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 Exploring Pentation - Base e GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 02/06/2008, 03:01 PM I think that the infinite (contable) hyper-operation hierarchy y = b[s]x can (... probably!) be extended also to the ranks lower than zero. Nevertheless, please wait for the next thread on zeration. Concerning fractional (... rational) ranks, there is a possibility to define an operation between addition and multiplication (s=0.5 ?) apparently justified by the Gauss' Arithmetic-Geometric mean. We shall talk also of that. All this needs careful analysis and very precise demonstrations. All non-commutable hyper-operations imply two inverses (the left- and the right- inverse operation), that we can define as belonging to the root and to the log types. This is the case of all integer ranks s >= 3 (exponentiatoion). For the moment (...), we know that at ranks s=1 (addition) and s= 2 (multiplication), both commutable, these two inverse operations coincide. GFR « Next Oldest | Next Newest »

 Messages In This Thread Exploring Pentation - Base e - by jaydfox - 12/18/2007, 02:57 PM RE: Exploring Pentation - Base e - by andydude - 12/18/2007, 04:45 PM RE: Exploring Pentation - Base e - by jaydfox - 12/19/2007, 06:01 AM RE: Exploring Pentation - Base e - by Ivars - 01/28/2008, 11:01 AM RE: Exploring Pentation - Base e - by Ivars - 02/02/2008, 05:05 PM RE: Exploring Pentation - Base e - by Ivars - 02/02/2008, 10:50 PM RE: Exploring Pentation - Base e - by GFR - 02/02/2008, 11:01 PM RE: Exploring Pentation - Base e - by Ivars - 02/04/2008, 08:07 PM RE: Exploring Pentation - Base e - by quickfur - 02/22/2008, 12:21 AM RE: Exploring Pentation - Base e - by GFR - 02/04/2008, 09:19 PM RE: Exploring Pentation - Base e - by Ivars - 02/05/2008, 11:25 PM RE: Exploring Pentation - Base e - by GFR - 02/06/2008, 03:01 PM RE: Exploring Pentation - Base e - by Ivars - 02/06/2008, 06:23 PM RE: Exploring Pentation - Base e - by Ivars - 02/07/2008, 09:00 PM RE: Exploring Pentation - Base e - by Ivars - 02/07/2008, 09:30 PM RE: Exploring Pentation - Base e - by Ivars - 02/07/2008, 11:20 PM RE: Exploring Pentation - Base e - by Ivars - 02/08/2008, 10:32 AM RE: Exploring Pentation - Base e - by Ivars - 02/08/2008, 10:51 AM RE: Exploring Pentation - Base e - by Ivars - 02/08/2008, 10:56 AM RE: Exploring Pentation - Base e - by Ivars - 02/09/2008, 11:12 PM RE: Exploring Pentation - Base e - by Ivars - 02/15/2008, 08:24 PM RE: Exploring Pentation - Base e - by Ivars - 03/03/2008, 08:04 PM

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