```Date: Dec 21, 2009 8:23 AM
Author: Dik T. Winter
Subject: Re: Another AC anomaly?

In article <9ad63bf1-549b-4822-bf86-839dd7c64d58@j4g2000yqe.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes: > On 18 Dez., 15:19, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:... > >  > > 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?Indeed.  On the projective line (that precedes Cantor by quite some time asfar as I know) it does 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.But you are not a mathematician. > >  > 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.Darn, the paths 0.000 and 0.100 contain the following nodes:0.000 = {0., 0.0, 0.00, 0.000} and 0.100 = {0., 0.1, 0.10, 0.100}where a node is named by the path leading to it.  Their union containsthe following paths:       0., 0.0, 0.00, 0.000, 0.1, 0.10, 0.100and I count seven. > >  > 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?*What* mapping?  Do you mean from n in omega -> SUM...?  In that case theinfinite decimal expansion of 1/3 is unmapped.-- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
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