provide solution/explanation Theorem: for every real number x, x x. If x 0 and O > x, |x| > x. Thus, |x| > x. Q.E.D. Proof by Contradiction O Proof by Contraposition Proof by Cases O Mathematical...

provide solution/explanation

Theorem: for every real number x, x < |x|.<br>Proof:<br>If x 2 0, by definition |x| = x. Thus |x| > x.<br>If x < 0, by definition |x| = -x.<br>Since |x| = -x > 0 and O > x, |x| > x.<br>Thus, |x| > x. Q.E.D.<br>Proof by Contradiction<br>O Proof by Contraposition<br>Proof by Cases<br>O Mathematical Induction<br>

Extracted text: Theorem: for every real number x, x < |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, |x| > x. Q.E.D. Proof by Contradiction O Proof by Contraposition Proof by Cases O Mathematical Induction

Jun 04, 2022

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provide solution/explanation Theorem: for every real number x, x x. If x 0 and O > x, |x| > x. Thus, |x| > x. Q.E.D. Proof by Contradiction O Proof by Contraposition Proof by Cases O Mathematical...

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