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

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Graham Cooper

Posts: 4,344
Registered: 5/20/10
Re: The Diagonal Argument
Posted: Dec 27, 2012 9:37 PM
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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)



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