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Uniqueness Criterion for Tetration
#7
jaydfox Wrote:I'm not sure I follow why your solution is

The function is continuous, of course:



And for base e, the first derivative is continuous as well:



However, even at the second derivative, we begin to see problems:



For base e, we get a second derivative of 1 from the left, but 2 from the right. Due to the product rule, the second and higher derivatives will get quite complex, preventing a simple solution.

I see. I guess you are right.

Thanks for the correction.
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Messages In This Thread
Uniqueness Criterion for Tetration - by jaydfox - 08/09/2007, 07:01 AM
RE: Uniqueness Criterion for Tetration - by UVIR - 08/12/2007, 10:52 PM
RE: Uniqueness Criterion for Tetration - by UVIR - 08/13/2007, 01:33 PM

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