本文旨在研究康托（Georg Cantor）数学思想中的实无限概念（Aktual-Unendliches）。这种关于无限的新理解是康托在研究流形理论（Mannigfaltigkeitslehre）时形成的，它首先是一个数学概念，但带有哲学和形而上学意蕴。第一部分主要介绍康托对实无限的看法，偏重从数学方面进行解读，然后提及他对实无限的辩护，其中主要关注的是哲学层面的的辩护。第二部分处理康托流形理论的两个要素，这将勾勒出实无限概念的应用情境，深化我们对它的理解。第三部分处理前述思想对传统的一和多这一问题的助益，首先简要介绍一和多问题的基本框架，然后指出康托对这一问题的贡献，最后在此基础上展望一种新的存在论。

My paper is aimed to study Georg Cantor’s concept of actual-infinity (Aktual-Unendliches) in his mathematical thoughts. This new explanation of infinity, which is firstly in the field of math but then permeates in the field of philosophy and metaphysic, emerged from his study of the theory of manifolds (Mannigfaltigkeitslehre). In the first part, I will introduce Cantor’s mathematical opinion of actual-infinity and his defense of it, which is limited in the aspect of philosophy. In the second part, I will discuss two elements of his theory of manifolds, in which actual-infinity is applied; it will help us broaden our understanding of actual-infinity. In the third part, I will argue that his new concept throws a light to the old metaphysical problem of one and many. Firstly, the fundamental frame of this problem will be mentioned in brief; then, I will discuss Cantor’s contributions to this problem; at last, I insist that a new kind of ontology could be possible on the basis of the new frame.