# Category:Densely Ordered

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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 $a \ne b$.

## Subcategories

This category has only the following subcategory.

### R

## Pages in category "Densely Ordered"

The following 7 pages are in this category, out of 7 total.