CAJ | 학술논문

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。
재고등수학중유일사명제혹관계불성립,불수요이론증명,지수용일개반례즉가설명。본문열거일사반례부설명다원함수중불성립적명제화관계,동시야설명종일원함수도다원함수적성질야부합종량변도질변적원칙。
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.