Date: Dec 21, 2009 8:08 AM
Author: Dik T. Winter
Subject: Re: Another AC anomaly?
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.

With your definition:

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/