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

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

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 0 > x, \x| > x. Thus, |x| > x. Q.E.D. Mathematical Induction O Proof by Contraposition O Proof by Cases Proof by Contradiction

Jun 05, 2022

Get Answer To This Question

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here