Check proof of some simple inequality

Question

Can you check please my proof of this inequality? It's all right?

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See an easier proof of (a) at this question [here](http://math.stackexchange.com/questions/127372/reverse-triangle-inequality-proof) — JMoravitz, Jul 01 '15 at 15:16

score 2 · Accepted Answer · answered Jul 01 '15 at 15:12

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It's all right, but in point b) you have mistake: need $\ge$, not $\le$.

answered Jul 01 '15 at 15:12

MannGegenMann

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Oh, yes... Right. Thanks! – PersonaNonGrata Jul 01 '15 at 15:14

score 0 · Answer 2 · answered Jul 01 '15 at 15:19

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Most of your proof is right, while some errors occur in part b).
First, you need to prove that $|x+x_1+\cdots+x_n|\color{red}\ge|x|-(|x_1|+\cdots+|x_n|)$.
Also, it should be $|x|\le|\color{red}x+x_1+\cdots+x_n|+|-x_1|+\cdots+|-x_n|$.

answered Jul 01 '15 at 15:19

Eclipse Sun

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Check proof of some simple inequality

2 Answers2