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Talk:Density

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Asymptotic density

The article says:

Let be the set of fractions of . If has positive asymptotic density, then is (topologically) dense in the positive reals. If is not dense in the reals then has lower asymptotic density less than 1/2 and upper asymptotic density less than 1; and any such lower or upper density is achievable.

If is (topologically) dense in the positive reals, does it imply that has positive asymptotic density? If is the set of primes (which have null upper asymptotic density, and for which the Green–Tao theorem proved that it contains arbitrarily long arithmetic progressions), is (topologically) dense in the positive reals? — Daniel Forgues 05:03, 26 October 2012 (UTC)