Summary: 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 infinity are reviewed. The restriction of the repellency of two existing views on the infinity is pointed out, 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.
For the other parts see Zbl 1099.03506, Zbl 1097.01506, Zbl 1097.01507 and Zbl 1097.01508.