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Zeration = inconsistant ?
#17
(10/03/2014, 11:39 PM)GFR Wrote:
(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!

Im skeptical about deltation.

regards

tommy1729
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

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