\begin{definition}[Definition:Distance/Sets/Metric Spaces]
Let $M = \struct {A, d}$ be a metric space.
Let $x \in A$.
Let $S, T$ be subsets of $A$.
The '''distance between $x$ and $S$''' is defined and annotated $\ds \map d {x, S} = \inf_{y \mathop \in S} \paren {\map d {x, y} }$.
The '''distance between $S$ and $T$''' is defined and annotated $\ds \map d {S, T} = \inf_{\substack {x \mathop \in S \\ y \mathop \in T} } \paren {\map d {x, y} }$.
\end{definition}