1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    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|?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook