In article <884ef41b-cbdd-4681-b76e-6ac485b5bf77@j10g2000vbe.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 4 Dez., 22:11, Virgil <vir...@ligriv.com> wrote: > > In article > > <695379aa-abfc-44f7-8e33-5160e2c35...@gl2g2000vbb.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 3 Dez., 14:46, Daryl McCullough <stevendaryl3...@yahoo.com> wrote: > > > > > Do none of you realise you're all thick as bricks? > > > > > > > An infinite diagonal flip is an exercise in list shuffling. > > > > > > But you agree that given any list L, the anti-diagonal of > > > > L is not equal to the first element of L, right? You agree > > > > that it's not equal to the second element of L, right? > > > > You agree that it's not equal to the third element of L, > > > > right? > > > > > And you agree that there is no chance to get to an end of L, right? > > > > When one has a formula or rule which one can prove holds for any and > > every natural number collectively, one does not need to condsider such > > numbers individually. > > So one does not need to prove that any and every number of FISONs is a > FISON?
Why should one even want to prove that which is false?
A set of a finite number of fisons is not itself a fison, though ist union is.
A set of infinitely many fisons is not a fison and its union is not a fison either, but is |N. > > > > > > > > > You agree that *every* number you check has infinitely many > > > successors, right? > > > > We do not just check them one at a time, but do it for all of them > > simultaneously. So that your one-at-a-time is irrelevant. > > Same holds for every set of FISONs. Every FISON is subject to finite > mathematics. Every squence of FISONs (look: I do not say union) has > only finite elements.
It is not the finiteness of each element but the number of elements wish can be infinite here.
For any finite set of fisons, its union is fison, which is not the largest possible fison unless there is a largest possible natural. Which in sane set theories, there is not.
So no finite set of fisons can contain all fisons or have a union which contains all naturals.
At least not in any standard set theory.
> Every finite sequence of FISONs has a last > FISON.
But not every sequence of fisons need be a finite one.
In any standard set theory, like ZFC, which has a set of all naturals, NO finite set of fisons has union containing every natural, but EVERY infinite set of fisons has union containing all naturals.
And in standard mathematics, such standard set theories are the rule, and WM's notions are very much rejected exceptions to that rule. --
