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 the distributive property tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 05/23/2014, 11:12 PM More precisely : Uniqueness or at least a strong condition : Let B2 > B1 > e^(1/e). Base independance : r > 0 Define for base C : exp_C(z) = c^z a [r]_C b = b [r]_C a = exp_C^[r]( exp_C^[-r](a) + exp_C^[-r](b) ) Conjecture : a [r]_B2 b = b [r]_B2 a = exp_B2^[r]( exp_B2^[-r](a) + exp_B2^[-r](b) ) = a [r]_B1 b = b [r]_B1 a = exp_B1^[r]( exp_B1^[-r](a) + exp_B1^[-r](b) ) Or simply : a [r]_B2 b = a [r]_B1 b. Remark : its known to be true for r a positive integer. (it fails for r = -1 though ) Unfortunately I lost some data concerning this idea. So if you see it mentioned here before , plz let me know. I am also intrested in other " base independance " equations. https://sites.google.com/site/tommy1729/...e-property regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread the distributive property - by tommy1729 - 09/25/2010, 12:05 AM RE: the distributive property - by tommy1729 - 09/28/2010, 12:22 PM RE: the distributive property - by tommy1729 - 10/13/2010, 11:07 PM RE: the distributive property - by tommy1729 - 05/23/2014, 11:12 PM RE: the distributive property - by MphLee - 05/24/2014, 09:46 AM RE: the distributive property - by tommy1729 - 05/25/2014, 12:16 AM RE: the distributive property - by MphLee - 05/25/2014, 09:35 AM RE: the distributive property - by tommy1729 - 05/26/2014, 11:37 PM RE: the distributive property - by MphLee - 05/27/2014, 07:43 AM RE: the distributive property - by tommy1729 - 05/27/2014, 12:23 PM RE: the distributive property - by MphLee - 05/27/2014, 12:46 PM RE: the distributive property - by tommy1729 - 05/27/2014, 10:49 PM RE: the distributive property - by andydude - 05/27/2014, 07:45 PM RE: the distributive property - by MphLee - 05/27/2014, 08:22 PM RE: the distributive property - by tommy1729 - 05/27/2014, 10:55 PM RE: the distributive property - by MphLee - 06/06/2014, 09:56 AM RE: the distributive property - by tommy1729 - 06/06/2014, 11:56 AM RE: the distributive property - by MphLee - 06/06/2014, 12:09 PM

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