On 10 Dez., 16:29, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> Without the axiom of infinity omega would not be immediately existing. > So apparently there is a definition of omega without the axiom of infinity. > Can you state that definition?
Look into Cantor's papers. Look into my book. > > There are no concepts of mathematics without definitions.
So? What is a set? >
> > An infinite union *is* not at all. But if it were, it was a limit. > > It *is* according to one of the axioms of ZF, and as such it is not a limit.
It *was* according to Cantor, without any axioms.
> Where? Why do you think taking a limit and taking cardinality should > commute? Should also the limit of te sequence of integral of functions > be equal to the integral of the limit of a sequence of fuctions?
If an infinite set exists as a limit, then it has gotten from the finite to the infinite one by one element. During this process there is no chance for any divergence between this set-function and its cardinality.