Definition:Densely Ordered

Definition
Let $\left({S, \preceq}\right)$ be a totally ordered set.

Then $\left({S, \preceq}\right)$ is defined as close packed iff between every two elements of $S$ there exists another element of $S$.

That is, iff:
 * $\forall a, b \in S: a \prec b \implies \exists c \in S: a \prec c \prec b$