\begin{definition}[Definition:Densely Ordered]
Let $\struct {S, \preceq}$ be an ordered set.
Then $\struct {S, \preceq}$ is defined as '''densely ordered''' {{iff}} strictly between every two elements of $S$ there exists another element of $S$:
:$\forall a, b \in S: a \prec b \implies \exists c \in S: a \prec c \prec b$
where $a \prec b$ denotes that $a \preceq b$ but $a \ne b$.
\end{definition}