摘要/Abstract

众所周知，有限无限问题是数学的基本问题，也是哲学的基本问题。本文基于辩证唯物主义无限观对诸流派无限思想进行了详细分析、评论，进一步理清无限思想的发展历程，以期对基础数学的健康发展贡献微薄之力。与此同时，本文作者还提出了无限交换悖论，对Hilbert旅馆问题中的实无限思想进行了强有力的质疑。

It is well known that the problem of finity and infinity is the basic problem of mathematics, and it is also the basic problem of Philosophy. Based on the infinite view of dialectical materialism, this paper makes a detailed analysis and comments on infinite thoughts of various schools, and further clarifies the development course of infinite thoughts in order to contribute to the healthy development of basic mathematics. At the same time, the author puts forward the Infinite Exchange Paradox, which strongly questions the idea of actual infinity in Hilbert Hotel Problem.