Re: A new definition of natural numbers

In article <455B1DD0.2020209@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

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

EB is unable to attack transfinite set theory without insult and
hoity-toity phrases.

1) what "fundamental" remains unproven?

I would like to appeal to sufficiently intelligent open-minded people.
Most likely, individuals like Virgil will not accept any deviating
opinion.

As what EB offers is only opinion unsupported by any mathematical facts,
I see no reason to accept any of it.

What follows from ZF or NBG, however little EB may like it, remains
valid within ZF or NBG quite independently of EB's opinions, until those
axiom systems can be shown to be internally inconsistent.
EB's objections are always based on assumptions not a part of ZF or NBG,
and are, therefore, totally irrelevant to the issue of internal
consistency.
.

Relevant Pages

  • Re: A new definition of natural numbers
    ... Eckard Blumschein wrote: ... Not by modern standards. ... view that further discovery or development in mathematics is impossible. ...
    (sci.math)
  • Re: A new definition of natural numbers
    ... Eckard Blumschein wrote: ... Not by modern standards. ... Concerning the basics of mathematics: ... conclusions is notoriously based on obedience to set theory ...
    (sci.math)
  • Re: A new definition of natural numbers
    ... Eckard Blumschein wrote: ... Not by modern standards. ... view that further discovery or development in mathematics is impossible. ...
    (sci.math)
  • Re: Cantor Confusion
    ... Eckard Blumschein wrote: ... The vast majority of extant mathematics was created since Cantor's death. ... Requiring everything to have a use or application is not a requirement ... would be an acceptable printed definition. ...
    (sci.math)
  • Re: .999... ?= 1
    ... Eckard Blumschein wrote: ... >> Can you explain what Buridan's donkey has to do with any of this? ... Concerning the "fundamental crisis in mathematics" I quote: ... I dealt with theory of distributions and fundamentals of ...
    (sci.math)
Quantcast