| 实数连续性等价性命题的证明 |
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| 引用本文： | 邹斌.实数连续性等价性命题的证明[J].安徽广播电视大学学报,2009(2):125-128. |
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| 作者姓名： | 邹斌 |
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| 作者单位： | 安徽广播电视大学,合肥,230022 |
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| 摘 要： | 以戴德金分划说为基础来研究实数的连续性，对于实数连续性的九个等价性命题：确界定理、戴德金定理、单调有界定理、区间套定理、有限覆盖定理、聚点定理、致密性定理、柯西收敛准则以及Botsko定理，采用循环论证，从命题1出发，依次证明下一命题，最后由命题9证明命题1，从而组成一个环路，证明了它们的等价性。
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| 关 键 词： | 实数连续性 单调有界 区间套 聚点 |
The Proof on Equivalent Proposition of the Real Number Continuity |
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| ZOU Bing.The Proof on Equivalent Proposition of the Real Number Continuity[J].Journal of Anhui Television University,2009(2):125-128. |
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| Authors: | ZOU Bing |
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| Institution: | Anhui Radio and TV University;Hefei 230022;China |
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| Abstract: | This paper analyzes the real number continuity on the basis of Dedekind＇s cut theory. As to the nine equivalent propositions of the real number continutiy, supremum theorem, Dedekind＇s principle, monotonic bounded theorem, nested interval theorem, finite covering theorem, accumulation principle, Bozano- Weierstrass theorem, Cauchy＇s convergence criterion and Botsko theory, it adopts the circular argument methodology to prove their equivalence in a circle： from proposition 1 to the next till proposition 9, then using proposition 9 to prove the first one. |
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| Keywords: | real number continuity monotonic boundary nested interval accumulation |
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