In combinatorial mathematics, a large set of positive integers is one such that the infinite sum of the reciprocals diverges.
A small set is any subset of the positive integers that is not large; that is, one whose sum of reciprocals converges.
Large sets appear in the Müntz–Szász theorem and in the Erdős conjecture on arithmetic progressions.
Paul Erdős conjectured that all large sets contain arbitrarily long arithmetic progressions.
It is not known how to identify whether a given set is large or small in general.