\begin{definition}[Definition:Metric Space/Distance Function]
Let $\struct {A, d}$ be a metric space.
The mapping $d: A \times A \to \R$ is referred to as a '''distance function on $A$''' or simply '''distance'''.
Here, $d: A \times A \to \R$ is a real-valued function satisfying the metric space axioms:
{{:Axiom:Metric Space Axioms}}
\end{definition}