In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> In mathematics, there are two fundamental axioms, they are so obvious > that they are not spoken out: > > 1) The limit of a sequence of numbers or of sets or of anything else > is determined by the finite terms of the sequence only. > > 2) The limit of a sequence of numbers or of sets or of anything else > cannot be changed by some ado that does not belong to the sequence.
Both of which, while true, do not in any way support WM's delusions or comradict the actual infiniteness of certain sets like the set of al;l natural numbers.
Note that, in general, the limit, if it exists, of a sequence or series need not be a member of that sequence or series, not even in Wolkenmuekenheim.
For example the sequence of all FISONs (finite initials sets of naturals), taken in order of increasing size, has a limitset which is not a FISON but is the union of all FISONs or, equivalently, of any infinite set of FISONs.
At least everywhere outside of Wolkenmuekenheim. -- --