Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Virgil

Posts: 6,993
Registered: 1/6/11
Re: The Diagonal Argument
Posted: Dec 28, 2012 12:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.
--





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.