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 Status of proofs bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/25/2007, 12:07 AM (This post was last modified: 08/25/2007, 12:12 AM by bo198214.) Daniel Wrote:bo198214 Wrote:Is Andrew's solution for bases$b\le e^{1/e}$ identical with the solution obtained by regular development at the lower fixed point?Can you clarify this comment please? If I correctly understood you then your approach was to develop the function $b^x=\exp_b(x)$ at a fixed point and then regularly iterate the function there $\exp_b^{\circ t}(x)$ and then define tetration as ${}^tb=\exp_b^{\circ t}(1)$. It quite looks (as I numerically verified in this post) as if this yields the same result as Andrew's approach (of course only for bases $b\le\eta=e^{1/e}$ because only there exists a real fixed point at all. The solution can also only applied to the lower fixed point (of the two fixed points of $b^x$ for $b<\eta$), because the other fixed point is not reachable from 1.) « Next Oldest | Next Newest »

 Messages In This Thread Status of proofs - by Daniel - 08/24/2007, 06:56 PM RE: Status of proofs - by bo198214 - 08/24/2007, 07:16 PM RE: Status of proofs - by bo198214 - 08/24/2007, 07:23 PM RE: Status of proofs - by Daniel - 08/24/2007, 11:09 PM RE: Status of proofs - by bo198214 - 08/25/2007, 12:07 AM RE: Status of proofs - by bo198214 - 08/27/2007, 08:54 AM RE: Status of proofs - by Gottfried - 08/24/2007, 10:06 PM RE: Status of proofs - by Daniel - 08/24/2007, 11:02 PM RE: Status of proofs - by Gottfried - 08/29/2007, 06:07 AM RE: Status of proofs - by andydude - 08/29/2007, 05:04 AM RE: Status of proofs - by tommy1729 - 07/20/2010, 10:02 PM RE: Status of proofs - by bo198214 - 07/21/2010, 03:08 AM RE: Status of proofs - by tommy1729 - 07/21/2010, 10:39 PM

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