Let (X, d) be a metric space. Show that the metric d is continuous.

Question

Let (X, d) be a metric space. Show that the metric d is continuous.

A metric space is a pair (X, d), formed by a nonempty set X and a function d: X × X → R≥0, called the distance or metric function of X, such that

1. d (x, y) = 0 if and only if x = y,
2. d (x, y) = d (y, x) for all x, y ∈ X
3. d (x, y) ≤ d (x, z) + d (z, y) for all x, y, z ∈ X please help