{"title":"有理数和实数","authors":"Julius Wihelm Richard, Dedekind","doi":"10.1142/9789811219986_0004","DOIUrl":null,"url":null,"abstract":"• What other properties do the Rational Numbers have that characterize them? Rational Order Is (Q,+,•) an ordered integral domain? Recall the definition of ordered. Ordered Integral Domain: Contains a subset D+ with the following properties. 1. If a, b ∈ D+ ,then a + b ∈ D+ (closure) 2. If a , b ∈ D+ , then a • b ∈ D+ (closure) 3. For each a ∈ Integral Domain D exactly one of these holds a = 0, a ∈ D+, -a ∈ D+ (Trichotomy)","PeriodicalId":146786,"journal":{"name":"Invitation to Algebra","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"RATIONAL AND REAL NUMBERS\",\"authors\":\"Julius Wihelm Richard, Dedekind\",\"doi\":\"10.1142/9789811219986_0004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"• What other properties do the Rational Numbers have that characterize them? Rational Order Is (Q,+,•) an ordered integral domain? Recall the definition of ordered. Ordered Integral Domain: Contains a subset D+ with the following properties. 1. If a, b ∈ D+ ,then a + b ∈ D+ (closure) 2. If a , b ∈ D+ , then a • b ∈ D+ (closure) 3. For each a ∈ Integral Domain D exactly one of these holds a = 0, a ∈ D+, -a ∈ D+ (Trichotomy)\",\"PeriodicalId\":146786,\"journal\":{\"name\":\"Invitation to Algebra\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Invitation to Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789811219986_0004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Invitation to Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789811219986_0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
• What other properties do the Rational Numbers have that characterize them? Rational Order Is (Q,+,•) an ordered integral domain? Recall the definition of ordered. Ordered Integral Domain: Contains a subset D+ with the following properties. 1. If a, b ∈ D+ ,then a + b ∈ D+ (closure) 2. If a , b ∈ D+ , then a • b ∈ D+ (closure) 3. For each a ∈ Integral Domain D exactly one of these holds a = 0, a ∈ D+, -a ∈ D+ (Trichotomy)
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