In article <email@example.com>, firstname.lastname@example.org wrote:
> In article <email@example.com>, > muec...@rz.fh-augsburg.de wrote: > > > muec...@rz.fh-augsburg.de wrote: > > > > > Re: WMytheology § 293 > > > In article > > > <firstname.lastname@example.org>, > > > WM <muec...@rz.fh-augsburg.de> wrote: > > > > > > > > > Any and every union of infinitely many FISONs includes all of |N, > > > > > >> The sequence contains only sets each of which lack aleph_0 natural > >> numbers. > > But it contains a list of aleph_0 sets each of which contains one natural > > not contained in any previous set in the list. > > Yes, in such cases logic yields everything. To contain and not to contains, > that is the question
And logic, at least all the logic not perverted by WMytheology, requires that the union of all FISONs contains |N. > > > > > >>> Lacking infinitely many natural numbers cannot be compensated by > > >>> unioning infinitely many of such deficient sets. > > > > > > >> It can, and does, > > > >> That would require that a union after infinitely many unions yields > >> infinitely many more numbers than infinitely many unions before. That is > >> not acceptable.
That the union of a family of sets contains every member of every set of that family is eminently acceptable everywhere outside of WM's wild weird world of WMytheology > > > NOt if one's first union uses up any set of infinitely many FISONs, as the > > leaves no naturals unused. > > Wrong. The first union supplies onl FISONs. Every FISON is lacking infinitely > many natural numbers.
It is WM who is wrong, a union of all FISONs uses all FISONs, Every natual is in infinitely many of those infinitely many FISONs so is infinitely often inserted into their union. > > Look: The sequence of terms a_n = 1 - 1/n has infinitely many terms, each of > which is less than 10. Why should the limit be 10?
It is only in Wolkenmuekenheim that that could happen. Everywhere else that limit would be 0. > > But exactly such nonsense is what you advocate
No! It is what WM advocates.
WM keeps claiming that the union of all FISONs does NOT contain every member of every FISON.
Outside of the wild weird world of WMytheology, the union of any family of set, even infinite families of sets, contains every member of every set in the family.
inside WM's wild weird world of WMytheology , he claims that when one unions the members of an infinite family of sets like the set of fisons, some members of some sets must be left out of the union.
But no one finds WM's alibis for this contrary-to-logic behavior acceptable. --