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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 9, 2009 9:27 AM
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On 9 Dez., 08:35, Virgil <Vir...@home.esc> wrote:
> In article <c8idnc6JG6hv34LWnZ2dnUVZ_q-dn...@giganews.com>,


> However, in the discussion between Dik and WM, Dik gave SPECIFIC
> definition of what HE meant by the limit of a seqeunce of sets which
> differed from that in your citation.


Dik:
Given a sequence of sets S_n then:
lim sup{n -> oo} S_n contains those elements that occur in
infinitely
many S_n
lim inf{n -> oo} S_n contains those elements that occur in all S_n
from
a certain S_n (which can be different for each
element).
lim{n -> oo} S_n exists whenever lim sup and lim inf are equal.
>
> > Define infimum and supremum as follows:
>
> > liminf X_n=\/(n=0, oo)[/\(m=n, oo) X_m]
> > (n-->oo)

>
> > limsup X_n=/\(n=0, oo)[\/(m=n, oo) X_m]
> > (n-->oo)

>
> > If these two are the same then the limit exists and is both
> > of them.

>
> The issue is not whether the naturals are such a limit but whether for
> every so defined limit the cardinality of the limit equals the limit
> cardinality of their cardinalities, which is different sort of limit


If the limit set emerges continuously (i.e. growing one-by-one) from
the sets of the sequence, then the cardinality will be bound to this
process and will also continuously emerge from the cardinalities of
the sets of the sequence.

If there is a gap in one sequence and no gap in the other, then this
indicates that at least one of the limits does not exist, probably
both do not exist.

This has been substanciated by the following thought-experiment:
If N is generated as a limit, then it is generated by adding number
after number.
When using an intermediate reservoir, as shown in my lesson
http://www.hs-augsburg.de/~mueckenh/GU/GU12.PPT#394,22,Folie 22
it becomes clear that N cannot be generated by adding number after
number.

Therefore neither N nor Card(N) are meaningful concepts - at least not
in mathematics.

Regards, WM


Date Subject Author
11/23/09
Read Re: Another AC anomaly?
Jesse F. Hughes
11/23/09
Read Re: Another AC anomaly?
Herman Jurjus
11/23/09
Read Re: Another AC anomaly?
master1729
11/25/09
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T.H. Ray
11/24/09
Read Re: Another AC anomaly?
george
12/1/09
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11/25/09
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11/26/09
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11/30/09
Read What's wrong with supertasks? (was Re: Another AC anomaly?)
Herman Jurjus
12/1/09
Read Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
plutonium.archimedes@gmail.com
12/1/09
Read Re: Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
Marshall
12/1/09
Read using signature-blocks to defame innocent people Re: Jesse Hughes of
Bentley College
plutonium.archimedes@gmail.com
12/1/09
Read Re: Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
Seth Breidbart
12/1/09
Read Re: using signature-blocks to defame innocent people Re: Jesse Hughes
of Bentley College
Marshall
12/2/09
Read Re: using signature-blocks to defame innocent people Re: Jesse Hughes
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
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/28/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/28/09
Read Re: Another AC anomaly?
Virgil
11/26/09
Read Re: Another AC anomaly?
William Hughes
11/28/09
Read Re: Another AC anomaly?
William Hughes
11/26/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/28/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
LauLuna
11/26/09
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William Hughes
11/26/09
Read Re: Another AC anomaly?
anonymous.rubbertube@yahoo.com
11/29/09
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?
Virgil
11/27/09
Read Re: Another AC anomaly?
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11/29/09
Read Re: Another AC anomaly?
William Hughes
11/30/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/30/09
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?
Virgil
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?
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11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Dik T. Winter
11/27/09
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mueckenh@rz.fh-augsburg.de
11/30/09
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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
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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?
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12/1/09
Read Re: Another AC anomaly?
Virgil
12/1/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
Virgil
12/1/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
12/1/09
Read Re: Another AC anomaly?
Virgil
12/1/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
12/1/09
Read Re: Another AC anomaly?
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12/2/09
Read Re: Another AC anomaly?
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12/2/09
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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12/11/09
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12/11/09
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12/12/09
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12/10/09
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12/10/09
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Read Re: Another AC anomaly?
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12/7/09
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12/3/09
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12/3/09
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12/8/09
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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
Read Re: Another AC anomaly?
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12/15/09
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12/16/09
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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
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
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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
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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12/10/09
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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12/11/09
Read Re: Another AC anomaly?
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12/11/09
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12/12/09
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12/12/09
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12/12/09
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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?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
Virgil
12/19/09
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12/27/09
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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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mueckenh@rz.fh-augsburg.de
12/4/09
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12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
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12/5/09
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12/5/09
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12/2/09
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12/1/09
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12/1/09
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11/27/09
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11/27/09
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anonymous.rubbertube@yahoo.com
11/30/09
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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
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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
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11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil

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