On Nov 27, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 27 Nov., 18:42, William Hughes <wpihug...@gmail.com> wrote: > > > On Nov 27, 4:37 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > <snip> > > > > According to set theory the limit set is empty. > > > Indeed. > > Nice to hear that. > > > And the proof of this does not depend > > on "actual infinity". > > Of course it does, because every digits moves to the right side.
1 10 100 ....
The 1 moves to the left.
We do not have to check the positions one by one. It is easy to show by induction (which requires only potential infinity) that for each n in |N the nth position is not occupied. This is equivalent to saying that the set of all possible occupied positions is empty.