On Dec 12, 12:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > The union of all natural numbers is, according to set theory, omega.
YOU ARE *LYING*. You DON'T KNOW shit about set theory. You ESPECIALLY do not know what set theory means by "Union". In set theory, you CAN'T SAY "all natural numbers". In set theory (in first-order ZF, anyway), EVERYthing that you can talk about IS *ALREADY* a set! "All natural numbers" IS *THE SET OF* all natural numbers! There is no other way TO EVEN SAY it! Moreover, ZF has AN AXIOM of union! You MUST ALREADY have A SET of things BEFORE you can take the union OF THAT *ONE SINGLE* set! You CANNOT (in set theory) take the union of MORE than one thing UNTIL AFTER you have collected those multiple things INTO ONE set!
In other words, in ZF, U(w)=w. You have TO ALREADY HAVE omega before you can take the union of it. The union does NOT CREATE something out of infinitely many things. w in set theory is created BY AN AXIOM. It is just FORCED into existence BY FIAT. THE AXIOM of infinity just STATES that a set containing (as a subset) omega MUST exist. There IS NO mechanism (not union OR ANYTHING ELSE) for creating it!