Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Zeration = inconsistant ?
#5



This is the Rubtsov's definition of Zeration.
It satisfies the distributivity.
Addition distributes over the addition (easy to see).

As I said before
Quote:Using a classic definition over the naturals (starting from the addition) leaves an opening for a non-trivial solution for zeration below the addition because if we try to define it starting from the higher Hos. (the addition) we have to use the cutoff subtraction (not defined if ).

This means that for the recursive definition of the hyperoperation sequence on the naturals we have an infinite ammount of functions that "models" Zeration (some are commutative!) and each of those contains the successor function: in other worlds, those models should behave as the successor function over a restricted subset of ).
the recursive definition of the hyperoperations over the naturals make us able to have alot of different solution for Zeration, the most interesting solutions are probably the ones definable via Max operator.

example:
Rubtsov's Zeration



Trappman's Zeration


Both are possible models of Zeration inside the Rubtsov-Romerio Hyperoperations Sequence.

Inside the classic sequence we could use



Those three solutions are related witht he max operator. We could call them "tropical solutions for Zeration" maybe.
MathStackExchange account:MphLee
Reply


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

Possibly Related Threads...
Thread Author Replies Views Last Post
  Zeration GFR 80 99,960 10/31/2016, 02:57 PM
Last Post: Stanislav
  Zeration reconsidered using plusation. tommy1729 1 2,847 10/23/2015, 03:39 PM
Last Post: MphLee
  Is this close to zeration ? tommy1729 0 1,930 03/30/2015, 11:34 PM
Last Post: tommy1729
  [2015] 4th Zeration from base change pentation tommy1729 5 5,543 03/29/2015, 05:47 PM
Last Post: tommy1729
  [2015] New zeration and matrix log ? tommy1729 1 3,042 03/24/2015, 07:07 AM
Last Post: marraco
  [2014] Inconsistant equation ? tommy1729 0 1,725 07/27/2014, 02:38 PM
Last Post: tommy1729
  base change inconsistant ? tommy1729 2 3,033 11/26/2012, 08:13 AM
Last Post: Nasser



Users browsing this thread: 1 Guest(s)