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 Quote by micromass Yes, that is very good! Try $$\mathbb{N}$$ with the discrete metric. Isn't that the counterexample you're looking for?
I wasn't sure about $$\mathbb{N}$$ being separable, but after thinking about it, it is dense in itself. Because every natural number is either in $$\mathbb{N}$$ 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 $$\mathbb{N}$$ ???!!!