Supremum and infimum are very important concept in mathematics analysis.As the foundation of the limit theory,they play a very important role in the calculus theory.Therefore,the understanding of the concept of supremum and infimum is particularly important in study mathematics analysis.However,students often do not understand how to use them to solve the problem in exercises.First of all,give the definition of supremum and infimum,and then explain the application of the concept by several kinds of proof methods for a exercise.%确界是数学分析中一个非常重要的概念，确界原理作为极限理论的基石在微积分理论中占有极为重要的地位，故而确界概念的理解在数学分析学习中就显得尤为重要。但是，在练习中，学生往往不懂如何使用确界概念来解答。因此，首先给出确界的定义，然后通过一道确界习题的几种证明方法来说明确界概念的应用。
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