On 14 Apr., 02:42, Virgil <vir...@ligriv.com> wrote:
> The question was whether A was in C, which it is provably not.
Wrong. A is provably in C, because "all" numbers that can be in a union of FISONs are in a union of FISONs in C, because the sequence has all possible unions of FISONs as elements.
But this is never a complete infinity.
Proof: The table T
1 2, 1 3, 2, 1 x, 3, 2, 1 ...
contains all natural numbers that can be contained. All numbers that can be contained in T are in one line (by construction of T). All numbers that can be contained are in the first column. By the pivot element x we see that every x in the first column with all its predecessors is also in the xth line. So it is impossible that in the first column, there is more than in any line. But we know that there is no line with the actually infite set |N of numbers (because T is a sequence of lines containing FISONs). Conclusion: |N cannot be in the first column either.