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If $\vec{x}, \vec{y} \in \mathbb{R}^n$. Is it always true that $ \|\vec{x} + \vec{y}\| \geq \|\vec{x}\| - \|\vec{y}\| $ ?

Any advice or proofs would be greatly appreciated.

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    A [similar](http://math.stackexcha$n$ge.com/questio$n$s/127372/reverse-triangle-inequality-proof) question.2012-04-05

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Hint: Apply the triangular inequality to $x=(x+y)+(-y)$.

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    Thanks! I don't know why I avoided this before. I think I was overlooking the obvious fact that $\|-\vec{y}\| = \|\vec{y}\|$.2012-04-05