> > > 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
> > >>> 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.
> 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.
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?
But exactly such nonsense is what you advocate and what matheologians need so much that they even pretend to believe it.