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 | References | Similar Articles | Additional Information
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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Additional Information
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