Fundamentals of Abstract Analysis最新文献

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The Set-Theoretic Machinery 集合论机制
Fundamentals of Abstract Analysis Pub Date : 2018-10-08 DOI: 10.1201/9781315275444-9
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引用次数: 0
Counting and the Size of Sets 计数和集合的大小
Fundamentals of Abstract Analysis Pub Date : 2018-10-08 DOI: 10.1201/9781315275444-17
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引用次数: 0
The Construction of the Real Numbers 实数的构造
Fundamentals of Abstract Analysis Pub Date : 2018-10-08 DOI: 10.1201/9781315275444-15
Holmes
{"title":"The Construction of the Real Numbers","authors":"Holmes","doi":"10.1201/9781315275444-15","DOIUrl":"https://doi.org/10.1201/9781315275444-15","url":null,"abstract":"Commutative laws: Addition and multiplication are commutative operations. Associative laws: Addition and multiplication are associative operations. Distributive law: x(y + z) = xy + xz as usual. Identity for multiplication: 1 is the identity element for multiplication. Inverse law for multiplication: Every number a has a multiplicative inverse a. (recall that zero is not in our system). Definition: We define x < y as ∃z(x + z = y) then >, ≤, ≥ are defined using < as usual. Trichotomy 1: For any x and y, either x < y, y < x, or x = y. Trichotomy 2: For any x and y, either ¬x < y or ¬y < x.","PeriodicalId":371419,"journal":{"name":"Fundamentals of Abstract Analysis","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121243355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An Introduction to Analytic Functions 解析函数导论
Fundamentals of Abstract Analysis Pub Date : 2018-10-08 DOI: 10.1007/978-3-030-42085-7
Mac Nerney
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引用次数: 3
Sums and Products 和与积
Fundamentals of Abstract Analysis Pub Date : 2018-10-08 DOI: 10.1201/9781315275444-19
C. Pomerance, A. Schinzel
{"title":"Sums and Products","authors":"C. Pomerance, A. Schinzel","doi":"10.1201/9781315275444-19","DOIUrl":"https://doi.org/10.1201/9781315275444-19","url":null,"abstract":"What could be simpler than to study sums and products of integers? Well maybe it is not so simple since there is a major unsolved problem: For any positive and arbitrarily large numbers N, is there a set of N positive integers where the number of pairwise sums is at most N2− and likewise, the number of pairwise products is at most N2−? Erdös and Szemerédi conjecture no. This talk is directed at another problem concerning sums and products, namely how dense can a set of positive integers be if it contains none of its pairwise sums and products? For example, take the numbers that are 2 or 3 mod 5, a set with density 2/5. Can you do better? This talk reports on recent joint work with P. Kurlberg and J.C. Lagarias. Sums and Products Carl Pomerance Dartmouth College FEATURED LECTURE BY: Marc-Thorsten Hütt","PeriodicalId":371419,"journal":{"name":"Fundamentals of Abstract Analysis","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128399597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical Configurations 数学的配置
Fundamentals of Abstract Analysis Pub Date : 2018-10-08 DOI: 10.1201/9781315275444-10
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引用次数: 0
The Topology of Metric Spaces 度量空间的拓扑
Fundamentals of Abstract Analysis Pub Date : 2005-01-30 DOI: 10.1201/9781315275444-20
S. Kumaresan
{"title":"The Topology of Metric Spaces","authors":"S. Kumaresan","doi":"10.1201/9781315275444-20","DOIUrl":"https://doi.org/10.1201/9781315275444-20","url":null,"abstract":"Preface / Basic Notions / Convergence / Continuity / Compactness / Connectedness / Complete Metric Spaces / Answers, Hints and Solutions / Bibliography / Index.","PeriodicalId":371419,"journal":{"name":"Fundamentals of Abstract Analysis","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127754103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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