Definition:Syndetic Subset of Natural Numbers

Definition

Let $E \subseteq \N_{>0}$ be a subset of the non-zero natural numbers.

$E$ is called syndetic if and only if there exists a finite subset $F \subseteq \N_{>0}$ such that:

$\ds \N_{>0} \subseteq \bigcup_{k \mathop \in F} \paren {E - k}$

Sources

• 2013: Peter Walters: An Introduction to Ergodic Theory (4th ed.) $2.5$: The Mean Ergodic Theorem