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, but that does not mean that all positions are unoccupied: It is as easy to show by induction that there are never aleph_0 zeros right to the 1.
> This is equivalent to > saying that the set of all possible occupied positions is empty.-
Only if the mistake is made to consider infinity as finished, every as synonymous to all, namely to consider all finite positions occupied by zeros.
But as I mentioned already, this example has nothing at all to do with my proof.