# 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.

## Pages in category "Definitions/Ordinals"

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