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Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: some amateurish opinions on CH
Posted: Apr 7, 2013 8:11 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 7 Apr., 20:32, Dan <dan.ms.ch...@gmail.com> wrote:
> > On Apr 7, 9:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > On 7 Apr., 20:00, Dan <dan.ms.ch...@gmail.com> wrote:
> >
> > > > So , we have a set that you can't count (all meaningful finite
> > > > sentences of words , it's simply too complex for you to count) , stuck
> > > > inside a set you can count (all random words/sequences of
> > > > letters) .

> >
> > > You need not count a set in order to prove its countability. A subset
> > > of a countable set is countable in set theory and wherever
> > > countability appears to be a meaningful notion. You cannot save
> > > uncountability in set theory after violating this theorem.

> >
> > > Regards, WM
> >
> > How can you say a set is countable if you can't "actually"  count it?

>
> "Countably infinity" is the least infinity. A subset of it cannot have
> larger cardinality if cardinality should have any meaning. IIRC
> otherwise already Schroeder-Bernstein would fail.
>

> > Countability needs to be effective :
>
> No. I cannot count the rabbits on earth, nevertheless I know they are
> countable. Every meaningful application of set theory needs the
> theorem that a subset cannot have larger cardinailty than its
> superset.
>
> But, of course, this yields a contradiction.

Only in Wolkenmuekenheim!
> >
> > The difference between countable and uncountable is as obvious as the
> > difference between playing ALL POSSIBLE lottery numbers and playing
> > only the WINNING ones .

Outside of Wolkenmuekenheim, a set is countable if and only if there is
surjection from the set of all natural numbers, |N, to the set in
question. Thus both |N and each of its subsets is countabla, though the
set of all its subsets is not.

>
> In set theory we have the theorem that a subset of a countable set has
> cardinality aleph_0 or is finite. If you want to introduce "effective
> countability" in order to save set theory, you destroy it.

Just as introducing WMytheology to mathematics destroys almost oll of
its mathematical validity.
--

Date Subject Author
4/7/13 fom
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Bergholt Stuttley Johnson
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Virgil
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 Virgil
4/8/13 Virgil
4/9/13 apoorv
4/8/13 Virgil
4/7/13 Virgil
4/9/13 Guest
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 Guest
4/10/13 dan.ms.chaos@gmail.com
4/10/13 fom
4/10/13 JT
4/11/13 apoorv
4/11/13 dan.ms.chaos@gmail.com
4/11/13 apoorv
4/11/13 fom
4/15/13 apoorv
4/15/13 fom
4/16/13 Shmuel (Seymour J.) Metz
4/16/13 fom
4/7/13 Virgil
4/7/13 William Elliot
4/7/13 fom
4/7/13 fom
4/8/13 William Elliot
4/8/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/9/13 fom