Abstract

In this paper, we show that a ring of p-adic integers Z_p can be used to represent subsets of a bounded number set. We propose an approach to define a set of p-adic balls. The union of their images is a subset of the bounded number set. The cover of the set of p-adic balls and the p-adic density of the subset of the bounded number set are defined. We also define the operations of p-adic intersection, union, and complement over sets of p-adic balls that can generate the corresponding algebra.

中文翻译：

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有界数集子集的 p-Adic 表示

摘要

在本文中，我们展示了一个 p-adic 整数环Z _p可用于表示有界数字集的子集。我们提出了一种定义一组 p-adic 球的方法。他们的图像的并集是有界数字集的子集。定义了 p-adic 球集的覆盖和有界数集子集的 p-adic 密度。我们还定义了可以生成相应代数的 p-adic 球集上的 p-adic 交、并和补运算。