Category:Definitions/Ordinals

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

$\alpha$ is an ordinal if and only if it fulfils the following conditions:

$(1)$	$:$	$\alpha$ is a transitive set
$(2)$	$:$	the epsilon relation is connected on $\alpha$:	$\ds \forall x, y \in \alpha: x \ne y \implies x \in y \lor y \in x $
$(3)$	$:$	$\alpha$ is well-founded.

Subcategories

This category has the following 3 subcategories, out of 3 total.

The following 30 pages are in this category, out of 30 total.

\((1)\)	$:$	$\alpha$ is a transitive set
\((2)\)	$:$	the epsilon relation is connected on $\alpha$:	\(\ds \forall x, y \in \alpha: x \ne y \implies x \in y \lor y \in x \)
\((3)\)	$:$	$\alpha$ is well-founded.