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Property of a metric

  1. Aug 31, 2009 #1
    d1 and d2 are metrics on a space X. Does min(d1,d2) satisfy the triangle inequality.

    I think it does not but I am having a hard time finding a counter example.
     
    Last edited: Sep 1, 2009
  2. jcsd
  3. Sep 1, 2009 #2
    Try looking at the special case of the triangle inequality where equality holds.
     
  4. Sep 1, 2009 #3
    Oh neat this works: euclidean and discrete metric dmin(0,2)=1
    dmin(0,1)=1
    dmin(1,2)=1
    does not satisfy the triangle inequality.
     
  5. Sep 1, 2009 #4

    Dick

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    dmin(0,2)<=dmin(0,1)+dmin(1,2). 1<=1+1. I think it does work.
     
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