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Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF
CANTOR: THE REALS ARE UNCOUNTABLE!

Posted: Jan 10, 2013 12:58 PM

On 10 Jan., 18:29, Zuhair <zaljo...@gmail.com> wrote:
> On Jan 10, 2:31 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > > That is correct and natural and Cantor's
> > > arguments Agrees with that completely.

>
> > Can you quote the relevant paragraph?
>
Of course you cannot. Again you have been convicted of lying.

> I don't need to quote any such paragraphs because this is just ABC of
> logic, and definitely Cantor is aware of such Trivial issue,

You are wrong. Cantor said exactly: "so sieht man ohne weiteres, daß
die Gleichung E_0 = E_mue für keinen positiven ganzzahligen Wert von
mue erfüllt sein kann." My translation (you may look for a better
one): It is obvious that the equality E_0 = E_mue for no integer value
of mue can be satisfied.

From that follows, that for every entry of the list, there is a finite
integer mue where it deviates from the anti-diagonal E_0. And if there
is a finite integer mue, then there is also a finite initial segment,
namely (1, 2, 3, ..., mue).

> these
> trivialities are not mentioned in papers of that importance because
> they are minor details that are very well understood and so trivial to
> mention.

There are not "papers" by Cantor, but there is only one single short
paper, published in 1892, from which I quoted above the only relevant
paragraph.
>
> I really really don't know why you think that a man of Cantor's
> caliber and that THOUSANDS of mathematicians among which are some who
> are regarded as geniuses of all times

but obviously only by contemporaries who neither were geniusses
themselves nor could judge about that matter.

would really miss such a trivial
> remark that a clever child perhaps even at primary level school can
> capture. Are you serious? or you are just wasting our time? I'm really
> beginning to question your intentions, I think you are just playing
> around nothing more nothing less, because really I can't believe that
> you think that such a famous argument that lived for around a century
> or more can suffer from such trivial nonsensical error.

That is the point. The argument is trivially wrong, but so famaous
that you cant't believe what you must conclude. Again, you could wake
up when recognizing that you don't know what paths I use to construct
the Binary Tree. If you don't forget that all infromation that in real
mathematics concerns the decimal expansion of a real number (here
path) is contained in its digits (here nodes). Of course you will not
be able to find any used or missing path. But most matheologians are
not able to recognize this for psycological reasons, because their
brains have been devastatingly spoilt by Cantor (Kronecker was right!)
and blinded by thousands of "geniusses".

Regards, WM