If you are interested in the subject, you can take a look at this (unfortunately it's in Italian, but the meaning would be clear):
http://www.scribd.com/doc/77714896/The-l...dei-record
Using my notation, 2↑[k(k(1))]2>>Graham's number.
So, IMO, the best notation is the "slowest one" for the size of the numbers/operators we are talking about.
Obviously there are more "powerful" techniques to obtain super-large numbers in only a few steps (for example the fε0(n) based hierarchy, etc).
MR
http://www.scribd.com/doc/77714896/The-l...dei-record
Using my notation, 2↑[k(k(1))]2>>Graham's number.
So, IMO, the best notation is the "slowest one" for the size of the numbers/operators we are talking about.
Obviously there are more "powerful" techniques to obtain super-large numbers in only a few steps (for example the fε0(n) based hierarchy, etc).
MR
Let \(G(n)\) be a generic reverse-concatenated sequence. If \(G(1) \notin \{2, 3, 7\}\), then \(^{G(n)}G(n) \pmod {10^d}≡^{G({n+1})}G({n+1}) \pmod {10^d}\), \(\forall n \in \mathbb{N}-\{0\}\)
("La strana coda della serie n^n^...^n", p. 60).
("La strana coda della serie n^n^...^n", p. 60).
