On Nov 29, 6:54 pm, Marshall <marshall.spi...@gmail.com> wrote: > On Nov 29, 5:32 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com> > wrote: > > > > > On Nov 28, 8:38 pm, Virgil <Vir...@home.esc> wrote: > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > On Nov 28, 12:43 pm, Virgil <Vir...@home.esc> wrote: > > > > > > Given a specific list of endless binary sequences, the so called Cantor > > > > > diagonal is the result of a specific and unambiguous algorithm applied > > > > > to that list, so it is, for any given list, unique, and not a member of > > > > > the list from which it is constructed. > > > > > > Which WM would have known if he had any sense. > > > > > Binary sequences aren't unique representations of real numbers. > > > > The original Cantor diagonal argument did not deal with real numbers > > > either, so what is your point? > > > The point was that your hasty overgeneralization was false and that it > > represents in your non-acknowledgment hypocritical criticism. > > You haven't identified any mistake of Virgil's. You've merely made > the well-worn point that some real numbers have multiple digit > strings. > > > > > (Binary and ternary (trinary) anti-diagonal cases require refinement.) > > > > But as neither I nor Cantor were not dealing with numbers in any base, > > > your objections are, as usual, irrelevant. > > > No, it was just noted a specific constructive counterexample to that > > lists of (expansions representing) real numbers don't contain their > > antidiagonals. > > It wasn't even that. > > Marshall
In binary or ternary an everywhere-non-diagonal isn't not on the list.
Using AC, in ZFC, given a well-ordering of the reals, I described a symmetry based construction of a distribution of the natural integers at uniform random.
EF is its CDF.
Yeah and I am familiar with the other fundamental results of transfinite cardinals and show how they don't hold in nonstandard frameworks suitable to represent the number system for application.