Change of base formula for Tetration
#24
jaydfox Wrote:How do you figure that it only works for a<b? It works for any two bases greater than eta, regardless of relative size.
Did you try it?
The sequence is decreasing for \( b<a \) (you can even prove this, similar to my proof that it increases for \( a<b \)) and after some steps it becomes negative and after that the logarithm yields complex numbers. Its quite obvious also from the experimentation.

And I would expect real numbers from a change of base, as the tetration is real for real arguments.
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Messages In This Thread
Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:39 AM
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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