# equivalence in absolute values

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• Nov 5th 2012, 03:04 PM
psolaki
equivalence in absolute values
Is the following equivalence true:

$|x+y|=|x|+|y| \Longleftrightarrow (x+y\geq 0\Longrightarrow x+y =|x| +|y|)\wedge(x+y<0\Longrightarrow x+y=-(|x|+|y|)$
because i can only prove that:

$|x+y|=|x|+|y| \Longrightarrow (x+y\geq 0\Longrightarrow x+y =|x| +|y|)\vee(x+y<0\Longrightarrow x+y=-(|x|+|y|)$