User blog comment:B1mb0w/Fundamental Sequences/@comment-27513631-20160101022425

Basic mistake in Cantor's Normal Form section:

ω[n] = n, but ω = ω0+1, so ω[n] = (ω0+1)[n] = ω(0+1)[n] = ω0 = 1

You haven't specified when γ and δ need to be limits, and this combines with (γ+1)[n] to produce messy results.

Also, εζ_0 is well defined, and equal to ζ0. Most systems of fundamental sequences, where it matters, requires ordinals to be in a 'normal form', which force the ordinal to be represented in a specific, unique way. (e.g. Cantor's Normal Form only allows the base to be ω.)