Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 K_h Posts: 419 Registered: 4/12/07
Re: Another AC anomaly?
Posted: Dec 16, 2009 7:44 PM

"Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
news:KuqwG3.qv@cwi.nl...
> 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.
> > >
> > > 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.

What case did you have in mind? I found cases where it
works fine.

k

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