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

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Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: Another AC anomaly?
Posted: Dec 12, 2009 12:23 PM
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"K_h" <KHolmes@SX729.com> writes:

> The only way lim(n ->oo){n}={} is if limsup and liminf both
> equal {}. If limsup and liminf are different then the limit
> does not exist and cannot equal an existing set like {}.
> Since the empty set exists, and since you are claiming that
> lim(n ->oo){n}={}, you need to show that limsup and liminf
> are both {} by the definition you are using.


Yes, he needs to show that, but it is utterly trivial and obvious from
the definition of limsup and liminf given here. I'm not sure why you
think it's not obvious, but here's the proof.

Now, let X_n = {n}. Thus, n is in X_k <-> n = k.

n in lim sup X_k iff n is in infinitely many X_k, but we see from the
above that n is in only one X_k. Thus, lim sup X_k = {}.

n in lim inf X_k iff there are only finitely many X_k such that n not
in X_k, but again, we see that this is false for every n. Hence
lim inf X_k = {}.


--
Jesse F. Hughes
"It is a clear sign that something is very, very, very wrong, as human
beings are, well human. Maybe some people think that mathematicians
are not, but I disagree. They are human beings." -- James S. Harris


Date Subject Author
11/23/09
Read Re: Another AC anomaly?
Jesse F. Hughes
11/23/09
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Herman Jurjus
11/23/09
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master1729
11/25/09
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T.H. Ray
11/24/09
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george
12/1/09
Read Re: Another AC anomaly?
george
11/25/09
Read Re: Another AC anomaly?
Bill Taylor
11/26/09
Read Re: Another AC anomaly?
Daryl McCullough
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
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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
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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
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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
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
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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
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
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Alan Smaill
11/29/09
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William Hughes
11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil
11/27/09
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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
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mueckenh@rz.fh-augsburg.de
11/27/09
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Alan Smaill
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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Dik T. Winter
11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
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Virgil
12/1/09
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Dik T. Winter
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
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Dik T. Winter
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
William Hughes
12/1/09
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Virgil
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
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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
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ross.finlayson@gmail.com
12/1/09
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Virgil
12/2/09
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Dik T. Winter
12/2/09
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mueckenh@rz.fh-augsburg.de
12/2/09
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Dik T. Winter
12/2/09
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mueckenh@rz.fh-augsburg.de
12/2/09
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Virgil
12/3/09
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Dik T. Winter
12/3/09
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mueckenh@rz.fh-augsburg.de
12/3/09
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Dik T. Winter
12/3/09
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K_h
12/7/09
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Dik T. Winter
12/7/09
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Virgil
12/8/09
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K_h
12/8/09
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Virgil
12/9/09
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K_h
12/9/09
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Virgil
12/9/09
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mueckenh@rz.fh-augsburg.de
12/9/09
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Virgil
12/9/09
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K_h
12/10/09
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Dik T. Winter
12/9/09
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K_h
12/9/09
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Virgil
12/10/09
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Dik T. Winter
12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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Virgil
12/10/09
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Dik T. Winter
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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Virgil
12/15/09
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Dik T. Winter
12/15/09
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mueckenh@rz.fh-augsburg.de
12/15/09
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Dik T. Winter
12/15/09
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K_h
12/16/09
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Virgil
12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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Virgil
12/17/09
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Dik T. Winter
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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Virgil
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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YBM
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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Quaestor
12/18/09
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mueckenh@rz.fh-augsburg.de
12/18/09
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Virgil
12/18/09
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Dik T. Winter
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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Virgil
12/22/09
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Dik T. Winter
12/22/09
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Virgil
12/18/09
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Dik T. Winter
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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Quaestor
12/21/09
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Dik T. Winter
12/21/09
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mueckenh@rz.fh-augsburg.de
12/21/09
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Marshall
12/21/09
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Virgil
12/22/09
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Dik T. Winter
12/27/09
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mueckenh@rz.fh-augsburg.de
12/27/09
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Virgil
12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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Virgil
12/11/09
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K_h
12/11/09
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Dik T. Winter
12/11/09
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K_h
12/11/09
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Marshall
12/12/09
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Jesse F. Hughes
12/12/09
Read Re: Another AC anomaly?
K_h
12/12/09
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K_h
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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Virgil
12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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Virgil
12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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Virgil
12/10/09
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Dik T. Winter
12/10/09
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Dik T. Winter
12/11/09
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K_h
12/11/09
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Virgil
12/7/09
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mueckenh@rz.fh-augsburg.de
12/7/09
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Virgil
12/8/09
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Dik T. Winter
12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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anonymous.rubbertube@yahoo.com
12/8/09
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Virgil
12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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Virgil
12/10/09
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Dik T. Winter
12/3/09
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Virgil
12/3/09
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mueckenh@rz.fh-augsburg.de
12/3/09
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Virgil
12/7/09
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Dik T. Winter
12/7/09
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Virgil
12/7/09
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mueckenh@rz.fh-augsburg.de
12/7/09
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Virgil
12/8/09
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Dik T. Winter
12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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Virgil
12/10/09
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Dik T. Winter
12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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Virgil
12/10/09
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Dik T. Winter
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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Virgil
12/11/09
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Virgil
12/15/09
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Dik T. Winter
12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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Dik T. Winter
12/16/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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T.H. Ray
12/17/09
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Dik T. Winter
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
12/4/09
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Marshall
12/7/09
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Dik T. Winter
12/7/09
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mueckenh@rz.fh-augsburg.de
12/7/09
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Virgil
12/8/09
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Dik T. Winter
12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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Virgil
12/10/09
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Dik T. Winter
12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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Virgil
12/10/09
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Dik T. Winter
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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Marshall
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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Virgil
12/11/09
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Virgil
12/11/09
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Marshall
12/12/09
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mueckenh@rz.fh-augsburg.de
12/12/09
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Virgil
12/12/09
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Marshall
12/12/09
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mueckenh@rz.fh-augsburg.de
12/12/09
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Virgil
12/12/09
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Marshall
12/12/09
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mueckenh@rz.fh-augsburg.de
12/12/09
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Virgil
12/12/09
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Marshall
12/12/09
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george
12/12/09
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Virgil
12/12/09
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george
12/13/09
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mueckenh@rz.fh-augsburg.de
12/13/09
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Virgil
12/15/09
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Dik T. Winter
12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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Virgil
12/17/09
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Dik T. Winter
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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Quaestor
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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Quaestor
12/18/09
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mueckenh@rz.fh-augsburg.de
12/18/09
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Virgil
12/18/09
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Dik T. Winter
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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Virgil
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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Marshall
12/19/09
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Virgil
12/19/09
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Virgil
12/19/09
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ross.finlayson@gmail.com
12/19/09
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Virgil
12/22/09
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ross.finlayson@gmail.com
12/22/09
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Marshall
12/27/09
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ross.finlayson@gmail.com
12/21/09
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Dik T. Winter
12/21/09
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mueckenh@rz.fh-augsburg.de
12/21/09
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Virgil
12/22/09
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Dik T. Winter
12/27/09
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mueckenh@rz.fh-augsburg.de
12/27/09
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Marshall
12/27/09
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Virgil
12/27/09
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Virgil
12/27/09
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Ralf Bader
12/27/09
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Virgil
12/13/09
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mueckenh@rz.fh-augsburg.de
12/13/09
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Virgil
12/4/09
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K_h
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
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Virgil
12/5/09
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mueckenh@rz.fh-augsburg.de
12/6/09
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Virgil
12/5/09
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Carsten Schultz
12/2/09
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Virgil
12/1/09
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george
12/1/09
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Virgil
11/27/09
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Virgil
11/27/09
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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
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mueckenh@rz.fh-augsburg.de
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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William Hughes
11/27/09
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anonymous.rubbertube@yahoo.com
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
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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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