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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 3:24 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<03e1afc6-ec37-4212-b958-063a237d2bb4@f16g2000yqm.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 11 Dez., 03:28, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > In article
> > <89fb6e91-b6b1-4926-afca-820492e3c...@r24g2000yqd.googlegroups.com> WM
> > <mueck...@rz.fh-augsburg.de> writes:
> >  > On 10 Dez., 15:40, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> >  >
> >  > > Have a look at <http://en.wikipedia.org/wiki/Lim_inf> in the section
> >  > > titled "Special case: dicrete metric". =A0An example is given with the
> >  > > sequence {0}, {1}, {0}, {1}, ...
> >  > > where lim sup is {0, 1} and lim inf is {}.
> >  > >
> >  > > Moreover, in what way can a definition be invalid?
> >  >
> >  > It can be nonsense like the definition: Let N be the set of all
> >  > natural numbers.
> >
> > In what way is it nonsense?  Either that set does exist or it does not
> > exist.
> > If it does exist there is indeed such a set, if it does not exist there is
> > no set satisfying the definition.  In both cases the definition is not
> > nonsense in itself.

>
> It is nonsense to define a pink unicorn.


It is not nonsense to define a thing, though it may be nonsense to
insist that such a definition is instanciated.

> The set N does not exist as
> the union of its finite initial segments.


It does in ZF and in other sensible places outside of Wolkenmuekenheim.

This is shown by the (not
> existing) path 0.000... in the binary tree.

Again, in Wolkenmuekenheim there does not exist an complete infinite
binary tree, though it does exist in ZF and other set theories that one
can find outside of Wolkenmuekenheim.
>
> Let {1} U {1, 2} U {1, 2, 3} U ... = {1, 2, 3, ...}.
> What then is
> {1} U {1, 2} U {1, 2, 3} U ... U {1, 2, 3, ...} ?
> If it is the same, then wie have a stop in transfinite counting.


{1} U {1, 2} U {1, 2, 3} U ... U {1, 2, 3, ...} is ambiguous, so is
meaningless.


> If it is not the same, what is it?

The expression, being ambiguous, has no meaning.
On the other hand, ({1} U {1, 2} U {1, 2, 3} U ...) U {1, 2, 3, ...}
does have meaning and equals {1,2,3,...}
> >
> > But apparently you are of the opinion that you are only allowed to define
> > things that do exist.

>
> Most essential things in mathematics exist without definitions and,
> above all, without axioms.


Nothing in mathematics can exist without some a priori assumptions about
its properties, which constitute the axioms WM would dispense with.

So that in WM's world, there are all these things floating around with
no known or knowable properties.
At least in Wolkenmuekenheim


Date Subject Author
11/23/09
Read Re: Another AC anomaly?
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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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mueckenh@rz.fh-augsburg.de
11/28/09
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Virgil
11/26/09
Read Re: Another AC anomaly?
William Hughes
11/28/09
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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ross.finlayson@gmail.com
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
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?
Virgil
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
Virgil
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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11/27/09
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mueckenh@rz.fh-augsburg.de
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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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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
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
11/30/09
Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
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Read Re: Another AC anomaly?
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mueckenh@rz.fh-augsburg.de
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Read Re: Another AC anomaly?
Virgil
12/1/09
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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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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12/3/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/3/09
Read Re: Another AC anomaly?
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12/3/09
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12/7/09
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12/9/09
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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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12/19/09
Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
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12/22/09
Read Re: Another AC anomaly?
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12/22/09
Read Re: Another AC anomaly?
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12/18/09
Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
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12/21/09
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12/21/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/21/09
Read Re: Another AC anomaly?
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12/21/09
Read Re: Another AC anomaly?
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12/22/09
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12/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/27/09
Read Re: Another AC anomaly?
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12/16/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/16/09
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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12/11/09
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12/11/09
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12/10/09
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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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12/10/09
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12/3/09
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12/3/09
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12/3/09
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12/7/09
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12/7/09
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12/7/09
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12/7/09
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12/8/09
Read Re: Another AC anomaly?
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12/8/09
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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?
mueckenh@rz.fh-augsburg.de
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
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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12/4/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
Dik T. Winter
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
Read Re: Another AC anomaly?
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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
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/11/09
Read Re: Another AC anomaly?
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12/11/09
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12/11/09
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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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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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12/19/09
Read Re: Another AC anomaly?
Virgil
12/19/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/22/09
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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
Read Re: Another AC anomaly?
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12/27/09
Read Re: Another AC anomaly?
Virgil
12/27/09
Read Re: Another AC anomaly?
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12/13/09
Read Re: Another AC anomaly?
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12/4/09
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12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
Read Re: Another AC anomaly?
Virgil
12/4/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/4/09
Read Re: Another AC anomaly?
Virgil
12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
Read Re: Another AC anomaly?
Virgil
12/5/09
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mueckenh@rz.fh-augsburg.de
12/6/09
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Virgil
12/5/09
Read Re: Another AC anomaly?
Carsten Schultz
12/2/09
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Virgil
12/1/09
Read Re: Another AC anomaly?
george
12/1/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
anonymous.rubbertube@yahoo.com
11/30/09
Read Re: Another AC anomaly?
William Hughes
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?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
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11/27/09
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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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