The Application of Reverse, Forward, and Interjection in Proof Problems of Limit Definition

极限是高等数学中的一个核心概念。它在高等数学起着举足轻重的作用。如何书写利用定义证明极限的证明过程，对于初学者来说难学，对于刚入职的教师来说难教。因此，本文介绍采用一种借鉴文学中“倒叙”、“顺叙”和“插叙”的写作手法来叙述解题过程的方法，并通过两个具体的例子，详细展示了如何利用“倒叙 + 插叙”和“顺叙”书写证明过程。此外，还探讨了证明过程中的“只须”和“只需”的区别。Limit, a core concept in advanced mathematics, plays a crucial role in advanced mathematics. The writing of the proof process for using limit definitions to prove limit problems is difficult for newly hired teachers and difficult for beginners to learn. Therefore, this article introduces a method of using the writing techniques of “reverse proof”, “forward proof”, and “interjection” borrowed from literature to describe the problem-solving process. Through two specific examples, it demonstrates in detail how to use “reverse proof + interjection” and “forward proof” to write proof of the process. In addition, the difference between “only necessary” and “only needed” in the proof process was also explored.