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Show something is a metric

  1. Feb 3, 2006 #1
    I need help on how to show something is a metric.
    U: R2 x R2 ----> R where U(x,y) = max { |x1-y1|,|x2-y2|}
    I can do all the properties except for the dreaded triangle inequality property. help me out please, thanks
     
  2. jcsd
  3. Feb 4, 2006 #2

    Galileo

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    What are your ideas so far?
    Here's the basic start, let a=|x1-y1|,b=|x_2-y2|,c=|x3-y3|. (a,b and c are three arbitrary non-negative numbers).

    To show:
    max(a,b)<=max(a,c)+max(b,c)

    Looks like, if it isn't obvious, you can always exhaust different cases.
     
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