Definition:Finite Ordinal

Definition
Let $\alpha$ be an ordinal.

Then $\alpha$ is said to be finite iff one of the following holds:


 * $\alpha = \varnothing$
 * $\alpha = \beta^+$ for some finite ordinal $\beta$

where $\varnothing$ denotes the empty set, and $\beta^+$ is the successor set of $\beta$.

Also see

 * Definition:Finite Set, which through the definition of $\N$ would be circular if used here.
 * Definition:Transfinite Ordinal