# Category:Definitions/Total Orderings

This category contains definitions related to Total Orderings.
Related results can be found in Category:Total Orderings.

Let $\mathcal R \subseteq S \times S$ be a relation on a set $S$.

$\RR$ is a total ordering on $S$ if and only if:

$(1): \quad \RR$ is an ordering on $S$
$(2): \quad \RR$ is connected

That is, $\RR$ is an ordering with no non-comparable pairs:

$\forall x, y \in S: x \mathop \RR y \lor y \mathop \RR x$

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Definitions/Total Orderings"

The following 16 pages are in this category, out of 16 total.