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Using Triangle Inequality to find a magnitude

  1. Feb 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Let a, x, and y be real numbers and let E > 0. Suppose that |x-a|< E and |y-a|< E. Use the Triangle Inequality to find an estimate for the magnitude |x-y|.


    2. Relevant equations
    The Triangle Inequality states that |a+b| <= |a| + |b| is valid for all real numbers a and b.


    3. The attempt at a solution

    |x-a| = |x-y+y-a| <= |x-y| + |y-a|

    I'm fairly certain this conversion/inequality is important because it contains three of the four elements from the problem ( |x-a|, |y-a|, and |x-y|). However, I am stuck on how to get E involved and determine an estimate for |x-y|.
     
  2. jcsd
  3. Feb 1, 2012 #2

    lanedance

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    Homework Helper

    you want to try and get |x-y| on the left of the <= sign

    now its a little confusing as you used "a" in the tri eq as well (good notation always helps avoid confusion), so lets re-write it
    |c+b| <= |c|+ |b|

    then how about letting
    c=x-a
    n=a-y
     
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