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

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: Another AC anomaly?
Posted: Dec 19, 2009 8:17 AM
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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?
>
>  >                                            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.
>  >
>  > 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?

Regards, WM



Date Subject Author
11/23/09
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11/23/09
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Marshall
11/27/09
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11/27/09
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11/26/09
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11/26/09
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11/28/09
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11/26/09
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mueckenh@rz.fh-augsburg.de
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11/28/09
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11/29/09
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mueckenh@rz.fh-augsburg.de
11/29/09
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Virgil
11/29/09
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ross.finlayson@gmail.com
11/29/09
Read Re: Another AC anomaly?
Marshall
11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
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ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
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11/30/09
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Read Re: Another AC anomaly?
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11/27/09
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
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mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
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11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
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12/19/09
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12/7/09
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mueckenh@rz.fh-augsburg.de
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12/5/09
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12/1/09
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11/27/09
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11/27/09
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anonymous.rubbertube@yahoo.com
11/30/09
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11/27/09
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11/27/09
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11/27/09
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