User blog comment:Mh314159/Rank and Argument Strings/@comment-35470197-20190612025508

> the statement that I cannot reach it by recursing numbers, that I need ordinals, cannot be true

Exactly, it is not true. I guess that the claim was cast in order to explain that it is very difficult to reach such a level without understanding ordinals. Actually, ordinals are not directly used in the definition of many strong notations, but are in fact used in the idea to define them.

Anyway, good trial! I hope that you will soon reach that level.