Natural density

Summary

The natural density, or asymptotic density, of a set $A$ of positive integers is a limit as $n \to \infty$. It is the limit of the proportion of $\set{1, \dots, n}$ that lies in $A$. It makes precise statements such as "half of all integers are even" or "almost all integers are composite". Not every set has a natural density, but every set has an upper and a lower density. Many results of number theory, such as the Chebotarev density theorem, are statements about densities.