User blog comment:Googleaarex/Factorial N-ational/@comment-24509095-20140921131516/@comment-25371339-20140921144238

Wait!

Recall function Q1(n).

Q1(n) = the largest number bigger than Q(n) that can be made with a function larger than Q(n), that can be based on Q(n), but CAN'T be an extension of Q(n).

For example, X(n) = Q(n)^(Q(n))^Q(n), where a^(n)^b = a^^^...^^^b with n arrows.

That grows larger than Q(n).