James Knight Wrote:I am also pondering when in Knightation whether there a limit to how far back you can go like with logarithms. (ie you can't take the logarithm of zero. This would mean an asymptotic relationship for zeration and knightation. This might be something to look in to.
James
If You take always ln( mod ln(x)) when iterating back (change negative numbers into positive) You end up at -Omega (=-LambertW(1)=ln(LmabertW(1)) for all x in average and for all iterations in average , but for each particular x it depends whether it is (contains) e, e^(1/e), 1/e, -e etc. in some combinations (is expressable by) or not.
e.g. ((e^(-e))^e)^(1/e)))^e^(-e))^(-e)^(-e))) will definitely stop after certain number of ln(ln(ln( while e.g. x=2 might be iterable infinitely.
I have a thread about it next door.
Iterating logarithms until ln(Omega)=-Omega is reached
Ivars