Syndetic set

In mathematics, a syndetic set is a subset of the natural numbers having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.

Definition
A set $$S \sub \mathbb{N}$$ is called syndetic if for some finite subset $$F$$ of $$\mathbb{N}$$


 * $$\bigcup_{n \in F} (S-n) = \mathbb{N}$$

where $$S-n = \{m \in \mathbb{N} : m+n \in S \}$$. Thus syndetic sets have "bounded gaps"; for a syndetic set $$S$$, there is an integer $$p=p(S)$$ such that $$[a, a+1, a+2, ..., a+p] \bigcap S \neq \emptyset$$ for any $$a \in \mathbb{N}$$.