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A metric space?

  1. Sep 17, 2007 #1
    1. The problem statement, all variables and given/known data
    In R^2, define d(x,y)=smallest integer greater or equal to usual distance between x and y. Is d a metric for R^2?

    3. The attempt at a solution
    All is left is to show the triangle inequality is satisfied. Since the distances are rounded upwards I'd say yes.
  2. jcsd
  3. Sep 17, 2007 #2
  4. Sep 17, 2007 #3


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    Homework Helper

    Apply the inequality to two segments in the same direction, each of length d<0.5.
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