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#1 2007-05-23 16:48:10
- Stanley_Marsh
- Member
- Registered: 2006-12-13
- Posts: 345
A bit confuse.
Numbers are the essence of the Universe
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#2 2007-05-23 17:56:03
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: A bit confuse.
So what happens when you go from finite to countable?
Consider the sets (-1/n, 1/n) for any integer n. Obviously, each is open.
But now what is in the intersection for all n? It should be clear that only 0 is (Archimedian property) in this set. So it can't be open since 0 is not an interior point.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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