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《Mathematics in Practice and Theory》 2007-01
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Proving Theorems in Real Number Field by Means of Continual Induction

XU Yong-chun, GUAN Jin-yu, LI Bo, MEI Rui(Department of Mathematics,Hebei North University,Zhangjiakou Hebei 075028,China)  
This article is to introduce continual induction and to prove Cauchy Convergence Principle by means of it,then to prove Monotone Convergence Theorem by using a new form of Continual Induction,which is put forward and proven in this article.
【Fund】: 国家自然科学基金(10571008)
【CateGory Index】: O171
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【References】
Chinese Journal Full-text Database 1 Hits
1 ZHANG Jingzhong1,2, FENG Yong1,3 1. Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041, China 2. Institute of Educational Softwares, Guangzhou University, Guangzhou 510006, China 3. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China;A General Inductive Principle for an Ordered Set and the Continual Induction[J];Science & Technology Review;2008-06
【Citations】
Chinese Journal Full-text Database 1 Hits
1 GUAN Jin-yu,XU Yong-chun,QI Jian-fang (Department of Mathematics,Hebei North University,Zhangjiakou,Hebei 075028,China);To Prove Several Theorems in Real Number Field by Using Full Covering Theorem[J];Journal of Hebei North University(Natural Science Edition);2006-03
【Co-citations】
Chinese Journal Full-text Database 8 Hits
1 ZHANG Jing-zhong(1.Research Institute for Computer Softwares,Guangzhou University,Guangzhou 510006,China;2.Chengdu Institute of Computer Applications,Academica Sinica,Chengdu 610041,China);Axiomatic method for the definition of definite integral[J];Journal of Guangzhou University(Natural Science Edition);2007-06
2 ZHANG Jingzhong~(1,2,3)(1.Engineering Center for Education Information Technology, Central China Normal University,Wuhan 430079;2.Chengdu Institute for Computer Applications,Chinese Academy of Sciences,Chengdu 610041;3.Institute for Educational Software,Guangzhou University,Guangzhou 510006);Let calculus more elementary[J];Journal of Central China Normal University(Natural Sciences);2006-04
3 TANG Cai-bin (Research Center for Modern Primary Mathematics Education,Hangzhou Zhejiang 310006,China);Thinking and Practice on Teaching Situations of Mathematics in Primary Schools[J];Curriculum, Teaching Material and Method;2008-03
4 YAN Xue-min,HUA Guo-dong(China National Institute for Educational Research,Beijing 100088,China);Review and Apocalypse of Study on Modern Mathematics Thought and Method[J];Journal of Mathematics Education;2008-03
5 ZHAO Lin-long(Department of Mathematics,Ankang College;Ankang,725000,China);The Research and the Fulfillment of Education Mathematics in the High School Mathematics[J];Taiyuan Science & Technology;2008-04
6 SHEN Wen-xuan,WU Ren-fang(Department of Mathematics of Science Faculty,Hunan Normal University,Hunan Changsha 410081,China);Step into Educational Mathematics——the Fourth Discussion on Mathematical Education and Educational Mathematics[J];Journal of Mathematics Education;2009-04
7 XU Yong-chun,GUAN Jin-yu,MEI Rui,LI Ming(Department of Mathematics,Hebei North University,Zhangjiakou 075000,Hebei,China);Proving of Theorems in Real Number Field in a Union Form[J];Journal of Hebei North University(Natural Science Edition);2006-06
8 LI Bo,MEI Rui(College of Science,Hebei North University,Zhangjiakou 075000,Hebei,China);Proving Several Complete Theorems in Two-dimensional Space with Complete Covering Theorem[J];Journal of Hebei North University(Natural Science Edition);2008-02
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