Syndetic set
Encyclopedia
In mathematics
, a syndetic set is a subset of the natural number
s, having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.
denote the set of finite subsets of 
. Then a set 
is called syndetic if for some 
where
. Thus syndetic sets have "bounded gaps"; for a syndetic set 
, there is an integer 
such that 
for any 
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a syndetic set is a subset of the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
s, having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.
Definition
Let denote the set of finite subsets of . Then a set is called syndetic if for some where
. Thus syndetic sets have "bounded gaps"; for a syndetic set , there is an integer such that for any .