Re: Cantor Confusion

In article <456692F9.7070103@xxxxxxxxxxxxxxxxxxx> Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> writes:
On 11/24/2006 2:25 AM, *** T. Winter wrote:

> Mathematicians like you are hopefully aware of the trifle that the
> relation >= cannot be applied to the really real numbers.

Oh. What are "really real numbers"?

Those, like the imagined numerical solution to the task pi, which are
just fictions. Those which are assumed as basis for DA2,

In that case what are the "not-really real numbers"?

What you are missing is that mathematics provides an idealisation of
arithmetic (amongst others), and from that background provides
processes to do "real" calculations to get results in (amongst others)
the physical world. The whole field of numerical mathematics could
barely have been build without the idealised mathematical background.

No no. I do not deny that numbers can come as close as you like to the
ideal concept of infinity and continuum. Rational numbers already do
that job.

You completely misunderstood what I wrote. Cholesky decomposition of
positive definite matrices will not work when you are using rationals
only. But it is commonly used. The reason is that in ideal mathematics
the decomposition will work, and numerical mathematics provides the
additional information you need to get it to work in finite precision.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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