Definition:Metric Space/Distance Function

Definition
Let $M = \left({A, d}\right)$ be a 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.

Also defined as
If $M = \left({A, d}\right)$ is a pseudometric space or quasimetric space, this definition still applies.

That is, a pseudometric and a quasimetric are also both found to be referred to in the literature as distance functions.

Also denoted as
Some authors use a variant of $d$ for a metric, for example $\eth$. Others use, for example, $\rho$.