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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Sets of natural numbers with no minimal asymptotic bases


Authors: Paul Erdős and Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 70 (1978), 100-102
MSC: Primary 10L05
DOI: https://doi.org/10.1090/S0002-9939-1978-0485761-6
MathSciNet review: 0485761
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Abstract: The set A of natural numbers is an asymptotic basis for S if the sets S and 2A 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.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0485761-6
Keywords: Addition of sequences, minimal bases, sum sets
Article copyright: © Copyright 1978 American Mathematical Society