```Date: Feb 5, 2013 8:01 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 5 Feb., 12:17, William Hughes <wpihug...@gmail.com> wrote:> On Feb 5, 10:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:> <snip>>> > So "there is no list of X" is> > true for every potentially infinite set.>> And so it goes.  Now there is no list> of |N.Now? Why should there ever have been a complete list, that means acomplete sequence, that means all terms with all their indices whichare all natural numbers which do not exist?>> So ends this round.  It has> taken 100 posts to get WM to> admit that different potentially> infinite sets have different> listability.Where had I conceded the complete existence of a list?> It would take another> 100 posts to get him to admit> that he admitted it.>> We now know> that the potentially infinite> series 0.111...>> is not a single line of the list>> 0.1000...> 0.11000...> 0.111000...> ...And we know that there is no line of the list that contains thepotentially infinite sequence of natural numbers or up to which thisis contained in the list.>> More importantly, we have learned that> we can use induction to show "every"> and that "every n -> P(n)" is equivalent> to "there is no m such that ~P(m)"> So we do not need to resort to "all"> to show something does not exist.Of course, that is true. For instance we can show that no list exists,that contains, as indices, all natural numbers.Regards, WM
```