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Apr1-11, 08:00 PM
P: 376
Quote Quote by micromass View Post
Yes, that is very good! Try [tex]\mathbb{N}[/tex] with the discrete metric. Isn't that the counterexample you're looking for?
I wasn't sure about [tex]\mathbb{N}[/tex] being separable, but after thinking about it, it is dense in itself. Because every natural number is either in [tex]\mathbb{N}[/tex] or is a limit point.

But the definition that states that A is dense in B iff for all b1 and b2 in B, with b1<b2 there exists a in A st b1<a<b2. still confuses me.

if you take the numbers 1 and 2, then there exists no such number between them in [tex]\mathbb{N}[/tex] ???!!!