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Topic: The Diagonal Argument
Replies: 28   Last Post: Dec 29, 2012 12:11 AM

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ross.finlayson@gmail.com

Posts: 1,219
Registered: 2/15/09
Re: The Diagonal Argument
Posted: Dec 27, 2012 9:58 PM
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On Dec 27, 6:37 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Dec 28, 10:03 am, Virgil <vir...@ligriv.com> wrote:
>
>
>
>
>
>
>
>
>

> > In article
> > <dc67df4d-c740-4c07-b66d-24dc52f8c...@pd8g2000pbc.googlegroups.com>,
> >  Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > Try to Visualise an example.
>
> > > > L(x,y)
> > > > +---------------->
> > > > | 0. 2 3 4 5 6 7 ..
> > > > | 0. 9 8 7 6 5 5 ..
> > > > | 0. 1 2 3 1 2 3 ..
> > > > | 0. 9 8 9 8 9 8 ..
> > > > | 0. 6 5 6 5 6 5 ..
> > > > | 0. 5 6 5 6 5 6 ..
> > > > |
> > > > v

>
> > > > Now apply your FLIP(d) function to the whole plane
>
> > > > T(x,y)
> > > > +---------------->
> > > > | 0. 6 6 6 6 5 5 ..
> > > > | 0. 5 5 5 5 6 6 ..
> > > > | 0. 6 6 6 6 6 6 ..
> > > > | 0. 5 5 5 5 5 5 ..
> > > > | 0. 5 6 5 6 5 6 ..
> > > > | 0. 6 5 6 5 6 5 ..
> > > > |
> > > > v

>
> > > > Your claim is that is you take any path from
>
> > > > T(1,?)
> > > > T(2,?)
> > > > T(3,?)
> > > > ...

>
> > > > and repeat that process you must end up with an infinite string absent
> > > > from L?

>
> > > i.e.   ANTIDIAG = T(1,1) T(2,2) T(3,3) T(4,4) ...
>
> > > But Obviously  T(1,1) T(2,99) T(3,10110) T(4,7) ...
>
> > > is not provably absent from L.
>
> > > Remember Given a Stack of ESSAYS with every possible sentence written
> > > in every possible order, taking the 1st word of Essay 1, changing it,
> > > then the 2nd word of Essay 2, changing it, never produces a unique
> > > sentence or any original writing at all!  Similarly the ANTIDIAG
> > > PROCESS never conjures a Unique Digit Sequence!

>
> > > In fact, using a Symmetric FLIP(d) Function
>
> > >  L(x,y)
> > >  +---------------->
> > >  | 0. 2 3 4 5 6 7 ..
> > >  | 0. 9 8 7 6 5 5 ..
> > >  | 0. 1 2 3 1 2 3 ..
> > >  | 0. 9 8 9 8 9 8 ..
> > >  | 0. 6 5 6 5 6 5 ..
> > >  | 0. 5 6 5 6 5 6 ..
> > >  |
> > >  v

>
> > > FLIP(d) = 9-d
>
> > > Minor Problem with:
>
> > > 0.49999...
> > > <=FLIP=>
> > > 0.50000...

>
> > >  T(x,y) = FLIP(L(x,y))
> > >  +---------------->
> > >  | 0. 7 6 5 4 3 2 ..
> > >  | 0. 0 1 2 3 4 4 ..
> > >  | 0. 8 7 6 8 7 6 ..
> > >  | 0. 0 1 0 1 0 1 ..
> > >  | 0. 3 4 3 4 3 4 ..
> > >  | 0. 4 3 4 3 4 3 ..
> > >  |
> > >  v

>
> > > NOW  DIAGONAL(T)  is supposedly proven absent from L
>
> > > 0.716133..  NOT COUNTED??
>
> > > yet  if L is the Computable Reals  then
>
> > > T=L
>
> > > PROOF:  For every computable real there is another computable real for
> > > all digit changing functions.

>
> > > which proves the DIGIT FLIP Operation is a NULL OPERATION
> > > THERFORE  ANTIDIAGONAL(L) is no more provably absent from L than
> > > DIAGONAL(L).

>
> > > QED
>
> > > Herc
>
> > Not even as near to being right as WM is, and WM isn't near at all.
> > --

>
> then post your correction FOOL!
>
> Herc
> --
> P: If Halts(P) Then Loop Else Halt.
> is obviously a paradoxical program if Halts() exists.
>
> BUT IF IT WEREN'T NAMED P then it might not be:
>
> Q: If Halts(P) Then Loop Else Halt.
> is NOT paradoxical.
>
> ~ GEORGE GREEN (sci.logic)


Gray,

It's one thing to prove that said item isn't absent, another to prove
it's there.

I suggest you inspect EF, the antidiagonal is at the end.

This is as I proved EF and compositions of EF unique among functions
re the otherwise-uncountability of reals via functions from naturals,
and as well that the range satisfies properties of being the unit
interval of real numbers.

Then re Halts() I'd review the discussion of this last year on "Sketch
of a Disproof of Rice's Theorem."

Regards,

Ross Finlayson



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