\begin{definition}[Definition:Producer of Dedekind Cut]
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 $\tuple {L, R}$ {{iff}}:
:$l \preceq \alpha$ for all $l \in L$
:$\alpha \preceq r$ for all $r \in R$.
\end{definition}