# Category:Ordinals

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

Let $S$ be a set.

Let $\Epsilon \! \restriction_S$ be the restriction of the epsilon relation on $S$.

Then $S$ is an ordinal if and only if:

$S$ is a transitive set
$\Epsilon \! \restriction_S$ strictly well-orders $S$.