Piecewise syndetic set
In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. A set S ⊂ N {\displaystyle S\subset \mathbb {N} } is called piecewise syndetic if there exists a finite subset G of N {\displaystyle \mathbb {N} } such that for every finite subset F of N {\displaystyle \mathbb {N} } there exists an x ∈ N {\displaystyle x\in \mathbb {N} } such that x + F ⊂ ⋃ n ∈ G ( S − n ) {\displaystyle x+F\subset \bigcup _{n\in G}(S-n)} where S − n = { m ∈ N : m + n ∈ S } {\displaystyle S-n=\{m\in \mathbb {N} :m+n\in S\}} .