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Change of base formula for Tetration
#7
bo198214 Wrote:Then I dont understand how you compute .

This is one of the logarithmic laws:



Then, we know that , and that . As epsilon goes to 0, this is in fact exact.

Therefore, if B is (1+epsilon), then we can state:


Quote:It is always unclear what you mean by "exact" solution. Isnt everything exact in mathematics except if we say its approximate? A limit for example is exact if it exists regardless what difficulties we have with numeric computation.

I mean exact only when the limits I provide are taken to infinity. Otherwise, they are definitely approximate, just like I say the following value is "approximately" equal to e for a finite n:



Do you see the distinction? For numerical computation purposes, the solution will always be approximate. However, I still claim exactness when the specified limits are taken to infinity.
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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, 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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