Syndetic set - Alchetron, The Free Social Encyclopedia

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 ⊂ N is called syndetic if for some finite subset F of N

⋃ n ∈ F ( S − n ) = N

where S − n = { m ∈ N : m + n ∈ 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 ] ⋂ S ≠ ∅ for any a ∈ N .

References

Syndetic set Wikipedia

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