Is R^2 a Metric Space with d(x,y)?

[pivoxa15]

Homework Statement

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?

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.

 

[pivoxa15]

Why?

 

[StatusX]

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