| 关于“可得”与“不可得”无限——与张伟平商榷 |
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| 引用本文： | 谢琳,惠俊烜. 关于“可得”与“不可得”无限——与张伟平商榷[J]. 数学教育学报, 2010, 0(2) |
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| 作者姓名： | 谢琳 惠俊烜 |
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| 作者单位： | 辽宁师范大学数学学院; |
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| 基金项目： | 国家自然科学基金项目——低维流形中若干问题的研究(10771023) |
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| 摘 要： | 张伟平对文[2]中提及的关于可得无限与不可得无限的层次区分概念存在十分严重的错误理解.这种错误的理解会在数学教学中引起混乱.要正确解读康托(Cantor)(其实是由多宾斯基(Dubinsky)命名)的所谓可得与不可得无限的本来含义,不应忽略近现代数学、逻辑,尤其是集合论的发展及其对数学研究对象描述方式的影响.
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| 关 键 词： | 无限 不可得无限 可得无限 集合 集合论 |
With Respect to Attainable and Unattainable Infinity |
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| XIE Lin,HUI Jun-xuan. With Respect to Attainable and Unattainable Infinity[J]. Journal of Mathematics Education, 2010, 0(2) |
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| Authors: | XIE Lin HUI Jun-xuan |
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| Affiliation: | XIE Lin,HUI Jun-xuan(Department of Mathematics,Liaoning Normal University,Liaoning Dalian 116029,China) |
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| Abstract: | The concept of attainable and unattainable infinity,which was quoted from [2] was completely misread by ZHANG Wei-ping in her note [1].This mistake could lead to ideological confusion in the process of teaching and studying.To understand the essence of attainable and unattainable infinity,which was inferred by Cantor(as a matter of fact,it was named by Dabinsky),it should be based on the development of set theory and combination with the modern mathematics and logic. |
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| Keywords: | infinity attainnable infinity unattainable infinity sets sets theory |
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