Virgil
Posts:
5,452
Registered:
1/6/11
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Re: Matheology � 238
Posted:
Apr 9, 2013 4:44 AM
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In article
<bab092d0-3095-4e87-881d-d8bcb4625155@cm2g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
>
> 2) Is there a difference between an infinite sequence of finite unions
> of elements and an infinite union of the same elements?
An infinite sequence of finite unions is still a sequence of sets, but
the infinite union is merely a set of objects which need not themselves
be sets at all, other than in such set theories as ZF where everything
is a set.
> >
> > No. [but note the fact that every element of the sequence
> > has property P does not mean the sequence has property P]
>
> In
> 0.1
> 0.11
> 0.111
> ...
> an infinite union is *in* the sequence and an infinite union is not in
> the sequence.
How does one form unions of things which are not sets?
>
> > Let D be the collection of all finite lines.
> >
> > Do you agree with
> >
> > If you remove the collection of all finite
> > lines from D there is nothing left.
>
> You have not yet answered my question which is necessary for me to
> know, in order what your collection is.
Why does it even have to be ordered at all? There is nothing in any set
theory that I am aware of that requires any set of more than one element
to have any specific ordering imposed on it at all.
Is the ordered set {1,a : 1 < a} and different AS A SET from the ordered
set {a,1 : 1 > a}, even though they have different orderings?
> Since every line is a finite
> union the collection contains infinite unions
It may contain infinitely many unions but does not contain any union of
infinitely many sets.
WM is, as usual, being deliberately ambiguous enough to confound clarity.
> Therefore I need to know
WM's need to know cannot be assuaged by anyone but WM himself learning
to think straight and use technical terms precisely rather than so
deliberately ambiguously.
--
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