
Re: Cantor's first proof in DETAILS
Posted:
Dec 1, 2012 4:45 PM


On Nov 30, 9:20 pm, Virgil <vir...@ligriv.com> wrote: > In article > <1e832cf727f54814b2ae5f9340a35...@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

