Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    StatusX

    User Avatar
    Homework Helper

    Apply the inequality to two segments in the same direction, each of length d<0.5.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook