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.
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.)