User blog comment:MilkyWay90/Not-Registered Users, tell your Googology ideas in the comments/@comment-2601:142:2:EC49:247C:A73D:AD4A:5ED9-20180803125948/@comment-30754445-20180803151737

This notation doesn't have a limit at all, because you can define  to be as large as you like. For example, there's nothing to stop you from defining <5,n> = BB(n) or Rayo(n) or whatever else you wish. Or if you prefer a more natural progression: <5,n> could get you to zeta-0, <6,n> to phi(w,0), <7,n> to gamma-0 and so on... you'll still run out of known ordinals way before you reach (say) <100,n>.

Unfortunately, this is also the weakness of the notation, because it doesn't really do anything(*). You're just choosing arbitrary functions for , so the strength of the notation comes solely from the functions you're "borrowing".

(*) to be precise, the notation does add a single factorial-like recursion to the borrowed functions, but as you've correctly pointed out in your own estimations, the resulting effect is negligable.