### 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 language | English |
---|---|

Pages (from-to) | 171-182 |

Number of pages | 12 |

Journal | Commentarii Mathematici Helvetici |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 1976 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Partitions of the natural numbers into infinitely oscillating bases and nonbases'. Together they form a unique fingerprint.

## Cite this

Erdös, P., & Nathanson, M. B. (1976). Partitions of the natural numbers into infinitely oscillating bases and nonbases.

*Commentarii Mathematici Helvetici*,*51*(1), 171-182. https://doi.org/10.1007/BF02568149