# Additive Systems and a Theorem of de Bruijn

@article{Nathanson2014AdditiveSA, title={Additive Systems and a Theorem of de Bruijn}, author={Melvyn B. Nathanson}, journal={The American Mathematical Monthly}, year={2014}, volume={121}, pages={5-17} }

- Published in The American Mathematical Monthly 2014
DOI:10.4169/amer.math.monthly.121.01.005

This paper proves a theorem of de Bruijn that classifies additive systems for the nonnegative integers, that is, families A = (Ai )i∈I of sets of nonnegative integers, each set containing 0, such that every nonnegative integer can be written uniquely in the form ∑ i∈I ai , with ai ∈ Ai for all i , and ai 6= 0 for only finitely many i . 1. ADDITIVE SYSTEMS. Let N, N0, and Z denote the sets of positive integers, nonnegative integers, and all integers, respectively. For integers a and b with a < b… CONTINUE READING