【摘要】 集合是现代数学中最基本的概念之一,并已深入到各种学科和技术领域中.而作为集合概念扩展的多重集合概念,却少有应用.通过对多重集合进行系统研究,提出了多重集合的包含、相等、多重幂集,以及多重集合补集等相关概念和运算,建立了多重集合完善的理论体系,并给出了多重集合在古典概率中的应用.为进一步研究多重集合在各种学科和技术领域中的应用打下了良好的基础.更多还原

【Abstract】 The set is one of the most basic concepts in modern mathematics,penetrating into in each discipline and the area of technology.But the multi-set which expands as the set is actually seldom applied.Through a systematic research on the multi-set,this paper proposes some correlated concepts and operations of the multi-set involvement,multi-set equality,multiple power set and multiple complementary set.It establishes a basic theory of the multi-set and illustrates its application to classical probability.This theory has laid a good foundation for a further study of the application of the multi-set to each discipline and area of science and technology.更多还原