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

 Messages: [ Previous | Next ]
 Marshall Posts: 1,936 Registered: 8/9/06
Re: Another AC anomaly?
Posted: Dec 11, 2009 10:49 PM

On Dec 11, 6:39 pm, "K_h" <KHol...@SX729.com> wrote:
> "Dik T. Winter" <Dik.Win...@cwi.nl> wrote in messagenews:KuHL7p.3zE@cwi.nl...
>
>
>

> > In article <5ZedndTmvoBac7zWnZ2dnUVZ_qOdn...@giganews.com>
> > "K_h" <KHol...@SX729.com> writes:

> > > "Dik T. Winter" <Dik.Win...@cwi.nl> wrote in message
> > >news:KuFy3L.Cxt@cwi.nl...

> > ...
> > > > Have a look at <http://en.wikipedia.org/wiki/Lim_inf>
> > > > in
> > > > the section
> > > > titled "Special case: dicrete metric".  An 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 depends on the context.  When it comes to supertasks,
> > > limsup={0,1} is basically useless.  That is why those
> > > definitions are not good, and invalid, for evaluating

>
> > I am not discussing supertasks, nor is WM here.  The
> > question is simply
> > whether it is possible that:
> >    lim | S_n | != | lim S_n |
> > with some form of limit.  And by the definitions I gave
> > (and which you
> >    lim(n -> oo) {n} = {}

>
> 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.  WM attributed
> this definition to you:
>
> - 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.
>
> definition WM attributes to you, give lim(n ->oo){n}=N.

It certainly appears to me that the definitions quoted give
lim(n -> oo){n} = {}. One of us is misreading it.

Marshall

Date Subject Author
11/23/09 Jesse F. Hughes
11/23/09 Herman Jurjus
11/23/09 master1729
11/25/09 T.H. Ray
11/24/09 george
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11/25/09 Bill Taylor
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11/30/09 Herman Jurjus
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12/1/09 Seth Breidbart
12/1/09 Marshall
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11/27/09 William Hughes
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11/29/09 William Hughes
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11/27/09 Virgil
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11/29/09 William Hughes
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11/27/09 mueckenh@rz.fh-augsburg.de
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11/30/09 Dik T. Winter
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11/30/09 Virgil
12/1/09 Dik T. Winter
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12/1/09 Dik T. Winter
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12/1/09 William Hughes
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12/1/09 Virgil
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12/2/09 Dik T. Winter
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12/2/09 Dik T. Winter
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12/3/09 Dik T. Winter
12/3/09 K_h
12/7/09 Dik T. Winter
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12/9/09 K_h
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12/10/09 Virgil
12/10/09 Dik T. Winter
12/11/09 mueckenh@rz.fh-augsburg.de
12/11/09 Virgil
12/15/09 Dik T. Winter
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12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Virgil
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12/17/09 Dik T. Winter
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12/17/09 Virgil
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12/17/09 YBM
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12/17/09 Quaestor
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12/18/09 Dik T. Winter
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12/21/09 Marshall
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12/22/09 Dik T. Winter
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12/27/09 Virgil
12/16/09 mueckenh@rz.fh-augsburg.de
12/16/09 Virgil
12/11/09 K_h
12/11/09 Dik T. Winter
12/11/09 K_h
12/11/09 Marshall
12/12/09 Jesse F. Hughes
12/12/09 K_h
12/12/09 K_h
12/11/09 mueckenh@rz.fh-augsburg.de
12/11/09 Virgil
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12/8/09 Dik T. Winter
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12/8/09 anonymous.rubbertube@yahoo.com
12/8/09 Virgil
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