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Topic: Another AC anomaly?
Replies: 280   Last Post: Dec 27, 2009 3:53 PM

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Virgil

Posts: 870
Registered: 7/27/09
Re: Another AC anomaly?
Posted: Dec 11, 2009 4:34 PM
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In article
<dad673b7-b69b-411a-abef-7c3d4e3bb999@a32g2000yqm.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 11 Dez., 19:53, Marshall <marshall.spi...@gmail.com> wrote:
> > On Dec 11, 9:13 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >

> > > On 11 Dez., 03:50, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > > >  > >
> > > >  > > If there are no infinite paths in that tree, 1/3 is not in that
> > > > tree.
> > > >  >
> > > >  > 1/3 does not exist as a path. But everything you can ask for will be
> > > >  > found in the tree.
> > > >  > Everything of that kind is in the tree.

> >
> > > > This makes no sense.  Every path in the tree (if all paths are finite)
> > > > is
> > > > a rational with a power of 2 as the denominator.  So 1/3 does not exist
> > > > as a path.  In what way does it exist in the tree?

> >
> > > It exists in that fundamentally arithmetical way: You can find every
> > > bit of it in my binary tree constructed from finite paths only. You
> > > will fail to point to a digit of 1/3 that is missing in my tree.
> > > Therefore I claim that every number that exists is in the tree.

> >
> > This argument can be inverted to "prove" the existence of
> > a natural number whose decimal expansion is an infinite
> > string of 3s.

>
> No. Why should it?



Why shouldn't it? It would make at least as much sense as your arguments.

> Of course the magnitude of natural numbers is not
> limited. For every number with n digits 333...333 there is another
> number with n^n digits. Nevertheless each one is finite.


But then, since all your paths are finite, they do not represent all
reals, which can have non-finite representations.
>
> > The infinite-3 number exists in a fundamentally
> > arithmetical way: you can find every digit of it in a preceding
> > natural number constructed from finite string of 3s only.
> > You will fail to point to a digit of ...333 that is missing in
> > the natural numbers.

>
> Of course. That is because there is no digit missing in the natural
> numbers.
>

> > Therefore you claim the naturals and
> > the reals are just the same, but in the reverse direction,
> > just as AP says they are.

>
> They *are* just the same, because your argument that above procedure
> would prove an infinite string of 3's is wrong.


If the string of binary digits's in a path has a last position, then it
does not represent 1/3. Then 1/3 can only be represented by an actually
infinite set of such strings, at which point actual infiniteness is
established and all of WM's objections to it fail.



> There is neither a
> natural nor a rational with an infinite string of digits.


There is no finite string of binary digit representing 1/3.
Or any rational not of form m/2^n for m an integer and n a natural.

> To be able
> to determine every digit of a number you like does not imply that
> there is a number with a never ending sequence of digits.


I like 1/3 which, in any base not divisible by 3, requires a never
ending sequence of digits to represent exactly.
>
> Why should it??? Because Cantor believed that God knows infinite
> strings? (He read it in civitate dei of St. Augustinus.)


Because it does.
>
> Or because Zermelo misunderstood Bolzana-Dedekind's definition of
> infinity? Are you really thinking that infinity comes into being
> because a Dr. Zermelo of Germany said so?


Does WM think he is more in touch with God than any of the many
mathematical geniuses whom he trashes here?


Date Subject Author
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of Bentley College
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12/2/09
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of Bentley College
Marshall
11/27/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
William Hughes
11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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mueckenh@rz.fh-augsburg.de
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11/26/09
Read Re: Another AC anomaly?
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11/28/09
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11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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11/28/09
Read Re: Another AC anomaly?
Virgil
11/29/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/29/09
Read Re: Another AC anomaly?
Virgil
11/29/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/29/09
Read Re: Another AC anomaly?
Marshall
11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
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Read Re: Another AC anomaly?
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11/30/09
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Read Re: Another AC anomaly?
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11/30/09
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Read Re: Another AC anomaly?
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11/29/09
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11/26/09
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11/26/09
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11/26/09
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11/27/09
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mueckenh@rz.fh-augsburg.de
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11/27/09
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mueckenh@rz.fh-augsburg.de
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11/27/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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11/27/09
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
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11/30/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
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Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
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12/22/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/18/09
Read Re: Another AC anomaly?
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12/22/09
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12/16/09
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12/11/09
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Read Re: Another AC anomaly?
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12/4/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/8/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/4/09
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12/4/09
Read Re: Another AC anomaly?
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12/4/09
Read Re: Another AC anomaly?
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12/4/09
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12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
Read Re: Another AC anomaly?
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12/5/09
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12/5/09
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12/1/09
Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
anonymous.rubbertube@yahoo.com
11/30/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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11/27/09
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11/27/09
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11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
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11/27/09
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11/27/09
Read Re: Another AC anomaly?
Virgil

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