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 October 24th, 2016, 10:13 AM #1 Senior Member   Joined: Sep 2012 Posts: 199 Thanks: 1 Verify rule for absolute value Hi guys, could someone help on how to tackle these two problems I am not quite how to tackle these. I think the first one is a triangle inequality but not too sure? I really don’t know about the second. Do I use the equation given and start from there or do I derive it some how from an absolute value.I can see if i plug number in it works but that it really. Questions are below: Q1. Verify the rule that for two real numbers x and y then $\displaystyle |x+y| < |x|-|y|$ (suppose to be less than equal too) Q2. Given that for two real numbers x and y, $\displaystyle |x+y|<|x|+|y|$, deduced that $\displaystyle |x-y|<|x|-|y|$ (once again suppose to be less than equal to.)
 October 24th, 2016, 01:42 PM #2 Global Moderator   Joined: May 2007 Posts: 6,203 Thanks: 486 They are both wrong. Counterexamples: for Q1, let x=y, while for Q2 let x=-y. Thanks from taylor_1989_2012 and topsquark

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