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Re: Matheology § 162
Posted:
Nov 27, 2012 1:21 PM
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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. This is equivalent to
saying that the set of all possible occupied positions is empty.
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