```Date: Jan 31, 2013 4:23 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 31 Jan., 10:04, William Hughes <wpihug...@gmail.com> wrote:> On Jan 31, 9:48 am, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>>> > On 30 Jan., 22:38, William Hughes <wpihug...@gmail.com> wrote:>> > > On Jan 30, 10:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > On 30 Jan., 22:14, William Hughes <wpihug...@gmail.com> wrote:>> > > > > On Jan 30, 6:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > > On 30 Jan., 12:32, William Hughes <wpihug...@gmail.com> wrote:>> > > > > > > On Jan 30, 12:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > > > > On 30 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:>> > > > > > > > > Summary.  We have agreed that>> > > > > > > > > For a potentially infinite list L, the> > > > > > > > > antidiagonal of L is not a line of L.>> > > > > > > Do you agree with the statement>> > > > > > > For a potentially infinite list, L,> > > > > > > of potentially infinite 0/1 sequences> > > > > > > the antidiagonal of L is not a line> > > > > > > of L>> > > > > > Yes, of course. We have a collection of which we can keep a general> > > > > > overview. And in finite sets (potential infinity is nothing but finity> > > > > > without an upper threshold) "for every" means the same as "for all".> > > > > > There is no place to hide.>> > > > > So now we have>> > > > > For a potentially infinite list, L,> > > > > of potentially infinite 0/1 sequences> > > > > the antidiagonal of L is not a line> > > > > of L>> > > > > Can a potentially infinite list, L,> > > > > of potentially infinite 0/1 sequences> > > > > have the property that every> > > > > potentially infinite 0/1 sequence> > > > > is a line of L?>> > > > Potential infinity is the opposite of completeness like "infinite" is> > > > the opposite of "finished". So *every* line number n would not imply> > > > *all* possible line numbers of the set |N defined by AxInf.>> > > This does not answer the question.  Please answer the question.->> > The question is not properly defined.> > Do you mean "every" in the potential sense of "all from 1 to n"? Or do> > you mean "every" in the sense of "all" of set theory?>> > The latter is wrong, the former is correct.> > (Note also every potentially infinite sequence only consist of finite> > initial segments.)>> Let L be the potentially infinite> list of natural numbers>> 1> 2> 3> ...>> Does L have the property that> every (in the sense of "all from 1 to n")> natural number is a line of L>Yes.Regards, WM
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