User blog comment:Vel!/1+w/@comment-2033667-20141011215630

Reading your comment again, I think I better understand what you're trying to say. You are manipulating not ordinals, but strings that resemble ordinals (which I will now call "ordinal-like strings," or OLS's). However, you are abusing notation and terminology in several ways, the biggest one being calling your function "FGH" when it is not an ordinal hierarchy at all. Also, you appropriate ordinal notations and functions like lim, ^, phi, etc. without bothering to define them explicitly in terms of OLS's.

If you want to modify the fundamentals of the system, that is absolutely fine, but then you have to go about redefining everything from the ground up.