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 Zeration = inconsistant ? GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 10/03/2014, 11:39 PM (This post was last modified: 10/03/2014, 11:53 PM by GFR.) (10/02/2014, 11:11 PM)tommy1729 Wrote: But what bothers me most is that zeration , unlike addition and multiplication does not have an inverse !!! a - b , a / b .............. Take the equations : a + b = c a = c - b a * b = c a = c/b max(a,b) + 1 = c a = max^-1(c - 1,b) ?? fail. tommy1729 As a matter of fact, Max-Plus algebra, applied to the 'Reals', is not a 'Field' but an 'Idempotent Semi-Ring', where a[max]b has some 'peculiarities': a[max](-oo) = (-oo)[max]a = a ; -oo is the 'unity element' a[max]a = a ; [max] is idempotent and there is NO max-inverse number. For zeration, this is only partially true. In fact a o (-oo) = (-oo) o a = a ; but: a o a = a + 2. We should discuss here the fact that Rubtsov thinks (and I agree) that zeration HAS an inverse operation, that he calls 'Deltation', producing a new set of numbers, called the 'Delta Numbers', which can be put in correlation with the log of negative numbers (multi-valued Complex numbers, but also ... transfinite extension of the 'Reals'). This would need a separate detailed discussion. A similar position is taken by Cesco Reale, with his definition of 'incrementation' and 'decrementation', giving an extension of the Reals that he calls 'Stigma-Reals'. Also to be seen. Regards! « 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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