Definition:Limit Ordinal/Definition 1

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An ordinal $\lambda$ is a limit ordinal if and only if it is a limit element in the well-ordering on the class of all ordinals $\On$ that is the subset relation.


The class of all non-limit ordinals can be denoted $K_I$, while the class of all limit ordinals can be denoted $K_{II}$.

Also defined as

Some sources also consider the zero ordinal a limit ordinal.

It's a matter of taste.

Also see

  • Results about limit ordinals can be found here.