Definition:Metric Space/Distance Function

Definition
Let $M = \left({A, d}\right)$ be an metric space. The function $d: X \times X \to \R$ is referred to as the distance function on $X$ or simply distance.

Also known as
The distance function on a metric space $M$ is frequently referred to as the metric on $M$.

The two terms are used interchangeably on this website.