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}
}
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

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