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Proof in Real Analysis

  • Thread starter mb55113
  • Start date
  • #1
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Homework Statement



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

Homework Equations



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

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?
 

Answers and Replies

  • #2
1,101
3
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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