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 Zeration tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 03/21/2015, 11:11 PM Not that I have become a " believer " but apart from a[0]b = max(a,b) + 1 reference : {max,+} algebra , linear algebra. a[0]b = ln( exp(a) + exp(b) ) reference : Bennet Hyperoperations, homomorphic defined operations and Tommy's distributive property. Another thing makes sense , and will probably lead to the above 2 ... but if not that would be intresting ( I doubt it ! ) : Rethinking : what is required for an operator [q] such that a[q]b = b[q]a and this is somehow related to iterations ? Probably this equation : Let N be a " neutral element " as a function of q. Call this N_q. then a[q]b = b[q]a implies : f and g are some function : f^[a - N_q](N_q[q]b) = g^[b - N_q](N_q[q]a) that makes sense ! example [q] = + a+b = b+a "add+1"^[a - 0](0+b) = "add+1"^[b - 0](0+a) example [q] = * a*b = b*a "add+b"^[a-1](1*b) = "add+a"^[b-1](1*a) However notice that an expression like f^[a - oo](...) does not make sense as a nonconstant function. Also combining " all nice properties " seems impossible for zeration. For instance max(a,b)+1 is not an analytic function. Or a^^b =/= b^^a ... regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Zeration - by GFR - 02/14/2008, 06:38 PM RE: Zeration - by Ivars - 02/14/2008, 08:10 PM RE: Zeration - by GFR - 02/14/2008, 10:41 PM RE: Zeration - by mathamateur - 07/30/2009, 06:31 AM RE: Zeration - by Ivars - 02/21/2008, 07:22 PM RE: Zeration - by quickfur - 02/21/2008, 09:34 PM RE: Zeration - by bo198214 - 02/21/2008, 10:18 PM RE: Zeration - by bo198214 - 02/21/2008, 10:25 PM RE: Zeration - by quickfur - 02/21/2008, 11:04 PM RE: Zeration - by quickfur - 02/21/2008, 11:12 PM RE: Zeration - by KAR - 02/21/2008, 11:04 PM RE: Zeration - by quickfur - 02/21/2008, 11:52 PM RE: Zeration - by GFR - 02/24/2008, 12:39 AM RE: Zeration - by Ivars - 02/24/2008, 02:50 PM RE: Zeration - by marraco - 03/20/2015, 09:59 PM RE: Zeration - by bo198214 - 02/24/2008, 11:02 AM RE: Zeration - by GFR - 03/19/2008, 12:40 PM Zeration - My Research / Investigation - by James Knight - 03/25/2008, 08:28 AM RE: Zeration - My Research / Investigation - by bo198214 - 03/25/2008, 09:09 AM More on Zeration - by James Knight - 03/25/2008, 03:44 PM Exponential Laws - New Zeration Law - by James Knight - 03/25/2008, 07:48 PM Delta Numbers As HyperReals - by James Knight - 03/26/2008, 12:50 AM RE: Delta Numbers As HyperReals - by Ivars - 03/26/2008, 12:15 PM RE: Zeration - by GFR - 03/26/2008, 12:22 AM RE: Zeration - by GFR - 04/05/2008, 08:58 PM RE: Zeration - by Igor M - 01/14/2009, 04:04 PM RE: Zeration - by bo198214 - 01/20/2009, 09:59 PM RE: Zeration - by 73939 - 07/05/2010, 12:00 AM RE: Zeration - by bo198214 - 07/05/2010, 07:37 AM RE: Zeration - by brangelito - 07/20/2010, 05:51 PM RE: Zeration - by bo198214 - 07/21/2010, 02:58 AM RE: Zeration - by JmsNxn - 11/09/2011, 01:40 AM RE: Zeration - by quickfur - 11/09/2011, 04:15 AM RE: Zeration - by JmsNxn - 11/10/2011, 01:20 AM RE: Zeration - by quickfur - 11/10/2011, 02:09 AM RE: Zeration - by marraco - 03/20/2015, 09:44 AM RE: Zeration - by marraco - 03/20/2015, 10:41 PM RE: Zeration - by marraco - 03/21/2015, 12:35 AM RE: Zeration - by marraco - 03/21/2015, 01:44 AM RE: Zeration - by marraco - 03/21/2015, 04:10 AM RE: Zeration - by MphLee - 03/21/2015, 11:53 AM RE: Zeration - by marraco - 03/23/2015, 07:58 AM RE: Zeration - by tommy1729 - 03/21/2015, 11:11 PM RE: Zeration - by marraco - 03/23/2015, 08:05 AM RE: Zeration - by marraco - 03/24/2015, 11:29 AM RE: Zeration - by MphLee - 03/23/2015, 09:00 AM RE: Zeration - by marraco - 03/23/2015, 01:39 PM RE: Zeration - by MphLee - 03/23/2015, 02:31 PM RE: Zeration - by Stanislav - 05/28/2015, 11:12 PM RE: Zeration - by marraco - 05/29/2015, 01:33 AM RE: Zeration - by Stanislav - 05/29/2015, 09:06 PM RE: Zeration - by MphLee - 06/03/2015, 01:40 PM RE: Zeration - by Stanislav - 06/04/2015, 06:44 AM RE: Zeration - by marraco - 06/04/2015, 08:44 PM RE: Zeration - by MphLee - 06/05/2015, 09:10 PM RE: Zeration - by Stanislav - 09/09/2015, 10:04 PM RE: Zeration - by Stanislav - 10/31/2016, 02:57 PM

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