论文标题
幼稚的无限分析：其构建及其特性
Naïve Infinitesimal Analysis: Its Construction and Its Properties
论文作者
论文摘要
本文旨在建立对非标准数学分析的新理解。本文的主要贡献是构建了一组新数字，即$ \ mathbb {r}^{\ mathbb {z} _ <} $，其中包括无限和无限量。这款新集合的构造是天真的，因为它不需要任何重型的数学机械，因此从长远来看，它的问题要小得多。尽管它具有幼稚的特征，但$ \ mathbb {r}^{\ mathbb {z} _ <} $仍然是一个强大而有意义的工作。我们进一步发展了一些分析和拓扑特性，在那里我们不仅是经典的基本理论，而且还恢复了一些新的概念，我们还恢复了一些新的核心概念。还探讨了该集合的可计算性问题。此处介绍的作品可以看作是对桥梁建设性分析和非标准分析的贡献，在过去的几年中，该作品已广泛（和强度）进行了广泛讨论。
This paper aims to build a new understanding of the nonstandard mathematical analysis. The main contribution of this paper is the construction of a new set of numbers, $\mathbb{R}^{\mathbb{Z}_< }$, which includes infinities and infinitesimals. The construction of this new set is done naïvely in the sense that it does not require any heavy mathematical machinery, and so it will be much less problematic in a long term. Despite its naïvety character, the set $\mathbb{R}^{\mathbb{Z}_< }$ is still a robust and rewarding set to work in. We further develop some analysis and topological properties of it, where not only we recover most of the basic theories that we have classically, but we also introduce some new enthralling notions in them. The computability issue of this set is also explored. The works presented here can be seen as a contribution to bridge constructive analysis and nonstandard analysis, which has been extensively (and intensively) discussed in the past few years.
