(06/17/2022, 08:47 PM)Gottfried Wrote:(06/17/2022, 04:57 PM)Daniel Wrote: Gottfried claimed that there were about fifteen approaches to tetration. Could someone list the more important techniques? Any additional information would be great.
Hi Daniel - there must have been a lightning in the air... frizzeling the electronic of our silicium cpus... I know of a handful of methods, but I think my hand has only 5 fingers ... ;-))
For the list of techniques a curated list in the tetration-wiki were really good. Unfortunately I did never understand the methods from Kneser on upwards: no cauchy-integral (Kouznetsov), no theta mapping, no fourier series, no beta method, no 2sin, no ... no no no ... ;-) otherwise I really would like to make it my hobby to undertake a catalogue of methods.
Gottfried
Tommy claimed your comment, Daniel. Tommy claimed about 10 of his formula's converge. Spoiler alert, they don't. But they are attempts.
As Gottfried spoke, he meant that he can think of less than 5 solutions to tetration which are intrinsically unique. This is true. There is Kneser. There is Sheldon. There is Carlemann (programmed by Gottfried). There is Kouznetsov. There is Paulsen and Cowgill.
The Only one that is really proven, which I referred to is, Kneser and Paulsen and Cowgill. This was pointed out by Gottfried, who said that even Sheldon's fatou.gp isn't mathematically proven. Even though we all believe it is true, it is not proven.
This whole thread is a dumpster fire of misunderstandings.
There are not 15 different tetrations.
There are maybe 4 different algorithms for Kneser. There are 2 or 3 offshoots of credible avenues. This includes Peter Walker/Andy's matrix avenue. The beta method (which includes Tommy's Gaussian method), which is an alternative method of constructing Kneser. Or the beta method itself which is used in the Shell-Thron region to create arbitrary periods. And the list goes on.
But Tommy, it's kind of dumb to say 15 different tetrations. There are not 15 different tetrations. Those are 15 different posts you made. They do not hold up in any sense that Daniel is asking. And if they do, show some evidence of that.
What Gottfried is saying, Daniel. Is that there are about 4-5 tetration formulas that hold up to scrutiny. As algorithms. And as mathematical ideas. And myself and Tommy are excluded from that list.
I apologize, but what Tommy is saying is wrong. There are not "15 tetrations." But, yes, there are 15 TOMMY TETRATIONS.