Thick set - Alchetron, The Free Social Encyclopedia

In mathematics, a thick set is a set of integers that contains arbitrarily long intervals. That is, given a thick set T , for every p ∈ N , there is some n ∈ N such that { n , n + 1 , n + 2 , . . . , n + p } ⊂ T .

Examples

Trivially N is a thick set. Other well-known sets that are thick include non-primes and non-squares. Thick sets can also be sparse, for example:

⋃ n ∈ N { x : x = 10 n + m : 0 ≤ m ≤ n } .

References

Thick set Wikipedia

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