Date: Feb 5, 2013 8:01 AM
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:
> > 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 a
complete sequence, that means all terms with all their indices which
are 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
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
And we know that there is no line of the list that contains the
potentially infinite sequence of natural numbers or up to which this
is 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.