10/24/2009, 09:54 AM

(10/24/2009, 08:27 AM)mike3 Wrote: The formulas are given for finite sequences of integers only. By the limit process, we could define it for infinite sequences, which would generate uncountably many new values. However I am not sure whether or not these points could be truly thought of as values of tetration, because there appear to be certain theorems (see this sci.math newsgroup posting and thread I had a few months ago) that say the analytic continuation of a complex function to a multivalued function must produce only countably many values: ...

Now that I read your article I revised my view on the number of branches, as there is an error contained in it which probably also Daniel Geisler was incorporating. I described my previous belief and the error in it here.

Applied to your model of branches in the limit formula I would just guess that the limit formula does not converge if you choose infinitely man branches different from the main branch.