User blog comment:Ubersketch/Homomorphism between Cantor's normal form of finite degree and primitive sequence system/@comment-35470197-20190809223713/@comment-35470197-20190812050042

Oh, I did not know that shocking episode... Although I do not understand his intension, I strongly believe that people should give sufficient credits for the orignal creators in order to make the community sound and more matured.

I agree with the consistency of a standard notation for ordinals. Baton-passing to another notation at the limit should be accepted only when the latter one is a precise extension of the former one in the sense that the same expression corresponds to the same ordinal.

I think that the point to argue is to what extent we need a standard notation. If people in this community rarely worked on ordinal beyond an ordinal X, then we might not need an ordinal notation beyond X. If we believe that majority of people will soon go beyond ordinals beyond X in the future, then we need a stronger notation for the standard. Even if we do not expect it, it might be good to use a stronger one in order to clarify ordinals beyond their understanding.

Maybe X is something like ψ(Ω_ω) for the current community, because I have never seen a completely well-defined large number which has been verified to go beyond that level other than variants of BMS this year. Moreover, many of table-based analysts are inactive now, and hence there are few opportunity to see ordinals beyond it in this community.

> How can UNOCF have "infinite loops" when it was never defined properly?

In the original "exlanation" by the creator, UNOCF beyond ε_0 is supposed to be expanded using an f function. A candicate of the f function is explicitly declared, and the algorithm using it makes sense. Then we can argue the existence of infinite loops. I agree that it has never been defined properly. At least, I can say that the "explanation" itself is inconsistent.

The phrase "infinite loop" might not be appropriate for such intuition-based ill-defined notation, but I sometimes use it in order to explain people who believe that it "works" without any formal definition, because telling that it is ill-defined because of the lack of the formal definition is not effective for such ones. For those, explaining that it has infinite loops is more "understandable".