Large set (combinatorics)

In combinatorial mathematics, a large set of positive integers S = { s 0 , s 1 , s 2 , s 3 , … } {\displaystyle S=\{s_{0},s_{1},s_{2},s_{3},\dots \}} is one such that the infinite sum of the reciprocals 1 s 0 + 1 s 1 + 1 s 2 + 1 s 3 + ⋯ {\displaystyle {\frac {1}{s_{0}}}+{\frac {1}{s_{1}}}+{\frac {1}{s_{2}}}+{\frac {1}{s_{3}}}+\cdots } diverges. A small set is any subset of the positive integers that is not large; that is, one whose sum of reciprocals converges.

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