Definition:Ordinal Sequence/Length

Definition

Let $\alpha$ be an ordinal.

Let $\theta$ be an ordinal sequence whose domain is $\alpha$.

Then $\alpha$ can be referred to as the length of $\theta$.

The length of $\theta$ can be denoted $\size \theta$.

Also see

• Definition:Length of Sequence

• Results about ordinal sequences can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $6$: Order Isomorphism and Transfinite Recursion: $\S 5$ Transfinite recursion theorems