On Sums of Sets of Integers

Abstract

Small italics denote integers. Let A, B, … be sets of non-negative integers. Let A (h) be the number of positive integers in A that are not greater than h. Finally let A + B denote the set of all integers of the form a + b where a ⊂ A, b ⊂ B. The following result is implicitly contained in Mann's Proposition 11 (4):Theorem 1. Let n > 0 and(1.1) 0⊂4, 0⊂B, n⊄C = A + B.