In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> No. Never. Since there is no "all numbers" of any infinite kind. I may have > claimed: > If there are all constructible numbers, then they form a countable set. A > countable set is by definition a set that can be listed.
But not necessarily finitely listed, and the set of all reals, which exists quite nicely OUTSIDE of WM's wild weird world of WMytheology, is provably incapable of being listed. > > > You should consider what > > your admission that this list must be non-constructable > > means (Note you cannot have non-constructable lists without > > non-constructable numbers). > > They would not help because only constructable numbers are under > consideration.
WM can limit such consideration within his his wild weird world of WMytheology, but not in the real world of real mathematics. > > But at present I assume the existence of a list of all rational numbers. > (Also that is nonsense, but we assume it like assuming that there is a > largest prime number in order to contradict it.)
Except that there are all sorts of examples of listing all rational numbers. I have a couple of my own.
> This list exist in > matheology. And it leads to the contradiction that every rational number > provably differs from the antidiagonal d but the antidiagonal provably does > not differ from all rational numbers.
Any such "proof" can only exist in WM's wild weird world of WMytheology, since outside of WMytheology such antidiagonals do NOT become eventually periodic but every rational must.
> Some matheologians want to make us > believe that that is not a contradiction, but obviously it is. Only inside of the hall of mirrors we call WMytheology > > Nevertheless I do not even attack this nonsensical claim but only state: > There is no sequence of digits that allows to distinguish d from all rational > numbers. That is all I claim.
But there is a general rule for the creation of such antidiagonals which makes it differ in at least one decimal place in an essential way from each number in the list, and (2) makes it impossible when constructed from a COMPLETE list of fractions to become eventually periodic.
Note that the original antidiagonal construction for a list of reals guaranteed that that antidiagonal differed from every member of the list from which it was constructed.
And that equally applies to any antidiagonalization. --