Re: Dense sets: Question
- From: David C. Ullrich <dullrich@xxxxxxxxxxx>
- Date: Mon, 25 Aug 2008 07:16:25 -0500
On Mon, 25 Aug 2008 04:16:21 -0700 (PDT), polymedes
<polymedes@xxxxxxxxx> wrote:
Let B be a dense set in R (=real numbers). B can be written as
infinite countable intersection of open sets.
That last is another assumption, not something you're
saying follows, right? In other words, assume B is
a dense G_delta.
Let C be an infinite
countable set.
The question is: Is B\C dense in R? and why?
Hint: It sounds like you just learned a big theorem
that says something about dense countable intersections
of open sets. B\C is the intersection of B and R\C,
and R\C is also a dense G_delta.
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.
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