Category:Densely Ordered

This category contains results about Densely Ordered.
Definitions specific to this category can be found in Definitions/Densely Ordered.

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

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