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 Universal uniqueness criterion? Kouznetsov Fellow Posts: 151 Threads: 9 Joined: Apr 2008 09/30/2008, 02:16 AM bo198214 Wrote:... And that implies that $f(S)$, which contains an open non-empty set, always contains points $w$ such that $\lim_{n\to\infty} \exp^{\circ n}(w)\neq\infty$. ...Why do you think that this set is open? Wiki says: In metric topology and related fields of mathematics, a set U is called open if, intuitively speaking, starting from any point x in U one can move by a small amount in any direction and still be in the set U. In other words, the distance between any point x in U and the edge of U is always greater than zero. http://en.wikipedia.org/wiki/Open_set The small deviation from a point where the limit is finite allows to get (in the limit) so high walues as you want, because the right hand side of the plot of tetration is pretty scratched. I would replace "open non-empty set" to "non-empty set". « Next Oldest | Next Newest »

 Messages In This Thread Universal uniqueness criterion? - by bo198214 - 05/21/2008, 06:24 PM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 05:19 AM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 06:42 AM RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 11:25 AM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 03:11 PM RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 05:55 PM RE: Universal uniqueness criterion? - by bo198214 - 05/23/2008, 12:07 PM RE: Universal uniqueness criterion? - by Gottfried - 06/25/2008, 06:15 AM Uniqueness of analytic tetration - by Kouznetsov - 09/30/2008, 07:58 AM RE: Uniqueness of analytic tetration - by bo198214 - 09/30/2008, 08:17 AM RE: Universal uniqueness criterion? - by bo198214 - 10/04/2008, 11:19 PM RE: Universal uniqueness criterion? - by Kouznetsov - 10/05/2008, 12:22 AM RE: Universal uniqueness criterion? - by Kouznetsov - 06/19/2009, 08:45 AM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 02:04 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 02:51 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 04:19 PM RE: miner error found in paper - by bo198214 - 06/19/2009, 04:53 PM i don't think it will work - by Base-Acid Tetration - 06/19/2009, 05:17 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 06:25 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 06:27 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 07:59 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/20/2009, 02:01 PM RE: Universal uniqueness criterion? - by bo198214 - 06/20/2009, 02:10 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 02:39 PM RE: Universal uniqueness criterion? - by Kouznetsov - 06/23/2009, 05:46 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 09:28 PM RE: Universal uniqueness criterion? - by Kouznetsov - 06/24/2009, 05:02 AM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 07/04/2009, 11:17 PM RE: Universal uniqueness criterion? - by Kouznetsov - 07/05/2009, 08:28 AM RE: Universal uniqueness criterion? - by bo198214 - 07/05/2009, 06:54 PM

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