# Definition:Non-Limit Ordinal

## Definition

An ordinal $\lambda$ is a non-limit ordinal if and only if it is not a limit ordinal.

That is, either the zero ordinal or a successor ordinal.

## Notation

The class of all non-limit 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.