We need to show that the discrete metric satisfies the three properties of a metric:
a) Non-negativity: $d(x, y) \geq 0$ for all $x, y \in X$.
b) Identity of indiscernibles: $d(x, y) = 0$ if and only if $x = y$.
c) Triangle inequality: $d(x, z) \leq d(x,
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