An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction

数学季刊 ›› 1998, Vol. 13 ›› Issue (3): 74-80.

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction

Department of Mathematics, Guangzhou Teacher's College, Guangzhou, 510400

收稿日期:1997-11-20 出版日期:1998-09-30 发布日期:2024-10-25
基金资助:
Project supported by the following：① the1352Project Fund of ninth five-year plan made by Higher Education Office of
Guangdong Province．② the Subject-supporting Fund for Colleges and University of Guangdong Province．③ the Important
Subject Fund for Colleges and Universities of Guangzhou．The project is included in National Educational Project of1998
2000．

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction

Department of Mathematics, Guangzhou Teacher's College, Guangzhou, 510400

Received:1997-11-20 Online:1998-09-30 Published:2024-10-25
Supported by:
Project supported by the following：① the1352Project Fund of ninth five-year plan made by Higher Education Office of
Guangdong Province．② the Subject-supporting Fund for Colleges and University of Guangdong Province．③ the Important
Subject Fund for Colleges and Universities of Guangzhou．The project is included in National Educational Project of1998
2000．

摘要/Abstract

摘要： In this paper,a converse and negated form of the continuous induction is indicated. We use it to prove six basic theorems of completeness of real numbers system,the existence theorem of limes superiores and limes inferiores of seqence and the properties of continuous function in closed interval by mode of unification.

关键词: continuous induction, the Dedekind Axiom, completeness

Abstract: In this paper,a converse and negated form of the continuous induction is indicated. We use it to prove six basic theorems of completeness of real numbers system,the existence theorem of limes superiores and limes inferiores of seqence and the properties of continuous function in closed interval by mode of unification.

Key words: continuous induction, the Dedekind Axiom, completeness

中图分类号:

O141

萧治经, 熊萍. An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction[J]. 数学季刊, 1998, 13(3): 74-80.

Xiao Zhijing, Xiong Ping. An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction[J]. Chinese Quarterly Journal of Mathematics, 1998, 13(3): 74-80.

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An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction

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