On Jun 2, 10:25 pm, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > What is the relevance of this? The logical rules of unions state that when > you have a union of sets that union does contain an element if it is in one > of the sets.
DAMN. This is the only reason I am still here (because you and Virgil are). YOU ARE TOO STUPID to be doing this! THERE ARE NO SUCH THINGS as "the logical rules of unions"! THERE IS AN *AXIOM* of union in ZFC! This axiom IS NOT a logical truth, or it would NOT NEED to exist at all! To the extent that "rules of unions" exist at all, THEY ARE *NOT* logical and MUST not be logical! IN ADDITION to the axiom of union, there is also, USUALLY, an axiom of pairing! THERE IS *NO LOGICAL* connection WHATEVER between the two! Either could get along FINE WITHOUT the other! But the axiom of pairing suffices to create ALL THE FINITE unions! YOU ONLY NEED the axiom of union FOR INFINITE unions!
> There is no difference between finite unions and infinite > unions.
THERE IS *SO*, TOO!! Finite unions can be built up ONE ELEMENT AT A TIME, THROUGH PAIRING! INFINITE UNIONS *CANNOT*!! THAT IS PRECISELY WHY WM IS WRONG to be generalizing from what happens with EVERY finite case TO the infinite case! a