高等数学中的一些反例

摘要

Counter examples are preferred than theoretical argumentation in proving some false propositions or relational expressions in higher mathematics. Employing counter examples, this paper first illustrates some false propositions and relational expressions in multivariate function and then demonstrates that the properties from u-nivariate function to multivariate function conform to the change from quantitative to qualitative.%在高等数学中有一些命题或关系不成立，不需要理论证明，只需用一个反例即可说明。本文列举一些反例仅说明多元函数中不成立的命题和关系，同时也说明从一元函数到多元函数的性质也符合从量变到质变的原则。