Re: 1-1/2+1/3-1/4+1/5-1/6+1/7

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Gonçalo Rodrigues wrote:

On Mon, 11 Feb 2008 09:13:50 -0500, "Jesse F. Hughes"
<jesse@xxxxxxxxxxxxx> fed this fish to the penguins:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Is there a problem while interchanging a set difference with our
limit ?

Not sure what set difference you're talking about. The problem is
that you think S[N] = lim S_n[N], but if you unravel the definitions
you'll see that this just isn't so.

Here is another reason that the bracket notation isn't so good. It's
true that

S(x) = lim S_n(x)

but it is not true that

S[N] = lim S_n[N].

In terms of that more categorical notation, we'd say something like:
S = lim S_n, but not PS = lim PS_n, i.e., that the powerset functor
doesn't commute with colimits. Something like that, anyway, but not
*quite* that, since s isn't really a function in the category Set.
But since category theory probably won't clear up your issues, let's
leave the details alone.

Is the limit notion involved here the one about lim sup and lim inf
of sequences of sets the G. Frege introduced with some quotes from
Halmos? If yes, then the answer to Han's question (if I understood
it correctly) is yes.

Oh, dear ! Confusion all over the place ! My poor head .. it hurts
...

I can't say that Goncala's post is all that clear, but it seems to me
that he is saying "yes" to the question:

Is there a problem while interchanging a set difference with our
limit ?

This doesn't contradict what I said. Both of us agree that your
mistake involves illegitimately commuting a (co)limit.

--
"Come on people!!! The US just blew up a lot of people in Iraq, don't
you realize that a person with my exposure might just end up dead, by
mysterious circumstances?"
--James Harris, on the dangers of "proving" Fermat's last theorem
.