Definition:Distance from Subset

Definition
Let $S$ be a subset 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 $\displaystyle d \left({x, S}\right) = \inf_{y \in S} \left({d \left({x, y}\right)}\right)$, where $d \left({x, y}\right)$ is the distance between $x$ and $y$.