On Nov 29, 11:53 pm, Virgil <Vir...@home.esc> wrote: > In article > <3bc52c73-77ee-479b-9a28-824fd9a4a...@z10g2000prh.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > > > (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. > > What does "an everywhere-non-diagonal" mean? >
Given a matrix, there is a main diagonal, called "the" diagonal. In binary, there's one anti-diagonal. In ternary, base three, an everywhere-non-diagonal is different at each place than the diagonal.
> And does "isn't not on the list" mean the same as "is on the list"? >
No. It means "isn't necessarily not on the list."
> In any integer base, from 2 on up, and any list, there are constructably > as many non-members of the list as members of it. >
No, that is in integer bases from 4 on up. Collecting across moduli reinterprets the input list in a higher radix, in terms of accesses to the elements of the "main diagonal".
> > > > > Using AC, in ZFC, given a well-ordering of the reals > > Since no one has yet been able to give an explicit well ordering of the > reals, we won't give it to you. >
I don't need it from you, the theory guarantees one exists (if ZFC were consistent).
As well, in a suitable nonstandard construction of the real numbers, the domain and range of EF are naturally well-ordered.
> > I described a > > symmetry based construction of a distribution of the natural integers > > at uniform random. > > Is that supposed to mean something in English? > > [Further garbage DELETED]
Yeah it means just what it says. It means that in the universe of mathematical objects there are features of these sets of numbers and their products that allow a notation and writing of, consistently applied, a consistent constant infinitesimal probability, (i.e., iota), the sum of those over that support space being as expected, unity.
Bishop and Cheng formulate a measure theory in a constructible universe that's countable: don't need the trans-finite.
The observation that your quote was simply mistaken stands for itself.