\begin{definition}[Definition:Cantor Normal Form]
Let $x$ be an ordinal.
The '''Cantor normal form''' of $x$ is an ordinal summation:
:$x = \omega^{a_1} n_1 + \dots + \omega^{a_k} n_k$
where:
:$k \in \N$ is a natural number
:$\omega$ is the minimal infinite successor set
:$\sequence {a_i}$ is a strictly decreasing finite sequence of ordinals.
:$\sequence {n_i}$ is a finite sequence of finite ordinals
In summation notation:
:$x = \ds \sum_{i \mathop = 1}^k \omega^{a_i} n_i$
{{explain|It still needs to be explained why, when used in pages that link to this, that the summation does not include the object $\omega$ in it, just some ordinal $x$ instead. It is unclear exactly what this definition means, because $\omega$, as currently defined on this website, is the Definition:Minimal Infinite Successor Set. Thus this definition appears to be saying: "Every ordinal (which of course has to include finite ones) can be expressed as finite sums of infinite ordinals." How can a finite number (an ordinal is a number, right?) be expressed as the sum of infinite numbers?}}
\end{definition}