| 实数完备性六大基本定理的等价性证明 |
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| 引用本文： | 扶炜.实数完备性六大基本定理的等价性证明[J].信阳农业高等专科学校学报,2012,22(2):122-123,126. |
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| 作者姓名： | 扶炜 |
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| 作者单位： | 信阳农业高等专科学校计算机科学系,河南信阳,464000 |
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| 摘 要： | 利用有限覆盖定理作为公理,按照A(有限覆盖定理)→B(聚点定理)→C(区间套定理)→D(单调有界定理)→E(柯西收敛准则)→F(确界原理)→A顺序来证明实数完备性六大基本定理之间的等价性,从而更加真实地体现实数完备性六大基本定理之间的相互依存关系。
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| 关 键 词： | 有限覆盖定理 聚点定理 区间套定理 单调有界定理 柯西收敛准则 确界原理 |
The proof of the equivalence relations in the six fundamental theorems of completeness real numbers |
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| FU Wei.The proof of the equivalence relations in the six fundamental theorems of completeness real numbers[J].Journal of Xinyang Agricultural College,2012,22(2):122-123,126. |
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| Authors: | FU Wei |
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| Institution: | FU Wei(Department of Computer Science,Xinyang Agricultural College,Xinyang 464000,China) |
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| Abstract: | In this paper,regarding restricted coverage theorem as axiom,we will prove their equivalence by symbol A→B→C→D→E→F→A,thus more really reflect the interdependence relationship of six fundamental theorems. |
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| Keywords: | restricted coverage theorem accumulation theorem nested interval theorem monotone finite theorem Cauchy convergence criteria supremum principle |
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