| 关于收敛级数的子级数和集性质的讨论 |
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| 引用本文： | 张晓光,杜红.关于收敛级数的子级数和集性质的讨论[J].黑龙江科技学院学报,2006,16(5):328-331. |
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| 作者姓名： | 张晓光 杜红 |
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| 作者单位： | 黑龙江科技学院,数力系,哈尔滨,150027 |
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| 摘 要： | 主要讨论了收敛级数的子级数和集的结构,得到了绝对收敛的子级数和集的一些有价值的性质,并首次给出了它的构造性证明.这是正项级数的一些性质推广和完善,作为和集性质的一个应用,证明了(0, 1]数的二进制无穷表示是惟一的.
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| 关 键 词： | 绝对收敛 条件收敛 子级数 |
| 文章编号： | 1671-0118(2006)05-0328-04 |
| 修稿时间： | 2006年6月8日 |
Discussion on properties of set of sum of convergent series |
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| ZHANG Xiaoguang,DU Hong.Discussion on properties of set of sum of convergent series[J].Journal of Heilongjiang Institute of Science and Technology,2006,16(5):328-331. |
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| Authors: | ZHANG Xiaoguang DU Hong |
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| Abstract: | In the paper,a major goal of the research on the set of the sum of sub series of convergent series is to investigate its structure.Some valuable properties of the set of the sum of absolute convergent series are obtained.It is generalized for some properties of positive series.A method of constructive proof is given for the first time.As an application of the properties of the set of the sum,the binary infinite representation of a number in the interval(0,1] is unique. |
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| Keywords: | absolute convergent conditional convergent sub series |
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