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Math Help - Triangle Inequality

  1. #1
    Member pberardi's Avatar
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    Triangle Inequality

    I am trying to understand the proof without using the square/square root function. From what I understand there are two equivalent statements i.e. |p+q| <= |p|+|q| and | |p|-|q| | <= |p-q|

    The first one I can derive. It is the second one that I am having trouble with. Can someone please show me the steps from the first to the second?
    Thank you.
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  2. #2
    Member
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    Just use the first one in the form  |p|\le |p-q|+|q| with the assumption that |q|\le |p|. If this isn't the case then just relabel since \left||p|-|q|\right|=\left||q|-|p|\right| and |p-q|=|q-p|
    Last edited by Jameson; May 30th 2009 at 11:53 AM.
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