08/30/2009, 04:29 PM
(08/30/2009, 04:32 AM)bo198214 Wrote: If they are equal to regular tetration how do they know how to choose the right (lower) fixed point?
This is a really good question. For some reason, I haven't really understood the dependence on the fixed point. I think I remember that if two fixed points are complex conjugates of each other, then the resulting tetrations will also be conjugate, but this is just a consequence of assuming analytic tetration (all analytic functions have this property). In the real case (1 < b < eta), I don't see any reason a priori why the resulting tetrations would be different, and my intuition would even want to believe that they are the same, for example that 2 and 4 should produce the same tetrations for b=sqrt(2). Maybe this intuition is wrong, but if it is, then could you point me to the threads in which we talk about this?