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The reverse Triangle Inequality states that $|a-b|\geq ||a|-|b||$ for any $a,b\in \mathbb R$. What about $$|a-b-c|\geq ||a|-|b|-|c|| \tag{*}$$ I know you will say its so elementary question, but I want to be sure:

So, repeating the original inequality for two numbers we get

$$|(a-b)-c|\geq \big||a-b|-|c|\big|\geq \bigg|\big||a|-|b|\big|-|c|\bigg|$$

should we have $|a|\geq |b|$ to get the required inequality in $(*)$?

  • 0
    In (*), what if $a=1$, $b=4$, $c=-4$?2012-06-24
  • 0
    [Related](http://math.stackexchange.com/q/734106/8271)2014-11-04

1 Answers 1