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Math Help - Prove || x|-|y|| ≤ |x-y|

  1. #1
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    Prove || x|-|y|| ≤ |x-y|

    Prove || x|-|y|| ≤ |x-y|, ∀x, y ∈ R
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  2. #2
    Senior Member Pinkk's Avatar
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    Hint: Use the triangle inequality and the fact that for all x,y, |x| = |x + (y-y)| = |(x-y) + y|.
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