Definition:Producer of Dedekind Cut

Definition
Let $\struct {S, \preceq}$ be a totally ordered set.

Let $S' \subseteq S$.

Let $\tuple {L, R}$ be a Dedekind cut of $S'$.

An $\alpha \in S$ is referred to as a producer of the $\tuple {L, R}$ $l \prec \alpha$ and $\alpha\ prec r$ for all $l \in L$ and for all $r \in R$.