Definition:Densely Ordered

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Then $\struct {S, \preceq}$ is defined as densely ordered 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 $a \ne b$.