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

 Messages: [ Previous | Next ]
 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: some amateurish opinions on CH
Posted: Apr 8, 2013 4:59 AM

On Apr 7, 11:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 7 Apr., 20:32, Dan <dan.ms.ch...@gmail.com> wrote:
>
>
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>
>
>
>
>
>

> > 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.
>
>
>

> > 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

Well, in "standard set theory" we also have uncountable sets .
Judging by your history on sci.math , you shouldn't be using "standard
set theory" as an argument .
This is called "special pleading" , or , to use a simpler term ,
hypocrisy .

Now , I'm sure you can say that "GOD can play the lottery and always
win" , or "GOD can count any subset of the natural numbers" ,
but do you really want to go there?

This isn't about what God MIGHT or MIGHT NOT be able to do, but what
YOU can and can't do .
Prove you know how to count the set I described by winning the lottery
a couple of times ,or admit you failure to do so with dignity.

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