In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 4 Feb., 13:19, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 4, 1:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > So we have according to WM > > > > 0.111... > > > > is not a single line of > > > > 0.1 > > 0.11 > > 0.111 > > ... > > > > and > > > > there is no list of every 0/1 sequence. > > You have to distinguish more carefully: There is nothing of such a 0/1- > sequence that you can name and that was missing from every line of an > appropriate list. Ever such FIS corresponds to a member of |N, and every list of FIS's that is not infinite has a last one, which has a successor. So WM cannot produce a list which is complete. > > And there is no list of every FISON in exaxtly the same sense. Thus it > is impossible to distinguish countability and uncountability in > potential infinity.
But it is impossible to impose the nonsense of potential infiniteness on ZF or most other set theories. --