```Date: Jan 29, 2013 3:28 PM
Author: William Hughes
Subject: Re: Matheology § 203

On Jan 29, 3:35 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 29 Jan., 14:27, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>>>> > On Jan 29, 12:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 29 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:>> > > > To summarize>> > > >   For every natural number, n, the antidiagonal,d, of a list L> > > >   is not equal to the nth line of L>> > > > A statement WM has made.>> > > >    A) For every natural number n, P(n) is true.> > > >    implies> > > >    B) There does not exist a natural number n such that P(n) is> > > > false.>> > > > A statement WM has made.>> > > >    There does not exist a natural number n such that d is> > > >    equal to the nth line of L>> > > > A statement WM disputes>> > > I do not dispute this statement (as I erroneously had said yesterday,> > > when being in a hurry). I dispute that this statement implies the> > > statement:> > > d is not in one of all lines of the infinite list L>> > It does, however, imply that d is not> > of the the lines of the infinite list L.>> Here we have again the ambivalence required for set theory. No, your> statement is incorrect if "infinite" is used in the sense of completed> or actual,It is not.  No concept of "completed" is needed or used.It does, however, imply that d in not oneof the lines of the list LThis is turn implies.There is no list of binary sequences, L, withthe property that give any binary sequence, s,s is one of the lines of L.So we can divide collections into two groups.Those, like the collection of all rationalnumbers, that can be listed, and thoselike the real number that cannot.
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