In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 1 Dez., 13:10, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > In article > > <887fb198-aa2f-46ae-ab6a-91a67cb73...@u20g2000vbq.googlegroups.com> WM > > <mueck...@rz.fh-augsburg.de> writes: > > > On 30 Nov., 14:39, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > > > > > > I think you are confusing the limit of a sequence of sets (which is a > > > > set) and the limit of the sequence of the cardinalities of sets ( > > which > > > > is a cardinality). =A0In general: the limit of the cardinalities is > > not > > > > necessarily the cardinality of the limit, however much you would like > > > > that to be the case. > > > > > > If the limit of cardinalities is 1, then the limit set has 1 element. > > > > No because the limit of cardinalities is not necessarily the cardinality > > of the limit, as I wrote just above. > > You may write this as often as you like, but you are wrong.
Limit processes do not automatically and universally commute with other processes, so it is not at all obvious that WM is right.
And without having incontrovertible supporting proofs, one would be a fool to take WM's word for anything having to do with mathematics.
> If there > is a limit set then there is a limit cardinality, namely the number of > elements in that limit set.
But unless the cardinality of the limit of a sequence of sets and the limit of the sequence of cardinalities of those sets are formed by identical processes, there is no guarantee of equality.