Definition:Limit Ordinal

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Definition

An ordinal $\lambda$ is a limit ordinal if and only if it is neither the zero ordinal nor a successor ordinal.


Notation

The class of all nonlimit ordinals is sometimes denoted $K_I$, while the class of all limit ordinals is sometimes denoted $K_{II}$.


Also defined as

Some sources also consider the zero ordinal a limit ordinal.

It's a matter of taste.


Sources