Thick set
In mathematics, a thick set is a set of integers that contains arbitrarily long intervals. That is, given a thick set, for every, there is some such that.Examples
Trivially 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:Generalisations
The notion of a thick set can also be defined more generally for a semigroup, as follows. Given a semigroup and, is said to be thick if for any finite subset, there exists such that
It can be verified that when the semigroup under consideration is the natural numbers with the addition operation, this definition is equivalent to the one given above.
