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: > > > > > > > > > > > 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 . http://en.wikipedia.org/wiki/Special_pleading
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.