Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


karl
Posts:
397
Registered:
8/11/06


Re: Discussion with WM  Frustration reaches boiling point (What is not clear?)
Posted:
Jul 8, 2014 4:14 AM


Am 08.07.2014 09:22, schrieb mueckenh@rz.fhaugsburg.de: > On Tuesday, 8 July 2014 05:58:51 UTC+2, PotatoSauce wrote: > > >> In the end, it's the same old argument (*). > >> lim card (s_n) = card( lim s_n) (**) > > No, I don't! But claim that, if something had to be used, the lefthand side would be the correct side to use. > >> And yet, he does so, clearly and blatantly, saying that there is no other interpretation of lim n> oo card(s_n) because no one has given one that he likes. > > You are wrong. I do not use this equation. I do not use the limit set lim s_n = { } at all!
>I use only the cardinalities of the sets s_n. Further I have shown that the limit
> of the sequence of cardinalities is infinite. This means nothing but:
> the limit of the sequence of cardinalities is infinite. It shows,
> by using real analysis, that the number of not enumerated
> rationals is never zero. Nothing else. Nothing more.
> What is wrong with this result in your opinion? > > Regards, WM >
The only thing you show is that a finite number of natural numbers is never
enough to enumerate all rationals; nobody doubts that.
But for increasing n all rationals gets their index number.
There is an enumeration of the rationals for example the one given by Virgil:
http://c2.com/cgi/wiki?WellOrdered
All rationals get their index here. But, certainly, always for a
given finite natural number there is an infinity of rationals which
have indices larger than this number n. But this shows nothing.
Where have you used "real analysis"? I guess you mean "calculus".
Is anything wrong with "complex analysis", i.e. "theory of functions"?
In your new thread
"§ 523 Can the manner of marking influence the result?"
I see that you have given up, since you don't answer anymore.
Don't be sad:
https://www.youtube.com/watch?v=6dinYJZhhj0
What is now with your proof that the reals are countable:
http://arxiv.org/abs/math/0306200v1
Why you don't say if it is right or wrong? I'm just curious.
I thought this clears the problem.



