无穷观问题的研究(I)——历史的回顾与思考

An Outlook on Infinity(Ⅰ)——Historical Studies and Remarks

本组系列论文 (I)～ (V)从数学和认识论的角度系统地研究了无穷观问题的历史发展和现状 ,确立了无穷观背景世界的三分法原则 ,指出了两种无穷观相互排斥的局限性 ,形成了统一两种无穷于同一框架中的基本观点 ,并建立了一个统一实无限与潜无限于同一框架中的公理集合论系统

In a view of mathematics and epistemology, in the series of papers from (Ⅰ) to (Ⅴ), the historical background and current situation of the problem of the infinity are reviewed, the restriction of the repellency of two existing views on the infinity is pointed, an outlook on the infinity to unify the actual infinity and the potential infinity into one framework are presented, and an axiomatic system of sets is established based on such a framework.