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Topic: Discussion with WM - Frustration reaches boiling point (What is not clear?)
Replies: 198   Last Post: Jul 10, 2014 12:04 AM

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 William Elliot Posts: 1,494 Registered: 1/8/12
Re: Discussion with WM - Frustration reaches boiling point (What is
not clear?)

Posted: Jul 2, 2014 3:52 AM

On Tue, 1 Jul 2014, PotatoSauce wrote:
> On Tuesday, July 1, 2014 11:15:32 PM UTC-4, William Elliot wrote:

> > > I have been discussing with WM about the following sequence of sets
> > > s_n = {-1/n, 1/n}.
> > > The standard product topology tells us that
> > > lim s_n = { }

> > What product?
> Given any set X, you can identify P(X) with { f | f: X -> {0,1} } (i.e.
> every subset of X can be identified with a characteristic function), and the
> latter space is Prod {0,1}, where Prod is taken over all elements of X.

That's just one of a number of ways of giving P(X) a topology or lim_j Aj
a definition. Yes, by that definition, the limit is empty.

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