Partitions of the natural numbers into infinitely oscillating bases and nonbases

Paul Erdös, Melvyn B. Nathanson

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The set A of nonnegative integers is a basis if every sufficiently large integer x can be written in the form x=a+a′ with a, a′∈A. If A is not a basis, then it is a nonbasis. We construct a partition of the natural numbers into a basis A and a nonbasis B such that, as random elements are moved one at a time from A to B, from B to A, from A to B, ..., the set A oscillates from basis to nonbasis to basis ... and the set B oscillates simultaneously from nonbasis to basis to nonbasis...

Original languageEnglish
Pages (from-to)171-182
Number of pages12
JournalCommentarii Mathematici Helvetici
Volume51
Issue number1
DOIs
Publication statusPublished - Dec 1 1976

ASJC Scopus subject areas

  • Mathematics(all)

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