User blog comment:Ubersketch/Hypernomial Hierarchy/@comment-35470197-20190604211432/@comment-35470197-20190605024155

> You pretty much missed the point of the whole thing. FSes aren't well defined for erdinals, but chances are, it works for hypernomials.

I am not talking about erdinals. In your definition of FS, you defined an FS for f(a), where a is a limit ordinal. It is not related to erdinal or hypermonomials.

Of course, I might be wrong, because I guessed undefined terminology in your blog post by myself. So could you write down the precise definition (not explanation) of "eldinal", "hypermonomial", and "H" in your context? In your explanation, "Hypermonomial" is defined by using "hypermonomial" without initial conditions, and hence is a circular logic. (I guessed that 0 and w are regarded as hypermonomial but you forgot to write so, or you were refering to other existing convention of "hypermonomial" outside your blog.) Also, "H" appearing in the explaation is undefined. In addition, what does "erdinal fundamental sequence" and "hypermonomial fundamental sequence" precisely mean?

> A property of hypernomials is that you can define an order relation like that of the ordinals, like so. a > b iff there exists n such that FS(a,n) > FS(b,n) or there is an ordinal x such that S(x) = a but S(x) =/= b

I think that it is not what you intend. According to your definition, you have S(0) > b for any b =/= S(0).