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 between addition and multiplication bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/11/2011, 10:59 PM (03/11/2011, 10:07 PM)martin Wrote: (03/11/2011, 12:42 PM)bo198214 Wrote: For me it seems important that the curve t |-> a [t] b is smooth (or better analytic) for fixed a and b. I mean you define it on the interval [1,2], i.e. between addition and multiplication, and then you would continue it to the higher operations t>2 by a [t+1] (b+1) = a [t] ( a [t+1] b ) And then it would be interesting whether the curve is (infinitely) differentiable at t=2, t=3, etc. Of course it would between the endpoints, i.e. on (2,3) and (3,4), etc. IIRC, this is exactly what I tried to do, some three years ago or so... It never really worked out, though some sample graphs for 2 [4] x and 3 [4] x looked quite good. Hey Martin, we are not talking about the function f(x) = a [4] x but about the function g(x) = a [x] b. But you are right that we expect the same smoothness also for f(x), which is how Andrew Robbins came to his tetration extension. « Next Oldest | Next Newest »

 Messages In This Thread between addition and multiplication - by lloyd - 03/10/2011, 09:10 PM RE: between addition and multiplication - by lloyd - 03/10/2011, 10:51 PM RE: between addition and multiplication - by tommy1729 - 03/10/2011, 10:56 PM RE: between addition and multiplication - by tommy1729 - 03/10/2011, 10:58 PM RE: between addition and multiplication - by JmsNxn - 03/10/2011, 11:42 PM RE: between addition and multiplication - by lloyd - 03/11/2011, 12:35 AM RE: between addition and multiplication - by JmsNxn - 03/11/2011, 06:12 PM RE: between addition and multiplication - by lloyd - 03/14/2011, 05:33 PM RE: between addition and multiplication - by bo198214 - 03/11/2011, 12:42 PM RE: between addition and multiplication - by martin - 03/11/2011, 10:07 PM RE: between addition and multiplication - by bo198214 - 03/11/2011, 10:59 PM RE: between addition and multiplication - by martin - 03/12/2011, 09:22 AM RE: between addition and multiplication - by nuninho1980 - 03/14/2011, 05:04 PM RE: between addition and multiplication - by lloyd - 03/14/2011, 06:21 PM RE: between addition and multiplication - by nuninho1980 - 03/14/2011, 07:47 PM RE: between addition and multiplication - by lloyd - 03/14/2011, 07:49 PM RE: between addition and multiplication - by JmsNxn - 03/15/2011, 06:11 PM RE: between addition and multiplication - by tommy1729 - 03/15/2011, 10:22 PM RE: between addition and multiplication - by JmsNxn - 03/15/2011, 10:49 PM RE: between addition and multiplication - by lloyd - 03/15/2011, 11:21 PM RE: between addition and multiplication - by tommy1729 - 03/16/2011, 12:04 AM RE: between addition and multiplication - by tommy1729 - 03/16/2011, 12:18 AM RE: between addition and multiplication - by JmsNxn - 03/16/2011, 12:20 AM RE: between addition and multiplication - by lloyd - 03/16/2011, 02:35 AM RE: between addition and multiplication - by JmsNxn - 03/16/2011, 02:43 AM RE: between addition and multiplication - by lloyd - 03/16/2011, 05:16 PM RE: between addition and multiplication - by JmsNxn - 03/16/2011, 05:47 PM RE: between addition and multiplication - by lloyd - 03/16/2011, 07:13 PM

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