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Homework Help: Proof in Real Analysis

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove: abs(abs(x)-abs(y))<=abs(x-y)

    2. Relevant equations

    Triangle Inequality:
    abs(a+b)<=abs(a)+abs(b)

    3. The attempt at a solution

    This is what i have so far:

    Let a=x-y and b=y. Then
    abs(x-y+y) <= abs(x-y)+abs(y) which becomes abs(x)-abs(y)<=abs(x-y). From here i get stuck can anybody help me?
     
  2. jcsd
  3. Feb 1, 2010 #2
    Well you've got half of it. The other inequality you need to demonstrate is |y| - |x| <= |x-y|. But what is an equivalent way of writing |x-y|?
     
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