Definition:Extending Operation

Definition
Let $S$ denote the class of all ordinal sequences.

Let $E: S \to S$ be a mapping whose behaviour is such that:


 * for all $\theta \in S$: if $\theta$ has length $\alpha$, then $\map E \theta$ has length $\alpha^+$

where $\alpha^+$ is the successor ordinal of $\alpha$.

Then $E$ is an extending operation.

That is, $E$ extends every ordinal sequence of length $\alpha$ to an ordinal sequence of length $\alpha^+$.