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实数集的程序数子集

发表时间:2008-03-15  浏览量:2288  下载量:820
全部作者: 陈必红
作者单位: 深圳大学数学与计算科学学院
摘 要: 实数集是不可数集,其中包括了有理数集和无理数集。无理数的小数部分是无限不循环的。但是无理数也可分为两类,一类虽然无限不循环,却也有规律可循,因此可用有限长度的程序语言对其进行描述或代表。称这类实数加上有理数所组成的集合叫程序数集,这个子集不仅包含有理数集,还包括了所有人类使用的无理数。这个子集形成一个数域,因此可构成它支持的线性空间。这个子集是可数集,这就不会具有不可数集的那些相应的性质。本文还提出了一个悖论,就是非程序数并不存在。
关 键 词: 基础数学;域论;程序数;集合论;实数
Title: The Program Number Subset of the Real Number Set
Author: CHEN Bihong
Organization: College of Mathematics, Shenzhen University
Abstract: The real number set is uncountable set which includes rational number and irrational number. Irrational numbers have decimal expansions that neither terminate nor become periodic. But the irrational numbers can be divided to two kinds. One kind of it which include real number with regularity so can be descript as program language with limited length adding rational number subset is defined as Program Number Set in this paper. The set include all rational numbers, and also include irrational numbers used by human being. The set forms a number field, so a linear space can be constructed on it. The set is countable, so it does not have the features owned by real number set.
Key words: basis mathematics; field theory; program number; set theory; real number
发表期数: 2008年7月第5期
引用格式: 陈必红. 实数集的程序数子集[J]. 中国科技论文在线精品论文,2008,1(5):607-610.
 
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