Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Open and Shut
Replies: 10   Last Post: Feb 4, 2013 10:50 PM

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
Re: Open and Shut
Posted: Feb 3, 2013 9:31 PM

On Sun, 3 Feb 2013, Virgil wrote:
> William Elliot <marsh@panix.com> wrote:
>

> > A subset A, of an ordered set is convex when
> > for all x,y in A, for all a, (x <= a <= y implies a in A).
> >
> > I will call an interval an order convex subset of Q.
> > Given an interval, what's the probablity that it's
> > open, closed, both, neither?

>
> The only probability that is certain in Q is that the probability of
> being both open and closed is zero, as Q and {} are the only non-empty
> order-convex sets in Q that are both open and closed under the order
> toology, and there are infinitely many other intervals which are not
> both open and closed.

(-pi,pi) /\ Q is a proper, not empty, clopen, order convex subset of Q.

> To do more one needs to make some assumptions about the probability
> of a non-empty set of rationals which is (finitely) bounded above
> containing its least upper bound or a non-empty set of rationals which
> is (finitely) bounded below containing its greatest lower bound.

> > Given an open subset of Q, what's the probablity that it's clopen?

> > Given an closed subset of Q, what's the probablity that it's clopen?

----

Date Subject Author
2/2/13 William Elliot
2/3/13 Shmuel (Seymour J.) Metz
2/3/13 David C. Ullrich
2/4/13 William Elliot
2/3/13 Virgil
2/3/13 Butch Malahide
2/3/13 William Elliot
2/4/13 Virgil
2/4/13 Butch Malahide
2/4/13 Virgil
2/4/13 Shmuel (Seymour J.) Metz