Virgil
Posts:
4,491
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 5, 2013 5:37 PM
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In article
<3c52bc20-0b3f-4074-8307-387942aef034@z9g2000vbx.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> 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?
If not all natural numbers exist then some of them must not exist.
WHich ones?
> >
> > 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?
Unless every set is listable, there must be sets which are not listable,
so which is it in WMytheology? Is every set listable or are some sets
not listable?
>
> > 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
When WM says "we know" something, it does not mean that anyone other
than WM "knows" it.
> >
> > 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.
Then let u see you try to show it without appealing to any of those
"axioms" that only hold in WMytheology and not elsewhere.
And if your believe you have a better set theory than, say, ZF, produce
an axiom system for it of equal clarity to the one for ZF.
Note that, in ZF, if A is a set then the union of {A} with A is also a
set, but apparently this rule does not hold in any set theory in
WMytheology.
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