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Topic: Discussion with WM - Frustration reaches boiling point (What
is not clear?)

Replies: 1   Last Post: Jul 8, 2014 4:14 AM

 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.fh-augsburg.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 left-hand 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"?

"§ 523 Can the manner of marking influence the result?"

I see that you have given up, since you don't answer anymore.

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.