\begin{definition}[Definition:Densely Ordered/Subset]
Let $\struct {S, \preceq}$ be an ordered set.
A subset $T \subseteq S$ is said to be '''densely ordered in $\struct {S, \preceq}$''' {{iff}}:
:$\forall a, b \in S: a \prec b \implies \exists c \in T: a \prec c \prec b$
\end{definition}