04/28/2010, 08:27 PM
(04/25/2010, 03:19 PM)tommy1729 Wrote: are all solutions to tetration consistant with x^^y = 1 for all x = 1 ?
There is one point that is different. (1^^-1) is undefined/indeterminate.
This is because we have a rule that states (x^^-1 == 0) for (almost) all x, and (1^^y == 1) for (almost) all y, and since both of them cannot be true, we leave it as undefined so that there is no conflict.
Also, to clarify what surprised me (I didn't say the right thing before), I wasn't so surprised about the limit to 1 as I was the limit to 0. Granted, the graph stops way before it gets to zero, but the indication is that it seems to have a limit of zero as well. This is interesting because (0^^y) is 0 for odd y and 1 for even y, and _undefined_ for all other y. This limit-to-zero may provide an insight that will allow (0^^y) to be defined for noninteger y.
Andrew Robbins