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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 21, 2009 8:08 AM

In article <QeCdnWPXUMnJqLHWnZ2dnUVZ_o-dnZ2d@giganews.com> "K_h" <KHolmes@SX729.com> writes:
> "Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message
> news:Kuuqrs.FJ7@cwi.nl...

...
> Let A_n and B_n be two sequences of sets of the form {X_n}.
> 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 and
> C_(2n+1) = B_n.
>
> Theorem:
> Since A_s = {a_s} and B_s = {b_s}
>
> lim sup C_n = {a_s \/ b_s}
>
> lim inf C_n = {a_i /\ b_i}

Let A_n = {{a}} for some object a, let B_n = {{n}} with n natural.
A_s = {{a}}, B_s = {{N}}
A_i = {{a}}, B_i = {{N}}
but
C_s = {{a}} and C_i = {{}}.
--
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