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+--- Thread: What are the different approaches of tetration? (/showthread.php?tid=1758)
What are the different approaches of tetration? - Shanghai46 - 05/31/2023
Thats the kind of question I'm always wandering. What are the kind of approaches into extending tetration, and what are the advantage 's and i' inconvenients of each? And what would be according to you the best one?
For example, mine could be described as a "limit ratio attractive ratio" method, with advantage to be easy and demonstrated mathematically.
So what are the others?
RE: What are the different approaches of tetration? - Daniel - 06/01/2023
Great question, in a sense answering that question is central to the Tetration Forum. I have asked that very question two or three times in the fifteen year history of the Forum. But at the moment understanding tetration is more about understanding the work of a number of individuals than the idea that anyone is sitting on a grand synthesis of all tetration techniques.
The following is a progression through the different levels of tetration research that I have seen a number of people make.
- Numerical simulation
- Algorithmic
- Complex tetration - power series, Schroeder's and Abel's equations, based on fixed points
- Aldrovandi, Helms - matrices
- Geisler - combinatorics
- Aldrovandi, Helms - matrices
- Dynamics - Kneser, Ecalle
- Real tetration - Trappmann, Kouznetsov, Paulsen, plus a number of members from this Forum.
RE: What are the different approaches of tetration? - Shanghai46 - 06/01/2023
(06/01/2023, 04:18 AM)Daniel Wrote: Great question, in a sense answering that question is central to the Tetration Forum. I have asked that very question two or three times in the fifteen year history of the Forum. But at the moment understanding tetration is more about understanding the work of a number of individuals than the idea that anyone is sitting on a grand synthesis of all tetration techniques.
The following is a progression through the different levels of tetration research that I have seen a number of people make.
- Numerical simulation
- Algorithmic
- Complex tetration - power series, Schroeder's and Abel's equations, based on fixed points
- Aldrovandi, Helms - matrices
- Geisler - combinatorics
- Dynamics - Kneser, Ecalle
- Real tetration - Trappmann, Kouznetsov, Paulsen, plus a number of members from this Forum.
The thing would be to actually gather all methods, list them, understanding their principle and driving their advantages and defaults.
Then idk, sending all that processed work to an institude of mathematics to once and for all solve that tertration problem.
Do you know anyone in the server who has a precise method for me to try gathering those?