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Re: Endorsement of Wolfgang Mueckenheim from a serious mathematician
Posted:
Feb 1, 2013 3:12 AM
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On 1 Feb., 06:01, forbisga...@gmail.com wrote:
> On Thursday, January 31, 2013 8:55:12 AM UTC-8, WM wrote:
> > On 31 Jan., 15:27, forbisga...@gmail.com wrote:
>
> > > The rational 1/3
>
> > > doesn't have a finite decimal expansion. None the less it is distinguishable
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> > > from every rational other than 1/3 at some place in the expansion
>
> > > and only the infinite expansion can be calculated to be 1/3.
>
> > If you are so sure about that than you should be able to find out
>
> > whether 1/3 is among the paths that I have used to construct the
>
> > complete infinite Binary Tree. Does it in fact differ from the union
>
> > of all its finite initial segments
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> > 0.01
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> > 0.0101
>
> > 0.010101
>
> > ...
>
> Yes it does, under the assumption that the continuation
> of all of your initial segments is not the repeating sequence
> [01]. If it is then I will
If you could determine it by nodes or digits, you need not make
provisions. So you cannot determine by nodes whether 1/3 it there or
not. QED.
There remains only a finite definition. But there are only conutably
many.
If it is then I will give you the repeating sequence
0.[001] and it will not be among your finite initial segments
unless you change your continuation at which point 0.[01] will
not be in your set.
And if I append to every finite path every infinite tail that has a
finite definition like 0.[001]? What will you choose then???
Nevertheles I will have used only countably many paths yet.
Regards, WM
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