Let $A \subset \mathbb N$ be a antichain with respect to divisibility. Does this imply that the density of $A$ is $0$?
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Such a subset is called "primitive"; such a set must have lower density zero but (as shown by Besicovitch) does not need to have asymptotic density zero. Check out the references and results of this recent paper of Greg Martin and Carl Pomerance: |
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