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 Change of base formula for Tetration andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 08/13/2007, 02:47 PM I'm going to re-write your equation in the form: ${}^{x}{a} = \lim_{n \rightarrow \infty} \log_a^{[n]}(\exp_b^{[n]}({}^{x+\mu_b(a)}{b}))$ Using this form of your equation, as $n \rightarrow \infty$ then $\exp_b^{[n]}(\cdots)$ becomes ${}^{\infty}b$ and $\log_a^{[n]}(\cdots)$ becomes ${}^{-\infty}a$. This then implies: ${}^{x}{a} = {}^{-\infty}a$ which is strictly not true. If you want to make a change-of-base formula for tetration, at least make one that is consistent. This one is not. I've spent a great deal of time looking for a change-of-base formula, and I'm convinced that one does not exist. It could be that I forgot something about the limit process, and the simplifications above do not occur, we'll have to investigate in more detail. Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:39 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:41 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 08:38 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 08:53 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 04:34 PM RE: Change of base formula for Tetration - by bo198214 - 08/12/2007, 06:39 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:00 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:09 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:30 PM RE: Change of base formula for Tetration - by andydude - 08/13/2007, 02:47 PM RE: Change of base formula for Tetration - by andydude - 08/13/2007, 02:58 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 06:34 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 07:31 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 07:37 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 08:03 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 08:23 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 08:32 PM RE: Change of base formula for Tetration - by bo198214 - 08/15/2007, 09:36 AM RE: Change of base formula for Tetration - by jaydfox - 08/15/2007, 10:15 AM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 03:42 PM RE: Change of base formula for Tetration - by jaydfox - 08/15/2007, 11:29 PM RE: Change of base formula for Tetration - by jaydfox - 08/16/2007, 09:21 PM RE: Change of base formula for Tetration - by bo198214 - 08/16/2007, 09:32 PM RE: Change of base formula for Tetration - by jaydfox - 08/16/2007, 09:49 PM RE: Change of base formula for Tetration - by bo198214 - 08/16/2007, 09:53 PM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 03:51 AM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 06:24 AM RE: Change of base formula for Tetration - by bo198214 - 08/31/2007, 09:03 AM RE: Change of base formula for Tetration - by tommy1729 - 05/03/2009, 10:20 PM RE: Change of base formula for Tetration - by sheldonison - 05/05/2009, 11:21 AM RE: Change of base formula for Tetration - by tommy1729 - 05/05/2009, 12:19 PM RE: Change of base formula for Tetration - by sheldonison - 05/05/2009, 01:29 PM RE: Change of base formula for Tetration - by bo198214 - 05/05/2009, 01:37 PM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 04:11 AM Convergence of Jay's change of base formula - by bo198214 - 08/15/2007, 09:00 PM RE: Parabolic Iteration - by jaydfox - 08/15/2007, 09:19 PM RE: Parabolic Iteration - by bo198214 - 08/15/2007, 09:30 PM RE: Parabolic Iteration - by jaydfox - 08/15/2007, 11:41 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 08:17 AM RE: Parabolic Iteration - by jaydfox - 08/16/2007, 05:51 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 06:40 PM RE: Parabolic Iteration - by jaydfox - 08/16/2007, 09:47 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 10:07 PM

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