深入理解数学概念是学好高等数学的基础。文中利用分段函数作为反例诠释高等数学中易混淆的几个概念，使抽象的数学概念更具体。构造分段函数作为反例有助于培养学生的思维能力和创新能力。%In-depth understanding of mathematical notions is the foundation to learn higher mathematics. In this paper, several confusing notions are interpreted by the use of piecewise function as a counter example in higher mathematics;counter example of piecewise function makes the abstract concepts more concrete. Piecewise function as a counter example can help students cultivate the thinking ability and improve innovation ability.
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