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Re: Matheology § 162
Posted:
Nov 27, 2012 3:48 PM
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On Nov 27, 4:07 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 27 Nov., 19:21, William Hughes <wpihug...@gmail.com> wrote:
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> > 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.
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> > > Nice to hear that.
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> > > > 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.
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> > Stick with
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> > 1
> > 10
> > 100
> > ....
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> > The 1 moves to the left.
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> > 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.
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> 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.
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