Re: A new definition of natural numbers


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
*************************************************************
Any use...where or in what? To go and buy eggs and milk in the grocery
store? I doubt it.
Transfinite theory is beautiful, works great, is consistent....what
else a mathematician needs to deal with some stuff?!! That there are no
practical uses for that? Who gives half a damn?! Proving FLT or the
insolubility of the quintic had hardly any practical application WITHIN
the math world itself, leave alone outside "in the real world"...who
cares?! It's fun, it's beautiful in some strange sense pretty similar
to listening to Bach or Rachmaninoff, and that's all a mathematician
needs. By the way, many non-mathematicians seem to think that this is
important, since they keep on supporting heavily this kiind of stuff.
Somebody, perhaps, will sometime find some application to this "in the
real world"...yes, perhaps. in the meantime, who cares?! Is that ALL
your argument against Dedekind-Cantor-Set theory? 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.
Regards
Tonio

.

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