06/19/2009, 05:17 PM
(This post was last modified: 06/19/2009, 06:22 PM by Base-Acid Tetration.)
In your paper it says something like:
"There exists only one holomorphic superlogarithm with b>e^1/e that maps G biholomorphically to *some* region with upper and lower unbounded imaginary part"
That must mean that we still don't know WHAT region the superlogarithm must map G (the crescent moon thingy) to. So our different tetration methods might map G to different infinitely long strips of width 1. So the condition you proved cannot be a uniqueness condition!
Here's the problem, represented with very sloppy ascii art, with the "uniqueness condition":
"There exists only one holomorphic superlogarithm with b>e^1/e that maps G biholomorphically to *some* region with upper and lower unbounded imaginary part"
That must mean that we still don't know WHAT region the superlogarithm must map G (the crescent moon thingy) to. So our different tetration methods might map G to different infinitely long strips of width 1. So the condition you proved cannot be a uniqueness condition!
Here's the problem, represented with very sloppy ascii art, with the "uniqueness condition":
Code:
- it could be (groups of two bars represent the infinitely long strip):
||or \\ or... yeah, basically anything with width 1 that contains part of Re[z]=0 !
\\ \\
\\ ||
|| ||
|| ||
|| ||
// ||
// //
||or //