Begin Lesson 1 A n l g e b r a R v i w Iam DP S N Z Q R C a 3 a 4 = a 7 ( ab ) 10 = a 10 b 10 ( ab (3 ab 4))=2 ab 4 ( ab ) 3 ( a 1 + b 1 )=( ab ) 2 ( a + b ) ( a b ) 3 = a 3 3 a 2 b +3 ab 2 b 3 2 x 2 3 x 2=(2 x + 1)( x 2) 1 2 x +13=0 = x = 26 G= { ( x, y ) | y = f ( x ) } f ( x )= mx + b y = sin x T L s o Copyright c ° 1995–2000 D. P. Story Last Revision Date: 2/2/2000
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Lesson 1: Setting Up the Environment Table of Contents 1. Setting Up the Environment 1.1. The Real Number System, and friends The Natural Numbers The Integers The Rational Num- bers The Irrational Numbers The Real Numbers 1.2. The Number Line, and relations Less than and Greater than 1.3. Distance and Absolute Value Absolute Value Distance between two numbers The Midpoint between two Numbers 1.4. Interval Notation
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1. Setting Up the Environment In this lesson, we review some very basic ideas and terminology of the so-called Real Number System . Do not take this Frst lesson lightly, your knowledge of the real number system and its properties is key to your understanding why certain algebraic manipulations are permissible, and why others are not. (When you are manipulating algebraic quantities, you are, in fact, manipulating numbers.) Terminology is important in all scientiFc, technical and professional Felds, and mathematics is no di±erent, it has a lot of it. When you speak or write, you use words; the words you use must be under- stood by the ones with whom you are trying to communicate. ²or someone to understand your communication, the words must have a universal meaning; therefore, it is necessary for you to use the correct terminology to be able to e±ectively and efficiently communicate with others. Correct use of (mathematical) terminology is a sign that you understand what you are saying or writing.
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Section 1: Setting Up the Environment 1.1. The Real Number System, and friends A pedestrian description of the real number system is that it is the set of all decimal numbers . Here are a few examples of decimal numbers: 1 . 456445 / Positive Number with Finite Decimal Expansion 3 . 54 / Negative Number with Finite Decimal Expansion 1 . 49773487234 ... / Positive Number with Infnite Decimal Expansion 3 . 4 × 10 9 / Negative Number in Scientifc Notation 5 . 65445 E 5 / Positive Number in Scientifc Notation You have been working with these representations of numbers all your life. You have worked long and hard to master the mechanics of adding, subtracting, multiplying, and dividing these numbers. More recently, the calculator makes many of the operations just mentioned automatic and routine, but the calculator does not diminish the need to still have a ‘pencil and paper’ understanding of these operations, nor does it diminish the need to be able to read, interpret and convert numbers.
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Section 1: Setting Up the Environment Decimal numbers are, in fact, the end product of a series of prelim- inary deFnitions. As important as decimal numbers are, let’s leave
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lesson01 - THE UNIVERSITY OF AKRON Mathematics and Computer...

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