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
For every radix \(r\geq 2\), the congruence speed of tetration stabilizes at a positive constant for all bases \(a>1\) with \(\mathrm{rad}(r )\nmid a\) if and only if \(r\) is squarefree. (NNTDM 32(3), Appendix B)
