Bases for sets of integers

Abstract We are interested in expressing each of a given set of non-negative integers as the sum of two members of a second set, the second set to be chosen as economically as possible. So let us call B a basis for A if to every a ∈ A there exist b , b ′ ∈ B such that a = b + b ′. We concern ourselves primarily with finite sets, A , since the results for infinite sets generally follow from these by the familiar process of condensation.