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Re: R > oo
Posted:
Mar 5, 2013 2:59 AM


On Mar 5, 5:26 pm, Rupert <rupertmccal...@yahoo.com> wrote: > On Monday, March 4, 2013 9:52:32 PM UTC+1, Graham Cooper wrote: > > On Mar 5, 6:02 am, Rupert <rupertmccal...@yahoo.com> wrote: > > > > On Monday, March 4, 2013 7:56:07 PM UTC+1, Graham Cooper wrote: > > > > > On Mar 4, 6:33 pm, Rupert <rupertmccal...@yahoo.com> wrote: > > > > > > > > > > This post is incoherent dribble. > > > > > > > > > I showed a partial infinite list of reals. > > > > > > > > > 0.00.. > > > > > > > > > 0;00.. > > > > > > > > > .. > > > > > > > > > Do you have an ANTIDIAGONAL function to support your claims it is > > > > > > > > > incomplete? > > > > > > > > > What is your antidiagonal function? > > > > > > > > > Herc > > > > > > > > Do you not know how to construct the antidiagonal given any list of reals? > > > > > > > Not with a halting Turing Machine no! > > > > > > Do you know what the definition of the antidiagonal is, given any list of reals? > > > > > Is it computable? > > > > It's a function from infinite sequences of real numbers to real numbers. How would you define "computable" in that context? > > > Computable means there is a Turing Machine that performs the defined > > > operation and then halts. > > But Turing machines accept as input finite sequences of symbols from a finite alphabet. Whereas in this case the input is an infinite sequence of real numbers. So it doesn't make any sense. Unless maybe you are making a requirement that there should exist some language with a finite alphabet such that in that language you can code for the infinite sequence of real numbers by means of a finite sequence of symbols. This is what you have to elaborate on; how you propose to code for infinite sequences of real numbers by means of finite sequences of symbols. > >
It appears your Set Theory of Higher Cardinalities is all Non Computable then!
I have outlined a Theory of Hyperreals (essentially random noise digits although they have finite entropy)
http://tinyurl.com/blueprintshyperreals

THERE ARE 2 CASES
A/ a FINITE ANTIDIAGONAL FUNCTION B/ an INFINITE CYPHER ANTIDIAGONAL FUNCTION
...
FUNCTION ANTIDIAG( DIAGONAL ) { RETURN DIAGONAL + 0.111111111.... }
...
where + is simple digit wise successor
Then it would input a HYPERREAL DIAGONAL
(DIAGONAL doesn't appear on any computable row)
HYPERREAL DIAG + 0.1111111111... AD(DIAG)  HYPERREAL AD
i.e. the computable reals list is not missing any computable real.
So EITHER WAY
ANTIDIAG() is FINITE > no missing computable real ANTIDIAG() is INFINITE > no computable missing real
...
Any way I'm going to focus on Finite Logics for the time being, temporal, modal, agent, real world, ...
Infinite Loops in PROLOG are a hassle as it is!
Herc  www.BLoCKPROLOG.com



