so . Reversing the roles of we get . So we have
and
which means...
Given y = (x+y)+(-x),
I have to prove, using triangle inequality that ||x|-|y|| <= |x+y|
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This is what I did:
|y| = |(x+y)+(-x)| <= |x+y|+|-x|
so, |y| <= |x+y|+|-x|
=> |y|-|x| <= |x+y|
How do I get to the conclusion?