Density of sets of natural numbers and the Levy group

Melvyn B. Nathanson, Rohit Parikh

Let $\mathbb{N}$ denote the set of positive integers. The asymptotic density of the set $A\subseteq \mathbb{N}$ is $d(A)={\lim }_{n\to \infty }|A\cap [1,n]|/n$, if this limit exists. Let $ \mathcal…