| 有限多重集的运算及性质 |
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| 引用本文： | 牟廉明.有限多重集的运算及性质[J].内江师范学院学报,2009,24(4):5-8. |
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| 作者姓名： | 牟廉明 |
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| 作者单位： | 四川省高等学校数值仿真重点实验室／／内江师范学院数学与信息科学学院,四川内江641112 |
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| 基金项目： | 国家自然科学基金，四川科技厅应用基础研究项目 |
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| 摘 要： | 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．
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| 关 键 词： | 多重集 重复度 有限多重集幂集 排中律 |
Research of the Nature & Operation of Finite Multiset |
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| MOU Lian-ming.Research of the Nature & Operation of Finite Multiset[J].Journal of Neijiang Teachers College,2009,24(4):5-8. |
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| Authors: | MOU Lian-ming |
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| Institution: | Key Laboratory of Numerical Simulation of Sichuan Province//School of Mathematics & Information Science;Neijiang Normal University;Neijiang;Sichuan 641112;China |
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| Abstract: | 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 m... |
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| Keywords: | multiset multiplicity of multiset power set of the finite multiset law of excluded middle |
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