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Re: Cantor's first proof in DETAILS
Posted:
Dec 1, 2012 4:45 PM
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On Nov 30, 9:20 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <1e832cf7-27f5-4814-b2ae-5f9340a35...@b4g2000pby.googlegroups.com>,
> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
>
> > The notion of a uniform probability distribution over all the naturals
> > is not necessarily intuitive, and I described how to build one in ZFC
> > besides that EF has the concomitant properties of being the CDF of a
> > uniform distribution of the naturals.
>
> It is well known, at least to those who are the least bit familiar with
> the mathematics of probability, that a uniform probability distribution
> over a set of pairwise disjoint outcomes that is countably infinite is
> an impossibility, and thus Ross' alleged CDF is purely mythical.
>
> This has been pointed out to him several times, but he apparently will
> not allow himself to learn from his mistakes.
> --
Meh, that's much the same concern as EF not being a "real" function
(while still being a function from natural integers to the unit
interval of reals).
How about a uniform distribution over an interval of the reals? For
example, this is "the" uniform distribution.
http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
EF is standardly modeled with real functions, each of which, connected
as steps, is the uniform CDF of the discrete and finite events.
Then, yes, such a legendary thing would be of an extension of modern,
standard, probability theory.
And then where modern mathematics hasn't yet discovered utility of
transfinite cardinals in probability (except as a simple convenience
to bound for rigor the proof space, for which simple exhaustively
finite methods suffice), then while I did actually describe a
reasoning for use of transfinite cardinals in probability theory, that
flew right over the collective head, where there is most definitely a
structure of real infinity in the numbers, as they define the
probabilisitic spaces, then a conscientious mathematician may well
wonder what real character and utility infinities have, in mathematics
generally and here in probability.
Well here's a bone, have to it. (Sorry, that's just for Virgil,
simply expecting more of his doggerel.)
Regards,
Ross Finlayson
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