distance

[[concept]]

A metric or distance is a function $d : M \times M \to R$ that satisfies

This is part of the definition of a metric space.

functional analysis

Metric

If $X$ is a set then $d : X \times X \to [0, \infty)$ is a metric if

(identifiability) $d (x, y) = 0 ⟺ x = y$
(symmetry) $\forall x, y \in X, d (x, y) = d (y, x)$
(triangle inequality) $\forall x, y, z \in X, d (x, y) \leq d (x, z) + d (z, y)$

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