### Abstract

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

Pages (from-to) | 100-102 |

Number of pages | 3 |

Journal | Proceedings of the American Mathematical Society |

Volume | 70 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 1978 |

### Keywords

- Addition of sequences
- Minimal bases
- Sum sets

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Sets of natural numbers with no minimal asymptotic bases'. Together they form a unique fingerprint.

## Cite this

ErdÖS, P., Nathanson, M. B., & Nathanson, M. B. (1978). Sets of natural numbers with no minimal asymptotic bases.

*Proceedings of the American Mathematical Society*,*70*(2), 100-102. https://doi.org/10.1090/S0002-9939-1978-0485761-6