| 重要不等式之间的互相等价性 |
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| 引用本文： | 景占策.重要不等式之间的互相等价性[J].湘南学院学报,2007,28(5):19-23. |
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| 作者姓名： | 景占策 |
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| 作者单位： | 青海师范大学,数学与信息科学系,青海,西宁,810008 |
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| 摘 要： | 在实数集合的紧致性为已知的前提下,证明算术平均值与几何平均值不等式,Cauchy不等式,ЧeóыⅢeв不等式,Hlǒder不等式,三角不等式之间的互相等价性,而且它们都等价于一个实数的平方不小于零.
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| 关 键 词： | 不等式 实数集合的紧致性 不等式之间的等价性 |
| 文章编号： | 1672-8173（2007）05-0019-05 |
| 修稿时间： | 2007-06-20 |
On the Equivalence between Some Important Inequalities |
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| JING Zhan-ce.On the Equivalence between Some Important Inequalities[J].Journal of Xiangnan University,2007,28(5):19-23. |
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| Authors: | JING Zhan-ce |
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| Institution: | Department of Mathematics, Qinghai Normal University, Xiling 810008, China |
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| Abstract: | In this paper it is shown that the basic inequality ,Cauchy inequality,Tchebychef inequality,Holder inequality,Lyapunov inequality, triangle inequality are all equivalent to the simple proposition that a20,,for every a∈R(set of real number),provided the proposition that the closure of the set of rational number equals R is known. |
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| Keywords: | inequality compactness of the set of real number equivalence between inequalities |
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