{"title":"多集的简单维恩图","authors":"Aurelian Radoaca","doi":"10.1109/SYNASC.2015.36","DOIUrl":null,"url":null,"abstract":"We introduce Venn diagrams for multisets and showhow they simplify the analysis of multisets. Venn diagrams arevery useful in proofs involving multisets and multiset orders, especially considering the complications introduced by the multiplicity of elements in multisets. We compare the Venn diagramsfor multisets with the corresponding ones for sets. Thus, wepresent two types of Venn diagrams for multisets, a simple onethat looks like a diagram for sets, but with areas that are notnecessarily disjoint, and a complex one (compared to sets), butwith certain delimited disjoint areas.","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"98 1","pages":"181-184"},"PeriodicalIF":0.0000,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Simple Venn Diagrams for Multisets\",\"authors\":\"Aurelian Radoaca\",\"doi\":\"10.1109/SYNASC.2015.36\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce Venn diagrams for multisets and showhow they simplify the analysis of multisets. Venn diagrams arevery useful in proofs involving multisets and multiset orders, especially considering the complications introduced by the multiplicity of elements in multisets. We compare the Venn diagramsfor multisets with the corresponding ones for sets. Thus, wepresent two types of Venn diagrams for multisets, a simple onethat looks like a diagram for sets, but with areas that are notnecessarily disjoint, and a complex one (compared to sets), butwith certain delimited disjoint areas.\",\"PeriodicalId\":6488,\"journal\":{\"name\":\"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"volume\":\"98 1\",\"pages\":\"181-184\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2015.36\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2015.36","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce Venn diagrams for multisets and showhow they simplify the analysis of multisets. Venn diagrams arevery useful in proofs involving multisets and multiset orders, especially considering the complications introduced by the multiplicity of elements in multisets. We compare the Venn diagramsfor multisets with the corresponding ones for sets. Thus, wepresent two types of Venn diagrams for multisets, a simple onethat looks like a diagram for sets, but with areas that are notnecessarily disjoint, and a complex one (compared to sets), butwith certain delimited disjoint areas.