Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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MAT102S - Introduction to Mathematical Proofs - Spring 2010 - UTM Problem Set B - NOT to be submitted. Quiz #1, to be written on Wednesday, January 20, from 10:15am to 10:45am at CC1080, will be based on this Problem Set. Work on the following exercises: ± Prove that for any x;y 2 R , we have ± ± j x j ² j y j ± ± ³ j x ² y j . Hint : Use the triangle inequality to prove that
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Unformatted text preview: j x j j y j j x y j and that j y j j x j j x y j . Chapter 1, Exercises 1.14, 1.20, 1.31, 1.34, 1.36, 1.38, 1.41 and 1.44(a). Note : Question 1.31 is not an easy problem. Start to work on it early. For part (a), start by substituting t = xy and s = zw in the inequality 2 ts t 2 + s 2 ....
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