11/10/2011, 02:09 AM

(11/10/2011, 01:20 AM)JmsNxn Wrote: [...]I guess it should just be acknowledged that if we want to analytically continue the Ackermann function, zeration doesn't come into play.On the contrary, if we ever manage to analytically continue the Ackermann function, I'd be very curious to find out what it does at the zeration level, if it's possible to continue it there. It may or may not match the max(a,b)+1 formula (I'm guessing it probably won't). The chances of this happening in our lifetime is slim, though... we have enough trouble already deciding which analytic continuation of tetration should be canonical, as this forum proves. To analytically continue over the Ackermann function would seem to require a continuation based on the canonical continuations of individual operations in the Grzegorczyk hierarchy. So if we can't even decide what is canonical, we aren't even ready to generalize across operations yet.