\begin{definition}[Definition:Approximating Relation]
Let $L = \struct {S, \preceq}$ be an ordered set.
Let $\RR$ be a relation on $S$.
Then $\RR$ is an '''approximating relation''' on $S$ {{iff}}
:$\forall x \in S: x = \map \sup {x^\RR}$
where $x^\RR$ denotes the $\RR$-segment of $x$.
\end{definition}