Virgil
Posts:
4,661
Registered:
1/6/11
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Re: The Diagonal Argument
Posted:
Dec 28, 2012 12:18 AM
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In article
<ce500b53-1436-4f00-96d3-09a3ea673727@r10g2000pbd.googlegroups.com>,
Graham Cooper <grahamcooper7@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
There is nothing there close enough to sane to be correctable.
Cantor's so-called diagonal argument is about whether one can list all
functions from N to {m,w}, sometimes denoted by {m,w}^|N
Where a list of them would be a surjection from |N to {m,w}^|N
And Cantor showed why no such mapping can be surjective, there must
always be some member of {m,w}^|N for which there is no member of |N.
--
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