User blog comment:Vel!/1+w/@comment-2033667-20141011215630/@comment-5982810-20141011220800

Fair enough. Maybe it is misleading to those who don't know enough about FGH and ordinals. As far as

" 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."

That tells me you didn't read the articles very carefully. I may use that stuff, but there is nothing in the definition that expects you to know what phi(b,a) means, or a^b (actually I use e(a,b) ). It simply tells you, whatever OLS you have, here is how you determine it's fundamental sequence. How do you know a particular string is an OLS? Make sure you can construct it within the delimiter set. Not is an understanding of what ordinal notations mean not required, but I do define everything from the ground up. I say right off the bat that "w" is an index, and that w[n] = n, thatnI'd just like to clarify that I am primarily trying to help the reader understand some things which aren't clear in the definition. These things are not themselves part of the definition. The "definition" is usually provided at the end of an article with a large bold (often colored) title. So when I'm talking about the "definition" I use, I mean that. Everything else is ... in some sense ... fluff. It's not necessary to say a = a[0] U a[1] U a[2] U ..., to evaluate a[n]. Furthermore, this already assumes a[0], a[1] , a[2] must be sets, or else how could I take the union of them? But this needn't be considered in the definition. We don't need to treat the indexes as if they are sets. The only set that is important is the set of ALL indexes.