Upper asymptotic density

Definition

Let $S$ be a subset of the set $\mathbb{N}$ of natural numbers. The upper asymptotic density of $S$ in $\mathbb{N}$ is defined as:

$lim{sup}_{n\to \mathrm{\infty }}\frac{S\cap \{1,2,\dots ,n\}}{n}$.

Related notions

• Lower asymptotic density
• Schnirelmann density