|
|
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
|
|
