On 20 Jul., 21:52, Gus Gassmann <horand.gassm...@googlemail.com> wrote: > On Jul 20, 2:48 pm, MoeBlee <modem...@gmail.com> wrote:
> > How are we defining 'continuous' in this context? > > lim card(B_k) = card (lim B_k), where the latter lim has to be defined > suitably, for instance as a union. > > > > and does not commute with his limit > > > operator. > > > Limit in this context is just union.
Correct. > > > What is the incorrect commutation he insists on? > > I am sure he is eventually going to tell you this himself, in his own > way, but he thinks that > > 0 = lim card(B_k) = card (lim B_k) = 2^aleph_0-
You can see that Gus has no the least knowledge about our discussion. card(lim B_k) = aleph_0. That was never in question. And card B_k = k, so lim card(B_k) = lim k = aleph_0 too.
But in some problems it is in fact not like set theorists (he is nothing of that kind) think. Here you can see an example:
This sequence does not converge in mathematics. But in set theory the limit is 10/99 or less, because for every digit we can determine when it will disappear behind the decimal point.
