Definition:Cantor Normal Form

Definition
Let $\omega$ denote the minimal infinite successor set.

Let $\langle a_i \rangle$ be a strictly decreasing finite sequence of ordinals.

Let $\langle n_i \rangle$ be a finite sequence of members of $\omega$.

Cantor normal form is of the form:


 * $\omega^{a_1} n_1 + \dots + \omega^{a_k} n_k$

In summation notation:


 * $\displaystyle \sum_{i \mathop = 1}^k \omega^{a_i} n_i$

Also see

 * Unique Representation of Ordinal as Sum shows that Cantor normal form exists for every ordinal and is unique.