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Topic: Another AC anomaly?
Replies: 280   Last Post: Dec 27, 2009 3:53 PM

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Quaestor

Posts: 11
Registered: 8/22/09
Re: Another AC anomaly?
Posted: Dec 19, 2009 3:24 PM
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In article
<9ad63bf1-549b-4822-bf86-839dd7c64d58@j4g2000yqe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 18 Dez., 15:19, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > In article
> > <2cd3c08a-a072-4ef5-bc0b-f0aaa9126...@a21g2000yqc.googlegroups.com> WM
> > <mueck...@rz.fh-augsburg.de> writes:
> >  > On 17 Dez., 15:08, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> >  > > In article
> > <6a57309a-a136-430c-a718-e38518c65...@q16g2000vbc.googlegroups=
> >  > .com> WM <mueck...@rz.fh-augsburg.de> writes:
> >  > >  > On 16 Dez., 03:44, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> >  > >  > >  > ({1} U {1, 2} U {1, 2, 3} U ... = ({1} U {1, 2} U {1, 2, 3} U
> >  > >  > >  > U {1, 2, 3, ...}
> >  > >  >
> >  > >  > That is a matter of taste.
> >  > >
> >  > > No, it is a matter of convention.  In mathematics
> >  > >     a, b, c, ..., z
> >  > > means a, b, c, continue this way until you reach z.  But starting
> >  > >     {1}, {1, 2}, {1, 2, 3}
> >  > > and going on you never reach
> >  > >     {1, 2, 3, ...}
> >  >
> >  > That is true. Therefore it does not exist.
> >
> > That you can not get there step by step does not mean that it does not
> > exist.

>
> That you cannot get step by step to 1/0 does not mean that it does not
> exist?


That's what he said! That's what he said! He said that!
> >
> >  >                                            However, see Cantor,
> >  > collected works, p 445:
> >  > 0, 1, 2, 3, ... w_0, w_0 + 1, ..., gamma, ...,
> >  > He seems to reach far more.
> >
> > Right, he uses a convention that is no longer used.

>
> Wrong, it is used presently, for instance by myself.

> >
> >  > >  > > A sequence of paths is not a path.
> >  > >  >
> >  > >  > But a union of paths is.
> >  > >
> >  > > No.  Suppose we have the paths 0.000 and 0.100, what is their union?
> > And
> >  > > is it a path?
> >  >
> >  > No. But the union contains two paths.
> >
> > Wrong.  If we look at the paths as sets, they are sets of nodes.  Their
> > union is a set of nodes, not a set of paths.  And as a set of nodes we
> > can form from them seven different paths.

>
> Wrong. The nodes of two paths give exactly two paths. But as I already
> said, it is so silly to argue about the uncountability of the paths in
> the tree that I will stop it here.


Then WM has been silly for years. And will no doubt continue being silly.
At least as long as he fails to comprehend that Cantor's several proofs
of uncountability of some sets trumps WM's lack of proofs to the
contrary.

> >  > Let every finite path of every infinite path be mapped on the elements
> >  > of omega. That was simple.
> >
> > By your statements infinite paths do not exist.  But pray give such a
> > mapping.  Until now you have only asserted that such a mapping exists
> > without showing that.

>
> Do you accept the mapping from omega on SUM{k = 1 to n} 3*10^-k yields
> the infinite decimal expansion of 1/3?


It merely creates an infinite sequence of rationals or finite decimals
numerals whose numerical values converge to the number whose rational
numeral is "1/3".


Date Subject Author
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of Bentley College
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11/27/09
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11/27/09
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11/26/09
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11/29/09
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11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil

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