Sets of natural numbers with no minimal asymptotic bases

Paul ErdÖS, Melvyn B. Nathanson, M. B. Nathanson

Research output: Contribution to journalArticle

3 Citations (Scopus)


The set A of natural numbers is an asymptotic basis for S if the sets S and 2.4 eventually coincide. An asymptotic basis A for S is minimal if no proper subset of A is a basis for S. Sets S are constructed which possess infinitely many asymptotic bases, but no minimal asymptotic basis.

Original languageEnglish
Pages (from-to)100-102
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number2
Publication statusPublished - Jul 1978


  • Addition of sequences
  • Minimal bases
  • Sum sets

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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