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 Infinite tetration and superroot of infinitesimal Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/10/2008, 08:33 AM (This post was last modified: 05/10/2008, 02:14 PM by Ivars.) I have stumbled upon Time calculus while searching for substructures of infinitesimals and how to include time in mathematics. I thought it might give a handle on infinitesimals, since, how I understand, it, structureless linear infinitesimal h->0 in derivative definition is replaced in general case by graininess $\mu(t) ->0$ to obtain normal continuous derivative. That means that infinite tetration etc of infinitesimal can be written(?): lim $\mu(t)->0$: $\mu(t) [4]\infty$ And superroot :lim $\mu(t)->0$: $q(t)^{q(t)}= \mu(t)$ And self root: lim $\mu(t)->0$: $\mu(t)^{1/\mu(t)}$ The limit may depend on how $\mu$ depends on t since it is not obvious what will happen faster- tetration or changes in $\mu(t)$. Gut feeling is, these speeds may be comparable. The next question is, what will happen with this tetration and time calculus if $\mu(t)$ itself is hyperoperation? for example, $\mu(t) = b[4]t$ ? or $\mu(t) = t[4]\infty$? Or $\mu(t) = t[x]y$? And generally, hyperoperations in time scales might be interesting. Please point out obvious mistakes. Thank You in advance, Ivars « Next Oldest | Next Newest »

 Messages In This Thread Infinite tetration and superroot of infinitesimal - by Ivars - 12/16/2007, 06:02 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/17/2007, 02:27 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/18/2007, 02:59 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/19/2007, 08:42 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/19/2007, 04:03 PM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/19/2007, 06:29 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/19/2007, 08:55 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/20/2007, 08:23 AM RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/20/2007, 06:31 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/20/2007, 03:16 AM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/20/2007, 07:25 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/20/2007, 09:02 PM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/20/2007, 09:08 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/20/2007, 09:50 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/21/2007, 02:08 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/21/2007, 05:49 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/21/2007, 08:06 PM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/21/2007, 08:40 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/21/2007, 10:41 PM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/21/2007, 11:00 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/24/2007, 09:56 AM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/24/2007, 04:40 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/25/2007, 09:31 AM RE: Infinite tetration and superroot of infinitesimal - by andydude - 12/25/2007, 06:46 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/25/2007, 09:37 PM RE: Infinite tetration and superroot of infinitesimal - by jaydfox - 12/26/2007, 09:27 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/04/2008, 06:51 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/04/2008, 07:08 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/04/2008, 09:48 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/05/2008, 07:37 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/05/2008, 07:49 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/05/2008, 10:30 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/06/2008, 01:10 AM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/06/2008, 09:42 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/06/2008, 04:54 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/06/2008, 09:26 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/28/2007, 12:31 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/02/2008, 08:56 AM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/02/2008, 10:34 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/02/2008, 11:47 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/05/2008, 09:38 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/07/2008, 10:04 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/08/2008, 08:28 AM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/08/2008, 08:52 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/08/2008, 03:44 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/09/2008, 12:50 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/09/2008, 01:53 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/08/2008, 03:41 PM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/08/2008, 11:44 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/10/2008, 09:19 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/13/2008, 01:14 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/15/2008, 01:09 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/23/2008, 11:25 AM RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/25/2008, 10:52 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/23/2008, 05:13 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/23/2008, 07:52 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/23/2008, 09:22 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/24/2008, 03:44 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/25/2008, 03:13 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/25/2008, 11:36 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/26/2008, 02:13 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/26/2008, 04:01 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/27/2008, 01:03 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/27/2008, 12:24 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/27/2008, 06:56 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/27/2008, 08:51 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/28/2008, 02:25 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/28/2008, 03:36 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/28/2008, 09:49 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/28/2008, 10:29 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/30/2008, 09:56 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/30/2008, 04:09 PM RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 01/30/2008, 05:09 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/30/2008, 07:28 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/30/2008, 08:21 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/31/2008, 07:41 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/31/2008, 11:13 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/31/2008, 03:56 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 01/31/2008, 05:06 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/01/2008, 07:42 AM RE: Infinite tetration and superroot of infinitesimal - by GFR - 02/01/2008, 10:31 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/01/2008, 11:14 AM RE: Infinite tetration and superroot of infinitesimal - by GFR - 02/01/2008, 08:56 PM RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 02/01/2008, 09:29 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/01/2008, 10:00 PM RE: Infinite tetration and superroot of infinitesimal - by GFR - 02/02/2008, 03:31 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/05/2008, 10:58 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/06/2008, 07:43 PM RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 02/26/2008, 09:26 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/26/2008, 09:31 PM RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 02/26/2008, 10:23 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/27/2008, 09:36 AM RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 02/27/2008, 03:14 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 02/27/2008, 09:00 PM RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 03/13/2008, 08:30 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 04/05/2008, 06:42 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 05/10/2008, 08:33 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 06/27/2008, 04:51 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 07/04/2008, 07:02 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 07/04/2008, 09:01 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 07/05/2008, 08:12 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 10/16/2008, 10:39 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 07/05/2008, 11:26 AM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 07/10/2008, 12:26 PM RE: Infinite tetration and superroot of infinitesimal - by Ivars - 07/11/2008, 09:27 AM

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