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Topic: |R| > oo
Replies: 8   Last Post: Mar 6, 2013 10:55 PM

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Graham Cooper

Posts: 4,340
Registered: 5/20/10
Re: |R| > oo
Posted: Mar 5, 2013 2:59 AM
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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 ANTI-DIAGONAL function to support your claims it is
>
> > > > > > > > incomplete?
>
> > > > > > > > What is your anti-diagonal function?
>
> > > > > > > > Herc
>
> > > > > > > Do you not know how to construct the anti-diagonal given any list of reals?
>
> > > > > > Not with a halting Turing Machine no!
>
> > > > > Do you know what the definition of the anti-diagonal 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/blueprints-hyperreals


---------------------------------------

THERE ARE 2 CASES

A/ a FINITE ANTI-DIAGONAL FUNCTION
B/ an INFINITE CYPHER ANTI-DIAGONAL 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




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