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<p>In this work, we present some results on the asymptotic density of sets of natural numbers. One of the results shows a relationship between the densities of two subsets, where the difference in their densities can be controlled by the upper limit of a sequence of real numbers. Another result introduces a function that maps the elements of a set of natural numbers, providing a way to calculate its density. We then introduce the notion of regular parametrization and show that any set admitting such a parametrization necessarily has asymptotic density, which can be computed directly from the growth of successive differences.</p>

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Some results on the asymptotic density of sets of natural numbers

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Renan J. S. Isneri,
  • Maxwell A. da Silva,
  • Vandenberg L. Vieira

摘要

In this work, we present some results on the asymptotic density of sets of natural numbers. One of the results shows a relationship between the densities of two subsets, where the difference in their densities can be controlled by the upper limit of a sequence of real numbers. Another result introduces a function that maps the elements of a set of natural numbers, providing a way to calculate its density. We then introduce the notion of regular parametrization and show that any set admitting such a parametrization necessarily has asymptotic density, which can be computed directly from the growth of successive differences.