Re: No Unique Initial Segment And No Characteristic Expansion.

From: Uncle Al (UncleAl0_at_hate.spam.net)
Date: 12/04/04 

Date: Fri, 03 Dec 2004 16:16:56 -0800

"Ross A. Finlayson" wrote:
>
> Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<41B0AC7A.A71D917B@hate.spam.net>...
> > HERC777 wrote:
> > >
> > > Infinite people each flip coins infinite times.
> > > Can you always find a different sequence of heads and tails?
> >
> > Wait for the data to fuly accumulate, then look. Idiot. Given n
> > flips there will be 2^n states. That will nicely outrace any
> > approximation to infinity you attempt.
> >
> > > sci.math and sci.logic went quiet on this question for about a week,
> > > then against all logic, probability theory, and common sense they all
> > > agreed YES. Believers of hyperinfinities have no shame!
> >
> > Georg Cantor. As for you, FOAD.
> >
> > [snip crap]
>
> Hi Al,
>
> Hey, for a length n, you get 2^n permutations, and they're all
> rational numbers. In base b, for p places, you get b^p permutations.

Are you flipping DnD dice instead of honest coins?
 
> You're a chemist, and respected for your knowledge of chemistry. Some
> people think you're great, others you're an over-the-top jerk, but
> it's generally accepted that you're a reliable scientist. I don't
> care about "Herc", it's a free country. So anyways, I want to know if
> you ever use the uncountability of the reals or transfinite
> cardinality in any form.

Our calculation of quantitative parity divergence of solid spheres of
crystal lattice is not valid for an infinite number of atoms, but we
only got to 4.44x10^19 atoms in alpha-quartz - so no problem in
long_double_precision. My only use of uncountability is drawing a
median line parallel to an equilateral triangle's base and inviting
the viewer to show where lines drawn from apex to points in the base
miss points in the half-length line.

HERC is a chronic abusive boring idiot. He and his kind should not be
allowed to proceed unmolested. What goes around comes around. Would
you prefer the Department of Education and its policy of "every child
left behind?"

> Georg Cantor's famous. He might be the most chronicled mathematician
> after Newton, and I never heard of him until the late 90's. He
> tackled the difficult task of trying to define the continuum in
> non-geometric terms.

He never really got aleph_1 well identified, either. It's big stuff
to juggle and there's lots of room for error.
 
> During the rush to reformalize mathematics in the 20th century,
> basically the Bourbaki school and perhaps Dresden with Russell and
> Whitehead being Englishmen readily used this notion of "set theory",
> and along with it Cantor's powerset mapping result. As the century
> progressed, in terms of foundations there are basically the Zermelo
> and Fraenkel, and the Goedelian period and the 70's, and mathematics
> at large flourished outside of it, with tremendous gains in concrete
> and differential mathematics since the 50's and 60's, and of course
> the tremendous jumps in the tensorial and algebraic geometrical and
> geometric algebraic methods, and of course the probability density
> functions in your field, and the unfortunately ready application of
> numerical methods with digital computers.

"Bourbaki" was condemned for negatively altering American math
education (requiring intelligence and furnishing insight). The
subsequently impressed solution was to diversely remove math education
through high school. An advocate makes virtue of failure. The worse
the cure the better the treatment - and the more that is required.
 
[snip]

> So anyways, do you use transfinite cardinals in your day-to-day
> operations or ever?

Not even on 15 April.
 
> What's the use of integrating over the natural numbers and getting a
> meaningful result?

Suppose you only integrated over half of them... to save time. "8^>) 

-- 
Uncle Al
http://www.mazepath.com/uncleal/
 (Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

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