Theorem: for every real number x, x s |x]. Proof: If x 2 0, by definition |x| = x. Thus |x| > x. If x < 0, by definition |x| = -x. Since |x| = -x > 0 and O > x, \x| > x. Thus, Ix| 2 x. Q.E.D.

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Q: Prove

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Q: 1- gn+1 Σ %3D :- 1-τ i=0

A: Solution

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Q: Prove the following using a proof by contrapositive: Let z be a rational number. Prove that if zy is…

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Q: 5. In Algebra you are taught that for any real numbers a > 0 and a that the inequality -a <x < a is…

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A: Here you go. Just use a square property and answer follows.

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