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Topic: Matheology � 258
Replies: 53   Last Post: May 11, 2013 10:07 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 258
Posted: May 7, 2013 4:56 PM

In article <kmbo3d\$e9h\$1@Kil-nws-1.UCIS.Dal.Ca>,
Gus Gassmann <noone@nospam.com> wrote:

> On 07/05/2013 4:47 PM, Virgil wrote:
> > In article
> > WM <mueckenh@rz.fh-augsburg.de> wrote:
> >

> >> On 7 Mai, 10:09, Virgil <vir...@ligriv.com> wrote:
> >>> In article
> >>>
> >>> WM <mueck...@rz.fh-augsburg.de> wrote:

> >>>> On 7 Mai, 00:14, Dan <dan.ms.ch...@gmail.com> wrote:
> >>>
> >>>>> 0.11111......
> >>>>> should also be a valid real number .
> >>>>> Infinite digits ,corresponding to an infinite row, are as valid as
> >>>>> infinite digits of the columns .

> >>>
> >>>> 0.11111...... it is not in the list
> >>>
> >>>> 0.1
> >>>> 0.11
> >>>> 0.111
> >>>> ...

> >>>
> >>> But, just like |N is the limit of the sequence of FISONs,
> >>> it is the limit of your sequence.
> >>>

> >> The union of lines
> >> cannot contain more elements than one line contains.

> >
> > Why not?

>
> It is really too bad that the great Professor is simply too dense to
> understand and use the following:
>
> A finite set of natural numbers contains a largest element.
> An infinite set of natural numbers does not contain a largest element.

Even more generally, a finite ordered set with no largest member is
empty, but a non-empty ordered set with no largest member cannot be
finite.

And a theorem true everywhere except in Wolkenmuekenheim:
Given a family of sets in which each set of the family is
a proper subset of some other set of the family,
then every set in the family is a proper subset of the
union of that family.
--