Re: A new definition of natural numbers

On 11/13/2006 9:10 PM, Tonico wrote:
Eckard Blumschein ha escrito:

On 11/6/2006 9:31 AM, Virgil wrote:
In article <454EE10F.7070506@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

Perhaps Archimedes was the first one who gave a still unrivalled
compelling description of natural numbers.

Not by modern standards.

Concerning the basics of mathematics: Do we need questionable modern
standards or a comprehensively correct and as plausible as possible
logic foundation?

Judge yourself: Methods by Euclid, Newton, Leibniz, Euler, Gauss etc.
were overly successful and will continue to do so.
Is there any need to use Cantor's transfinite set theory, any example of
useful application of aleph_2 or even more nonsensical phantasmagoria?

Eckard Blumschein
*************************************************************

Transfinite theory is beautiful,

One of the first reasons for me to ask for clarification was that I felt
beauty of mathematics hurt.


Is that ALL
your argument against Dedekind-Cantor-Set theory?

Elsewhere I listed more in detail several reasons, e.g.:
1) not a single proven fundamental,
in particuls obvious misinterpretation of DA2
2) ongoing use of the invalid definition of a set
3) obviously naive and populist arguments, exaggerating rhetoric
4) students are urged to belive rather than understand
5) lacking readiness of mathematicians to agree on some logical
conclusions is notoriously based on obedience to set theory
6) impossibility of looking at the natural numbers one by one and
simultaneously as an entity
7) apparently nobody her is in position to defend transfinte set theory
by tangible factual arguments without insult and hoity-toity phrases


Seems uncountably
weak to me...*sigh*...specially if you're trying to convince
mathematicians. You may try though in your city's bazar, or perhaps in
Mueck's college.

I would like to appeal to sufficiently intelligent open-minded people.
Most likely, individuals like Virgil will not accept any deviating
opinion. What about M., I disagree with him in part. He claimes that
there are physical limitations to numbers. I see numbers an independent
ideal concept. Also, I do not share his view on "intercession". He seems
not to follow yet my admittedly uncommon insight that the point of view
matters if one decides between contable and uncountable.

Regards,
Eckard


.

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