导数函数的定义:数学中的逻辑错误

T. Kalanov
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引用次数: 5

摘要

提出了对微分学基础的批判性分析。这种分析的方法论基础是形式逻辑和理性辩证法的统一。由于极限过程的概念是导数函数定义的起点,因此证明了微分学是一个虚构的数学理论。在导数函数的定义中,通过极限“零”表示变量取唯一的本质值“零”。这一事实导致了以下错误。(1)导数函数的定义是基于函数实参增量与函数实参增量之间关系有效性的充分必要条件的违反,因为在极限过程中,函数的增量除以实参的零增量。(2)导数函数的定义是基于在同一关系中参数的增量既为零又不为零的矛盾。这种矛盾违背了同一性的形式逻辑规律和无矛盾的形式逻辑规律。(3)函数的微分定义基于两个相互矛盾(互斥)的特征:在导数函数的定义中,实参的微分不为零,而实参的增量为零。
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Definition of Derivative Function: Logical Error in Mathematics
The critical analysis of the foundations of the differential calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that differential calculus is fictitious mathematical theory because the concept of the limiting process is the starting point for definition of the derivative function. The passage to the limit “zero” in the definition of the derivative function signifies that the variable quantity takes the only essential value “zero”. This fact leads to the following errors. (1) The definition of the derivative function is based on the violation of the necessary and sufficient condition for the validity of the relationship between the increment of the function argument and the increment of the function because the increment of the function is divided by the zero increment of the argument in the case of the limiting process. (2) The definition of the derivative function is based on the contradiction which is that the increment of the argument is both zero and not zero in the same relationship. This contradiction represents a violation of the formal-logical law of identity and of the formal-logical law of the lack of contradiction. (3) The definition of the differential of function is based on two contradictory (mutually exclusive) features: the differential of the argument is not zero while the increment of the argument in the definition of the derivative function is zero.
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