User blog comment:Vel!/1+w/@comment-5982810-20141011201056

The rules do not prove that f_1+w(n) = f_w(n). 1+w is not a legal argument, therefore f_1+w(n) is simply undefined. I understand that there is all this ordinal theory already assumed on the part of the reader, but it's simply not there and it's an irrelevance anyway! All we need to concern ourselves is with the formal rules of evaluation. An isomorphism with ordinals is entirely secondary.

The feature that I identity as "rogue-types" in my FGH variant is a naturally occuring thing in formal systems. It also occurs in ExE, and can be found in other notations as well. Just because 2 delimiters have fundamental sequences with the same supremum does not mean they are the same ... deal with it.