At P985 of the book, says

But there are cuts that are not determined by rational numbers. If we put into the first class all negative rational numbers and all positive ones whose squares are less than 2, and put into the second class all the other rationals, then this cut is not determined by a rational number. To each such cut "we create a new irrational member a which is fully defined by this cut; we will say that the number α corresponds to this cut or that it brings about this cut." Hence there corresponds to each cut one and only one either rational or irrational number.

The first class should also include zero, the definition of such two classes in Dedekind’s own words:   

A little issue in Mathematical Thought from Ancient to Modern Times, Vol. 3的更多相关文章

  1. x square x cube

    Mathematical Thought From Ancient To Modern Times

  2. UBIFS - UBI File-System

    参考:http://www.linux-mtd.infradead.org/doc/ubifs.html#L_raw_vs_ftl UBIFS - UBI File-System Table of c ...

  3. Android Weekly Notes Issue #237

    Android Weekly Issue #237 December 25th, 2016 Android Weekly Issue #237 这是本年的最后一篇issue, 感谢大家. 本期内容包括 ...

  4. Android Weekly Notes Issue #236

    Android Weekly Issue #236 December 18th, 2016 Android Weekly Issue #236 本期内容包括: Google的物联网平台Android ...

  5. Android Weekly Notes Issue #235

    Android Weekly Issue #235 December 11th, 2016 Android Weekly Issue #235 本期内容包括: 开发一个自定义View并发布为开源库的完 ...

  6. Android Weekly Notes Issue #234

    Android Weekly Issue #234 December 4th, 2016 Android Weekly Issue #234 本期内容包括: ConstraintLayout的使用; ...

  7. Android Weekly Notes Issue #231

    Android Weekly Issue #231 November 13th, 2016 Android Weekly Issue #231 Android Weekly阅读笔记, Issue #2 ...

  8. Android Weekly Notes Issue #233

    Android Weekly Issue #233 November 27th, 2016 Android Weekly Issue #233 本期内容包括: 用Mockito做RxJava的单元测试 ...

  9. Android Weekly Notes Issue #232

    Android Weekly Issue #232 November 20th, 2016 Android Weekly Issue #232 本期内容包括: Kotlin的优势讨论; MVVM模式结 ...

随机推荐

  1. C++的子类与父类强制转换产生的问题

    近日,在项目的一个类中如果碰上想要将子类强制转换成父类,然后再调用其父类版本的virtual虚函数. 就会出现gcc编译错误提示:error: ld returned 1 exit status gc ...

  2. sql操作总结

    SQL 语句的多表查询方式例如:按照 department_id 查询 employees(员工表)和 departments(部门表)的信息.方式一(通用型):SELECT ... FROM ... ...

  3. Paxos算法1-算法形成理论[转载]

    地址 http://blog.csdn.net/chen77716/article/details/6166675 中文wiki http://zh.wikipedia.org/zh-cn/Paxos ...

  4. 瀑布 敏捷 精益 devops

    敏捷:  分工角色  大项目分小项目   每个节点时间设置里程碑 Scrum实施的核心可以概括为“化繁为简”,从几个维度解释下: 团队角色的定义,将团队人员定义为三个角色,Scrum Master(主 ...

  5. Windows 8(64位)如何搭建 Android 开发环境与真机测试(转)

    可以参考http://wenku.baidu.com/link?url=ghU6IFS1WJXLFKfM_0efv9YQEnMDBrdi9CXwirSs5IOLLeUfdIOh8OOVv0DX89Lt ...

  6. python 守护进程，监控进程

    守护进程代码: import time, os import subprocess def run(): while True: taskList = os.popen('tasklist').rea ...

  7. [IR] Dictionary Coding

    [数据压缩]LZ77算法原理及实现 [数据压缩]LZ78算法原理及实现 Lempel–Ziv–Welch 年发表的论文<A Universal Algorithm for Sequential ...

  8. Flask框架（2）-JinJa2模板

    为了把业务逻辑和表现逻辑分开,Flask把表现逻辑移到JinJa2模板,模板是一个包含响应文本的文件.它用占位变量表示动态部分,其具体要从请求上下文才知道. 把真实值替换掉占位变量成为渲染,JinJa ...

  9. file类型input框设置上传相同文件，并都可以触发change事件。

    在使用file类型input框是,删除了第一次上传到文件,再次上传相同文件,无法触发change事件,所以在删除的js上添加如下js代码: document.getElementById('fileU ...

  10. MySQL 去除字段中的换行和回车符

    今天csv 导入关键词的时候遇到问题 字段结束会有 回车符号 解决方法: ), ),'');          char(10):  换行符          char(13):  回车符