Inmathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers.
A set is called piecewise syndetic if there exists a finite subset Gof such that for every finite subset Fof there exists an such that
where . Equivalently, S is piecewise syndetic if there is a constant b such that there are arbitrarily long intervalsof where the gaps in S are bounded by b.
There are many alternative definitions of largeness that also usefully distinguish subsets of natural numbers: