In article <firstname.lastname@example.org> WM <email@example.com> writes: > On 3 Jun., 04:25, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > There is no difference between finite unions and infinite > > unions. > > There should not be, but there is --- at least if ZF is taken to be > true.
You are again wrongly interpreting things. There is no question about ZF being true or not. ZF is only one of the many possible theories.
Mathematics is not a science that tries to find truth, it is a science where it is determined what a given set of axioms (i.e. presupposed valid statements) leads to.
> The union of FISONs (of natural numbers or of other finite linear > sets) is the last FISON.
ZF does agree, when there is a last FISON. Your problem is that the axiom of infinity states that here is no last FISON of all FISONs. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/