反例教学法与实数连续性
Counterexamples Teaching Method and Continuity of Real Numbers

关于实数的连续性命题是数学分析的基本工具，这一部分内容的教学效果直接影响到学生后续的学习。本文针对实数连续性命题阐述了将反例教学法融入课堂教学的必要性，同时给出了有理数中相关命题的几个具体的反例并讨论了在教学中引入这些反例的积极作用和意义。
The propositions about the continuity of real numbers are basic tools for mathematical analysis and the teaching effect of this part directly affects the students’ subsequent learning. This paper expounds on the necessity of integrating counterexample teaching method into classroom teaching aiming at the propositions about the continuity of real numbers, then gives some counterexamples of related propositions in rational numbers and discusses the positive role and significance of using counterexample teaching method.