All three cases are identical except for the type of ordinal considered. They do not formally need to be considered separately, but in practice the proofs are typically so different as to require separate presentations. Zero is sometimes considered a limit ordinal and then may sometimes be treated in proofs in the same case as limit ordinals.
All three cases are identical except for the type of ordinal considered They do not formally need to be considered separately but in practice the proofs are typically so different as to require sep.arate presentations. Zero is sometimes c,onsidered a limit ordinal and then may sometimes be treated in proofs in the same case as limit ordinals.