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

pivoxa15
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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.
 
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Why?
 
Apply the inequality to two segments in the same direction, each of length d<0.5.
 

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