| 闭区间上连续函数有最大值最小值的多种证明方法 |
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| 引用本文： | 杜素勤. 闭区间上连续函数有最大值最小值的多种证明方法[J]. 三明学院学报, 2003, 20(4): 64-66 |
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| 作者姓名： | 杜素勤 |
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| 作者单位： | 三明高等专科学校,数学系,福建,三明,365004 |
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| 摘 要： | 利用数学分析中的有界性定理、Weierstrass定理、有限覆盖定理、闭区间套定理、"单调有界数列有极限"定理、上下确界定义来证明闭区间上的连续函数能取到最大、最小值。
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| 关 键 词： | 最大值 区间序列 连续 上确界 极限 |
| 文章编号： | 1671-1343(2003)04-0064-03 |
| 修稿时间： | 2003-10-09 |
Multiple methods to Prove Continuous Function on a Closed Interval Containing a Maximum and Minimum Value |
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| DU Su-qin. Multiple methods to Prove Continuous Function on a Closed Interval Containing a Maximum and Minimum Value[J]. Journal of Sanming University, 2003, 20(4): 64-66 |
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| Authors: | DU Su-qin |
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| Abstract: | Continuous function on a closed interval containing a maximum and minimum is proved by bounded theorem, Weierstrass theorem, finite covering theorem, interval sequence theorem, monotone bounded theorem, infimum and supremum definition in mathematical analysis. |
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| Keywords: | maximum interval sequence continuous supremum limit |
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