Virgil
Posts:
8,833
Registered:
1/6/11


Re: Cantor's first proof in DETAILS
Posted:
Dec 1, 2012 6:28 PM


In article <c3dbc1ec254a4d70b5328b285db63f9d@u4g2000pbo.googlegroups.com>, "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> 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.
As described by Ross himself, his EF is not a single function but set of functions, having one member for each member of N together with a nonfunctional mishmash alleged to be the "limit function" > > Then, yes, such a legendary thing would be of an extension of modern, > standard, probability theory.
Except that modern, standard, probability theory proves that no such thing as Ross alleged limit function can exists in standard probability theory or standard set theory. erally and here in probability. > > Well here's a bone, have to it. (Sorry, that's just for Virgil, > simply expecting more of his doggerel.) It is the bite of my "doggerel" that Ross can't stand! 

