I know the easy way to show the inverse triangle inequality using the triangle inequality. As far as I‘m aware of the two are equivalent so I was wondering how to prove the triangle inequality using only the inverse triangle inequlality. I tried using cases and some substitutions but I didn‘t get far:/ Thanks for your help<3
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3$|x|=|(x+y+(-y)| \geq |x+y|-|y|$. – Kavi Rama Murthy Jun 19 '21 at 11:45
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Does this answer your question? https://math.stackexchange.com/q/127372 – Jun 19 '21 at 11:51
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@JitendraSingh: That question is the opposite of what's being asked here. – Hans Lundmark Jun 19 '21 at 12:24
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@HansLundmark well if OP will try to receive idea from the question then I feel he/she might be also to solve it – Jun 19 '21 at 12:36
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@JitendraSingh: Apparently not, since they already said “I know the easy way to show the inverse triangle inequality using the triangle inequality”, which is what that question was about. But never mind... – Hans Lundmark Jun 19 '21 at 12:59