```Date: Jun 3, 2009 3:34 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Answer to Dik T. Winter

On 3 Jun., 05:34, Virgil <virg...@nowhere.com> wrote:> In article <KKn5F7....@cwi.nl>, "Dik T. Winter" <Dik.Win...@cwi.nl>> wrote:>> > In article> > <5df917e3-517f-4a38-b28b-363843496...@t21g2000yqi.googlegroups.com> WM> > <mueck...@rz.fh-augsburg.de> writes:> >  > You drop the completeness condition in certain cases but you assume it> >  > in case of Cantor's proof. That is cheating.>> > You again misunderstand the proof completely.  There is an assumption that> > a complete list is provided and that is proven false.>> As I understand the Cantor diagonal proof, the only assumption is that> whenever one is provided with a list then that list has to omit at least> one sequence. I do not think it was, in its original form, an indirect> proof as your statement seems to indicate.Cantor understood it as a proof by contradiction. "da wir sonst vordem Widerspruch stehen würden, daß ein Ding E0 sowohl Element von M,wie auch nicht Element von M wäre." But probably you know better.The only thing that is interesting here is that the same holds for thelist of all natural numbers. Give me a list of natural numbers and Iwill show you that it is incomplete.Of course you are not allowed to say: All n in N! That would be acontradiction, because there is no last n and consequently no chanceto check whether your list would contain all n in N. (And if you didso, then one could also say: All r in R. The contracdiction would beof same size.)Regards, WM
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