On Nov 27, 4:07 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 27 Nov., 19:21, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > 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. > > > Stick with > > > 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. > > Correct. Every position is unoccupied,
My claim is *each* position is unoccupied.
> but that does not mean that all > positions are unoccupied:
But this is not what I am saying. Compare
Each natural number >1 is either prime or composite. The set of natural numbers >1 that are neither prime nor composite is empty. We do not say there are a bunch of natural numbers we have not checked yet, so maybe there is a natural number that is neither prime nor composite.