In article <firstname.lastname@example.org>, George Greene <email@example.com> wrote:
> 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!
While you are perfectly correct, WM has the great advantage of being both arrogantly stupid and invincibly ignorant, against which combination even gods strive in vain.