Metric

Metric

Definition 1. Given a nonempty set $X$, metric is a function $d: X \times X \rightarrow [0, \infty)$ such that $\forall x, y, z \in X$, the following hold:
(a) $d(x, y) = 0 \Longleftrightarrow x = y$
(b) $d(x, y) = d(y, x)$
(c) $d(x, z) \leq d(x, y) + d(y, z)$
Then $(X, d)$ is called a metric space.

위와 같은 성질을 만족하는 함수 $d$를 metric, 즉 거리라고 부른다.