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Re: Matheology § 162
Posted:
Nov 27, 2012 3:07 PM
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On 27 Nov., 19:21, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 27, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
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> > On 27 Nov., 18:42, William Hughes <wpihug...@gmail.com> wrote:
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> > > On Nov 27, 4:37 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > <snip>
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> > > > According to set theory the limit set is empty.
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> > > Indeed.
>
> > Nice to hear that.
>
> > > And the proof of this does not depend
> > > on "actual infinity".
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> > 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.
Regards. WM
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