Date: Nov 17, 2012 12:22 PM
Author: LudovicoVan
Subject: Re: Matheology § 152
"William Hughes" <wpihughes@gmail.com> wrote in message

news:1ec0c2cc-f926-4fd4-a413-37ba8809ea80@y8g2000yqy.googlegroups.com...

> On Nov 17, 9:59 am, "LudovicoVan" <ju...@diegidio.name> wrote:

>> "William Hughes" <wpihug...@gmail.com> wrote in message

>> news:28bff553-f679-4e23-8932-a1fb42f1b364@c17g2000yqe.googlegroups.com...

>>

>> > Note that *set* limits have some important properties.

>>

>> > Given a sequence of sets {B_1,B_2,B_3,...}

>> > then the set limit always exists (it

>> > may be the empty set).

>>

>> > If we have

>>

>> > A = set limit {B_1,B_2,B_3....}

>>

>> > Then

>>

>> > A is a set

>> > A cannot contain an element that is not contained

>> > in any of the B's

>>

>> Williams going around, in circles:

>>

>> It was already mentioned that it is wrong to use that specific definition

>> to

>> solve the balls and vase problem.

>>

>> <http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Special_case:_discrete_metric>

>

> The problem is the above applies to *any* definition of a *set* limit.

But those definitions are a *specific* case of these:

<http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Sequences_of_sets>

I sometimes wonder which planet you come from.

-LV