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Re: Matheology § 203
Posted:
Feb 5, 2013 8:01 AM
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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 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
> 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 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.
Regards, WM
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