User blog comment:Wythagoras/All my stuff/@comment-7484840-20130715121715/@comment-5150073-20130715144933

Yes, any function can have corresponding ordinal, that's why I speak about order type of functions. If two functions f(n) and g(n) have order type alpha and beta respectively, and alpha<beta, then f(n) necessarily outgrows g(n).

Trying to define unbeatable function is like making an absolute infinity (the limit of all ordinals).