A metric space?

1. Sep 17, 2007

pivoxa15

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. Sep 17, 2007

pivoxa15

Why?

3. Sep 17, 2007

StatusX

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