Quote by micromass
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 b
_{1} and b
_{2} in B, with b
_{1}<b
_{2} there exists a in A st b
_{1}<a<b
_{2}. still confuses me.
if you take the numbers 1 and 2, then there exists no such number between them in [tex]\mathbb{N}[/tex] ???!!!