User blog comment:ArtismScrub/Generalizing the fast-growing hierarchy towards positive real heights/@comment-32876686-20180125203146/@comment-32783837-20180125212144

Ah, yes, I considered at some point defining between f-1 and  f0 like that, however, it wouldn't fit with the normal hierarchy.

I'm assuming that when iterating a function a non-integer function of times, it will work the same way, that is:  f (a-1)×frac(b) ( f a-1 b(b) )?

In which case, that WOULD work, if  f 0 were  f 1.