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

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: some amateurish opinions on CH
Posted: Apr 7, 2013 4:22 PM

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

> 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.
>
> The difference between countable and uncountable is as obvious as the
> difference between playing ALL POSSIBLE lottery numbers and playing
> only the WINNING ones . You can make yourself a fantasy that you only
> play THE WINNING NUMBERS (after all, their just a subset of ALL
> POSSIBLE NUMBERS) , but that don't make it so .

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.

Regards, WM

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