有限多重集的运算及性质

Research of the Nature & Operation of Finite Multiset

给出了多重集的定义,讨论了有限多重集的若干运算及其性质,得出有限多重集容斥原理仍然成立,而排中律不成立;有限多重集幂集的交、并、补运算构成软代数.建立了有限多重集比较完善的理论体系.

The multiset is actually a natural prolongation of a common set. The definition of the multiset is proposed and a number of operations concerning the finite multiset and its nature are discussed in the paper. Through a systematic research of the finite multiset, the inclusion-exclusion principle still holds true but the law of excluded middle proves to be invalid. Operations like intersection, union and complement on the power set of the finite multiset constitute soft algebras. A systemic theory for the finite multiset is established, which has laid a solid foundation for the further study of the finite multiset and its application as well.