We never did resolve the question of which grows faster:
In this corner we have
Sequence 1 n^^n
1, 2^2, 3^3^3, 4^4^4^4, and so on.
And over here we have Sequence 2, defined recursively by
In short, we can define the second sequence as s(1) = 1; s(n) = n, followed by s(n-1) factorial signs.
Which sequence grows faster than the other??
We have many conflicting answers, and no decisive resolution; here was one idea .