Maximal asymptotic nonbases
Abstract: Let be a set of nonnegative integers. If all but a finite number of positive integers can be written as a sum of elements of , then is an asymptotic basis of order . Otherwise, is an asymptotic nonbasis of order . A class of maximal asymptotic nonbases is constructed, and it is proved that any asymptotic nonbasis of order 2 that satisfies a certain finiteness condition is a subset of a maximal asymptotic nonbasis of order 2.
Keywords: Addition of sequences, sum sets, asymptotic bases, asymptotic nonbases, maximal nonbases
Article copyright: © Copyright 1975 American Mathematical Society