Definition:Densely Ordered

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 $$\forall a, b \in S: a \prec b \implies \exists c \in S: a \prec c \prec b$$.