Definition:Distance/Sets/Real Numbers

Definition
Let $S, T$ be a subsets of the set of real numbers $\R$.

Let $x \in \R$ be a real number.

The distance between $x$ and $S$ is defined and annotated $\ds \map d {x, S} = \map {\inf_{y \mathop \in S} } {\map d {x, y} }$, where $\map d {x, y}$ is the distance between $x$ and $y$.

The distance between $S$ and $T$ is defined and annotated $\ds \map d {S, T} = \map {\inf_{\substack {x \mathop \in S \\ y \mathop \in T} } } {\map d {x, y} }$.

Also denoted as
Some sources write $\operatorname{dist}$ instead of $d$.