User blog comment:Edwin Shade/Understanding The Infinite/@comment-32213734-20171109192503

I noticed definition of Cantor normal form here differs from definition in Wikipedia article Ordinal arithmetic: here it it said that β1, β2, β3, ... βk are previously defined ordinal numbers (that is β1 is less than the ordinal itself), but in the Wikipedia article it is said: "The highest exponent β1 is called the degree of α, and satisfies β1 ≤ α".

Also, here it is said: "The ordinal known as "epsilon-nought" is the limit of Cantor Normal Form, and is equivalent to the smallest ordinal not representable in Cantor Normal Form". But in the Wikipedia article it is said: "Every ordinal number α can be uniquely written as..." then the Cantor Normal Form.

So, by the definition in Wikipedia, ε0 has Cantor Normal Form ωε0. Definition here is about "non-trivial where non-trivial means β1 < α when 0 < α."