Virgil
Posts:
4,479
Registered:
1/6/11
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Re: The Diagonal Argument
Posted:
Dec 27, 2012 7:03 PM
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In article
<dc67df4d-c740-4c07-b66d-24dc52f8ca59@pd8g2000pbc.googlegroups.com>,
Graham Cooper <grahamcooper7@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.
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