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Absolute inequalities

  1. Sep 27, 2004 #1
    prove the folowing and state when the inequality holds...


    i was thinking that i consider all the possible cases, ie x is positive, y positive, z positive; then the various combinations with negative as well.....
    is there another shorter method of doing it?
  2. jcsd
  3. Sep 27, 2004 #2


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    You can start with 2 terms first. |x+y|<=|x|+|y|. (I am assuming you are talking about real numbers). Equal if the same sign, less if opposite. Then the 3 term case can be proven in two steps using the 2 term case.
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