# Definition:Limit Ordinal

## Definition

### Definition 1

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.

### Definition 2

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 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.