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the distributive property
#4
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
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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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