闭区间上连续函数有最大值最小值的多种证明方法

Multiple methods to Prove Continuous Function on a Closed Interval Containing a Maximum and Minimum Value

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。

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.