Large set (combinatorics)

In combinatorial mathematics, a large set of positive integers

For other uses of the term, see Large set.

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.

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