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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 21, 2009 12:02 PM
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On 21 Dez., 14:17, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> In article <2fac8bb1-4c90-4421-b559-1ea7f0301...@e27g2000yqd.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes:
>  > On 18 Dez., 15:12, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> ...
>  > > Why need I to think about a last one (which there isn't) to be able to
>  > > think about a set that contains all natural numbers?  Apparently you
>  > > have some knowledge about how my mind works that I do not have.
>  >
>  > Yes. A very convincing and often required proof of completenes of a
>  > linear set is to know the last element.
>
> Oh, is it often required?


Except in matheology it is always required.
>
>  >                                         T talk about all in case there
>  > is no last is silly.
>
> And I think it is silly to require there being a last to be able to talk
> about all.


That's why you love matheology.
>
>  > >  > >  > > Right, but there is no finite initial segment that contains them
>  > >  > >  > > all.
> ...
>  > >  > > 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/46fa18c8bb=
>  > ...
>  > >
>  > > Where is the proof there?  I see only you writing a bit of nonsense and
>  > > two rebuttals.
>  >
>  > One of the rebuttals has meanwhile been changed. Peter Webb
>  > recognized: It is true that you cannot show pi as a finite decimal,
>  > but you can't show 1/3 as a finite decimal either.
>
> So what?  That is not contested and it does not show in *any* way that the
> axiom of infinity does not create uncountability.  So no proof at all.


It may create what you like. Either 1/3 can be identified at a finite
digit or 1/3 cannot be identified at a finite digit.

Even a matheologian should understand that: If there is no digit at a
finite place up to that the sequence 0.333... identifies the number
1/3, then there is no digit at a finite place up to that the number
1/3 can be identified.
>
>  > Just what I said.
>
> And just wat I said: see the quote above:
>  > >  > >  > > Right, but there is no finite initial segment that contains them
>  > >  > >  > > all.
>
> which you contested.


I did not contest it. I said, if there is a sequence that identifies
1/3, then the identifying digits must be at finite places. But we know
that for every finite place d_n, there is a sequence d_1, ..., d_n
that is not 1/3 but is identical to the sequence of 1/3. Therefore we
can conclude that there is no sequence identifying the number 1/3 by
means of digits at finite places only.
>
>  > >  > > 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 *existence* of a set N of finite numbers.
>  >
>  > What else should be established?
>
> Does not matter.  The axiom of infinity does *not* construct infinite paths
> in your tree, beacuse you stated that your tree did not contain infinite
> paths a priori.  


The union of finite ínitial segments cannot ield an infinite initial
segment? Does the sequence of 1/3 not consist of a union of all finite
initial segments?

Regards, WM



Date Subject Author
11/23/09
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11/27/09
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11/27/09
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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?
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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