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Topic: another boring critisism of Cantor's Theorem
Replies: 88   Last Post: May 3, 2004 6:56 AM

 Messages: [ Previous | Next ]
 Jesse F. Hughes Posts: 9,776 Registered: 12/6/04
Re: another boring critisism of Cantor's Theorem
Posted: Mar 31, 2004 8:27 AM

Eckard Blumschein <blumschein@et.uni-magdeburg.de> writes:

> Jesse F. Hughes wrote:
> Mathematics is about deductive consequence, and if the

>> consequences of our axioms are counterintuitive or surprising, well,
>> that's too bad for our intuitions (or perhaps we must in extreme cases
>> reconsider our axioms).

>
> Why not trying the latter?

Because the great advances in mathematics post-Cantor show that the
basic foundations are interesting? Good luck constructing a viable
alternative. Once you have it (and you have the initial results
showing that it is interesting, rich, useful, etc.), let me know.

> Were not distributions introduced like generalized density functions
> as to cope with some problems of physics? This reminds me of
> cosmetics rather than a fundamental recast. I tend to see Cantor's
> paradise the eggshells of a mathematics of discrete numbers while
> Hilbert was correct in that the infinitely large as well as the
> infinitely small evade our comprehension of numbers.
>
> Let me suggest some practical corrections.
>
> You will certainly agree that any single finite value xn of a continuous
> quantity x is per se completely irrelevant because it is surrounded by
> infinitely many nearly identical neighbours.

Sorry for being dense (no pun intended), but I won't agree to that. I
don't really know what it means.

> It simply has no comparable weight. Therefore it is not justified to
> distinguish between x>xn and x>=xn.

Uh. Well. Maybe you should get them results *first* and then provide
the motivational argument later. It doesn't seem to be going so well
this way.

[...]

--
"Naomi Klein reports that Microsoft is helping develop e-government in
Iraq, 'which Dees admits is a little ahead of the curve, since there
is no g-government in Iraq--not to mention functioning phones lines.'"
-- as reported in The Register, http://www.theregister.co.uk

Date Subject Author
3/29/04 Craig Feinstein
3/29/04 magidin@math.berkeley.edu
3/29/04 A N Niel
3/29/04 Craig Feinstein
3/29/04 Will Twentyman
3/30/04 Robin Chapman
3/30/04 Jose Carlos Santos
3/30/04 David McAnally
4/3/04 Richard Sabey
3/31/04 Jesse F. Hughes
3/31/04 Lee Rudolph
3/31/04 Jesse F. Hughes
3/31/04 Eckard Blumschein
3/31/04 Jesse F. Hughes
3/31/04 Lee Rudolph
3/31/04 Jesse F. Hughes
3/31/04 Detlef Mueller
4/1/04 Eckard Blumschein
4/1/04 Detlef Mueller
4/1/04 Eckard Blumschein
4/1/04 Herman Jurjus
4/2/04 Eckard Blumschein
4/2/04 Hermann Kremer
4/5/04 Eckard Blumschein
4/6/04 Hermann Kremer
4/7/04 Eckard Blumschein
4/2/04 Hermann Kremer
4/6/04 Eckard Blumschein
4/1/04 ZZBunker
4/1/04 David McAnally
4/1/04 Eckard Blumschein
4/1/04 Robin Chapman
4/1/04 Hermann Kremer
4/2/04 Eckard Blumschein
3/31/04 Robin Chapman
3/31/04 Hermann Kremer
4/1/04 Jesse F. Hughes
4/1/04 Hermann Kremer
4/1/04 Eckard Blumschein
3/31/04 Thomas Nordhaus
4/1/04 Detlef Mueller
4/1/04 Eckard Blumschein
4/1/04 Hermann Kremer
4/2/04 Eckard Blumschein
4/2/04 Jesse F. Hughes
4/1/04 Justin Davis
4/2/04 Eckard Blumschein
4/2/04 Robin Chapman
3/31/04 David McAnally
3/31/04 David Petry
3/31/04 Torkel Franzen
4/2/04 David Petry
4/2/04 Torkel Franzen
4/1/04 Rupert
4/2/04 David Petry
4/2/04 David C. Ullrich
4/3/04 Torkel Franzen
4/3/04 David C. Ullrich
4/4/04 David Petry
4/4/04 Daryl McCullough
4/5/04 Rupert
4/5/04 David Petry
4/6/04 Rupert
4/6/04 Rupert
4/7/04 David Petry
4/7/04 Rupert
4/9/04 Herman Jurjus
4/9/04 Rupert
4/13/04 David Petry
4/13/04 Rupert
4/14/04 David Petry
4/14/04 Rupert
4/14/04 Rupert
4/16/04 Herman Jurjus
4/16/04 Rupert
4/22/04 Eckard Blumschein
5/3/04 Herman Jurjus
4/6/04 Herman Rubin
4/6/04 David Petry
4/7/04 Rupert
4/7/04 Rupert
4/5/04 David C. Ullrich
4/6/04 Herman Rubin
4/3/04 Rupert
3/31/04 Ted Hwa
3/29/04 David Manheim
3/29/04 Jesse F. Hughes
3/29/04 Lee Rudolph
3/29/04 Jesse F. Hughes