关于极限概念的学习

On Learning of the Concept of Limit

摘要: 通过“溯源”，建立对抽象的数学概念——极限的直观理解和逻辑认知，从而更好地理解微积分的基石——极限理论。从三个物理与几何背景问题出发，深入浅出地剖析了数列极限严谨定义的由来，极限概念的特性、几何解释等，并进一步推广到了对函数极限概念的理解和相关应用中。

Abstract: Through tracing the origin, one can develop an intuitive grasp and logical comprehension of the abstract concept of limit, laying a solid foundation for mastering calculus. The paper starts from three problems in physical and geometric backgrounds. It makes an in-depth yet accessible analysis of the origin of the rigorous definition of the limit of a sequence, the characteristics of limit, its geometric interpretation, and so on. Moreover, it further extends these analyses to the understanding of the concept of the limit of a function and relevant applications.