 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?
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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] ???!!!