User blog comment:Nayuta Ito/tetrational logarithm/@comment-1605058-20150731105254

I'm not sure what you are trying to say. $$\lim\limits_{n\rightarrow\infty}x\uparrow\uparrow n$$ in most cases doesn't exist, and it doesn't then make sense to say that it is equal to $$(y\uparrow)^n a$$, let alone that for this expression we would need $$n$$ to be fixed.