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Topic: Another AC anomaly?
Replies: 43   Last Post: Dec 21, 2009 8:08 AM

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 Dik T. Winter Posts: 7,899 Registered: 12/6/04
Re: Another AC anomaly?
Posted: Dec 16, 2009 7:38 AM
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In article <k6idnaWIQNah0LXWnZ2dnUVZ_hqdnZ2d@giganews.com> "K_h" <KHolmes@SX729.com> writes:
>
> "Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
> news:Kup2G0.IBK@cwi.nl...

> > In article <iNWdnfmPh7NpQ7vWnZ2dnUVZ_hydnZ2d@giganews.com>
> > "K_h" <KHolmes@SX729.com> writes:

> > > "Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
> > > news:KunEFz.913@cwi.nl...

> > ...
> >
> > The definition you provided for a sequence of sets A_n
> > depends on whether
> > each A_n is or is not a set containing a single set as an
> > element.
> >
> > Your definition leads to some strange consequences. I can
> > state the
> > following theorem:
> >
> > Let A_n and B_n be two sequences of sets. Let A_s = lim
> > sup A_n and
> > A_i = lim inf A_n, similar for B_s and B_i. Let C_n be
> > the sequence
> > defined as:
> > C_2n = A_n
> > C_(2n+1) = B_n
> > Theorem:
> > lim sup C_n = union (A_s, B_s)
> > lim inf C_n = intersect (A_i, B_i)
> > Proof:
> > easy.

>
> Yes, my definition did not include a limsup and liminf but
> they can be added. With this addition, the limit of sets
> like {X_n} is more in line with the general notion of a
> limit.

Well, the above theorem is still not valid with your definition.
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Date Subject Author
12/12/09 Jesse F. Hughes
12/13/09 K_h
12/14/09 Dik T. Winter
12/14/09 K_h
12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Dik T. Winter
12/16/09 K_h
12/17/09 Dik T. Winter
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/21/09 Dik T. Winter
12/14/09 Dik T. Winter
12/14/09 K_h
12/15/09 Dik T. Winter
12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Dik T. Winter
12/17/09 K_h
12/17/09 Dik T. Winter
12/18/09 K_h
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/15/09 K_h
12/16/09 Jesse F. Hughes
12/17/09 Dik T. Winter
12/17/09 Jesse F. Hughes
12/16/09 Dik T. Winter
12/15/09 ross.finlayson@gmail.com
12/13/09 K_h
12/13/09 Jesse F. Hughes
12/13/09 Jesse F. Hughes
12/14/09 Ilmari Karonen
12/14/09 Jesse F. Hughes
12/15/09 Chas Brown

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