Definition:Densely Ordered

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

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


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

Also known as
The term close-packed is used interchangeably with densely ordered.

Also see

 * Dense-in-itself
 * Everywhere Dense
 * Nowhere Dense