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

