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

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: Another AC anomaly?
Posted: Dec 17, 2009 11:56 AM
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On 17 Dez., 14:44, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> In article <ba9f2c85-caa2-491d-9263-bea1bed3a...@p19g2000vbq.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes:
>  > On 16 Dez., 03:31, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>  > >  > Why that? Group, ring and field are treated in my lessons.
>  > >
>  > > You think that something that satisfies the ZF axioms being a collection
>  > > of sets is rubbish, while something that satisfies the ring axioms being
>  > > a ring is not rubbish?
>  >
>  > Yes, exactly that is true.
>
> And why, except by opinion?


Look here:
http://groups.google.com/group/sci.logic/browse_frm/thread/46fa18c8bb5da79d#

> Aha, you are clearly a mindreader.  Well, as far as I know mindreading is not
> part of mathematics.  Anyhow, I can think of numbers larger than that path.
> But that is completely irrelevant.  I am able to think about a set that
> contains all natural numbers, you apparently are not.


How do you know that without confirming it by thinking the last too?
>
>  > >  >       Every digit that is on the diagonal of Canbtor's list is a
>  > >  > member of a finite initial segment of a real number.
>  > >
>  > > Right, but there is no finite initial segment that contains them all.
>  >
>  > That is pure opinion, believd by the holy bible (Dominus regnabit in
>  > aeternum
>  > et ultra. [2. Buch Moses: Exodus 15 Vers 18]) or forced upon us by the
>  > men-made axiom of infinity.
>
> Sorry, I have no knowledge of the bible.  But live without that axiom when
> you can't stomach it.  And do not attack mathematicians who live with that
> axiom.


To live with that axiom does not create uncountability. See the proof
here:
http://groups.google.com/group/sci.logic/browse_frm/thread/46fa18c8bb5da79d#

>
>  > >  > You can only argue about such digits. And all of them (in form of
>  > >  > bits) are present in my binary tree.
>  > >
>  > > Right, but your tree does not contain infinite paths, as you explicitly
>  > > stated.
>  >
>  > The tree contains all paths that can be constructed by nodes, using
>  > the axiom of infinity. Which one would be missing?
>
> The infinite paths because you stated a priori that your tree did not
> contain infinite paths.  So it is impossible to construct in your tree
> infinite paths by the axiom of infinity.


The axiom of infinity establishes the set N from finite numbers.
It establishes the infinite paths as well in my tree from finite
paths.

>  You can construct infinite
> sequences of nodes, but as you stated *explicitly* that your tree did
> not contain infinite paths, those infinite sequences of nodes are
> apparently not paths within your terminology.


They are not constructed, but it might happen that the come in by the
union of some finite paths: The sequence of finite paths 1, 11,
111, ... may yield an infinite path 111... as a limit.

However, there is never more than one limit of a sequence and every
convergent sequence hat at least one finite term.
>
>  > >  > 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.
>  > >
>  > > In that case you have a very strange notion of "existing in the tree".
>  > > Apparently you do *not* mean "existing as a path".  So when you say that
>  > > the number of (finite) paths is countable, I agree, but 1/3 is not
>  > > included in that, because it is not a path according to your statements.
>  >
>  > It is. I constructed a finite path from the root node to each other
>  > node.
>
> Yup, you constructed a finite path, and that does not represent 1/3.


It 1/3 can be represented by a bit sequence, then it is represented in
my tree by the union of the node sets representing
0.0, 0.01, 0.010, ...
>
>  >       Then I appended an infinite tail.
>
> Whatever that may be, it is *not* a path according to your explicit statement
> that the tree did not contain infinite paths.


You have misread my construction. I use finite paths and then I append
an infinite tail.

Regards, WM



Date Subject Author
11/23/09
Read Re: Another AC anomaly?
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11/23/09
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12/1/09
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12/1/09
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12/1/09
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12/1/09
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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?
William Hughes
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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11/26/09
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11/28/09
Read Re: Another AC anomaly?
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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?
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11/29/09
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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
11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
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ross.finlayson@gmail.com
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?
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11/29/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/26/09
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11/26/09
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11/26/09
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11/29/09
Read Re: Another AC anomaly?
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11/27/09
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11/27/09
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Read Re: Another AC anomaly?
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11/27/09
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11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
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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
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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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?
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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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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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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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12/19/09
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Read Re: Another AC anomaly?
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12/22/09
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12/22/09
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12/18/09
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12/19/09
Read Re: Another AC anomaly?
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12/21/09
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12/21/09
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12/21/09
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12/27/09
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12/27/09
Read Re: Another AC anomaly?
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12/16/09
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12/16/09
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12/11/09
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12/11/09
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12/11/09
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12/11/09
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12/11/09
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12/10/09
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12/10/09
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
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12/7/09
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12/8/09
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12/8/09
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12/8/09
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12/8/09
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12/10/09
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12/3/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/7/09
Read Re: Another AC anomaly?
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12/8/09
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12/8/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/8/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
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12/10/09
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/15/09
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12/16/09
Read Re: Another AC anomaly?
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12/16/09
Read Re: Another AC anomaly?
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12/16/09
Read Re: Another AC anomaly?
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12/17/09
Read Re: Another AC anomaly?
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12/17/09
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12/4/09
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12/4/09
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12/4/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/7/09
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12/8/09
Read Re: Another AC anomaly?
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12/8/09
Read Re: Another AC anomaly?
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12/8/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
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12/10/09
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12/11/09
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12/11/09
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12/12/09
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/27/09
Read Re: Another AC anomaly?
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12/27/09
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12/27/09
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12/13/09
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12/4/09
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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
Read Re: Another AC anomaly?
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12/5/09
Read Re: Another AC anomaly?
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12/5/09
Read Re: Another AC anomaly?
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12/5/09
Read Re: Another AC anomaly?
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12/5/09
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12/1/09
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11/27/09
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11/27/09
Read Re: Another AC anomaly?
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11/30/09
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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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?
William Hughes
11/27/09
Read Re: Another AC anomaly?
anonymous.rubbertube@yahoo.com
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil

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