{"title":"Collatz猜想失败时的两种不同情况","authors":"M. Ahmed","doi":"10.31559/glm2021.11.2.4","DOIUrl":null,"url":null,"abstract":"In this article, we construct networks of Collatz sequences such that the initial odd terms of these sequences increase monotonically. We also show how the subsequence of odd numbers in a Collatz sequence can be extended backwards, forever. Convergent sequences cannot contain divergent subsequences. Thus, we conclude that the Collatz Conjecture is false.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Two different scenarios when the Collatz Conjecture fails\",\"authors\":\"M. Ahmed\",\"doi\":\"10.31559/glm2021.11.2.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we construct networks of Collatz sequences such that the initial odd terms of these sequences increase monotonically. We also show how the subsequence of odd numbers in a Collatz sequence can be extended backwards, forever. Convergent sequences cannot contain divergent subsequences. Thus, we conclude that the Collatz Conjecture is false.\",\"PeriodicalId\":32454,\"journal\":{\"name\":\"General Letters in Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Letters in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31559/glm2021.11.2.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Letters in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31559/glm2021.11.2.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Two different scenarios when the Collatz Conjecture fails
In this article, we construct networks of Collatz sequences such that the initial odd terms of these sequences increase monotonically. We also show how the subsequence of odd numbers in a Collatz sequence can be extended backwards, forever. Convergent sequences cannot contain divergent subsequences. Thus, we conclude that the Collatz Conjecture is false.