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 Zeration = inconsistant ? tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 10/02/2014, 10:58 PM It feels a bit strange ... A so called new concept " zeration " being almost equivalent to max[a,b]. Max[a,b] does not seem so intresting as a function. Max[12,100] = Max[13,100] = Max[91,100] Nothing special. zeration also still seems undefined or inconsistant for complex arguments. (15 + 13 i) [0] (- 41 +91 i) = ?? Consider Trapmann's solution : Max(a+2,b+1) This fails to be commutative ! Also Max does not have AN INTRESTING DERIVATIVE. Also iterations of max are usually not intresting. So , no complex numbers , no intresting calculus , no intresting dynamics. Also there is not much algebra or geometry about Max. Max+ algebra being a big exception. It seems tetration is more intresting than zeration. Zeration seems to loose properties rather then to gain ? A possible solution to that is finding intresting properties afterall for max or finding another zeration. Or ... Finding addional must-have properties. 1) commutative and distributive solution : max(a,b) + kroneckerdelta(a,b) + 1 Notice this is not (even) differentiable near a = b. Can we do better ? Im sure there are many nice algorithms that use max. ( even without max+ algebra ) Maybe one of those could help us out. --- Assume we agree on zeration(a,b) = max(a,b) + kroneckerdelta(a,b) + 1. What would then be the next question ?? " -1-ation " ? abel functions / superfunctions of zeration ? numerical methods based on zeration ? ( not equal to those from max+ algebra ofcourse ... remember we want to talk about NEW things right ? ) regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

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