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Absolute Value Equality

  1. Oct 19, 2013 #1
    1. The problem statement, all variables and given/known data
    abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement


    2. Relevant equations

    Triangle inequality?

    3. The attempt at a solution
    I have nothing :/
     
  2. jcsd
  3. Oct 19, 2013 #2

    UltrafastPED

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    What is the absolute value of x? if x => 0 then abs(x)=x, else it is -x.

    So make a table with all of the possible cases and see what happens!
     
  4. Oct 19, 2013 #3
    Drat, I was hoping that that I wouldn't have to do a case analysis; is there a more elegant way of solving this though?
     
  5. Oct 19, 2013 #4

    UltrafastPED

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    I don't know elegant ... I grew up on a farm!

    So once you have carried out the detailed work you can apply your own standards of elegance and cleverness ... and write something elegant!
     
  6. Oct 19, 2013 #5

    verty

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    Assume (by renaming of variables) that x ≤ y ≤ z. Then you have 4 cases to check, it shouldn't be too tedious.
     
  7. Oct 19, 2013 #6
    x + y + z <= |x| + |y| + |z|
    - x - y - z <= |x| + |y| + |z|

    (definition of the absolute value)
     
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