In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> > > and then take the Union over that set; then the result is N. > > Just that is surprising. Infinitely many + 1 union are sufficient.
Actually the union of all but infinitely many FISONs can be |N, so long as the "all but" is also infinitely many FISONs.
Any and every union of infinitely many FISONs results in |N. at least outside of WM's wild weird world of WMytheology.
THEOREM (valid everywhere despite WM's phony claims to the contrary): A necessary and sufficient condition for the union of a set of FISONs to equal |N is that the set contain infinitely many FISONs.
Note that there are several of set theories whose sets of rules/axioms have been published en bloc and as a consequence have been thoroughly analysed and found to be self-consistent.
WM claims a set theory whose rules and axioms have never been published en bloc, and apparently cannot be so published, and thus are not available for any sort of thorough analysis or validation of consistency.
So until the rules and axioms of WM's set theory's are published en bloc and are available for analysis, there can be no confidence in their consistency or utility. --