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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 7, 2013 2:32 PM

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?
Countability needs to be effective :
That is , you need to actually provide a way (finite description) to
I can make a function from N to the prime numbers , thus the prime
numbers are countable .

Let's say you construct an enumeration from N to the set S of pairs
(d, n) of a date ,and a lottery number .
You proved the set of all possible dates and lottery numbers is
countable .
Now , within this set , we have W , the set of "winning dates and
lottery numbers") .
If you manage to count W , give me a call .

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 .

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