18.099b Problem Set 4b Due: Thursday, March 11th (in class or before).

Let X be a set. Consider the map d : X × X → ℝ given by d(p, q) = 1 if p ≠ q and d(p, q) = 0 if p = q. This defines a metric on X, called the discrete metric.

Write a short exposé on the discrete metric: defining it, proving that it is a metric, and describing (with proof) the open, closed and compact sets. You are free to organize the material in whatever way you think best. Think of it as a tiny mathematical essay; it should be self-contained and flow smoothly. The exposé must be typeset in Tex.