微分定义的演变及其内蕴的逻辑错误

The Evolution of Differential Definition and Its Intrinsic Logic Error

本文认真梳理了微分概念产生、发展与演变的历史,搜集整理了各国数学分析相关教材中微分的定义并将其归纳为三类;详细分析了三类微分定义中内蕴的逻辑错误,在此基础上呼吁学界重新审视现行微积分体系,揭示真正的微积分原理并发展微积分方法。

This article carefully combs the history of the generation, development and evolution of differential concepts, collects and collates the definitions of differential in the relevant textbooks of mathematical analysis in various countries and classifies them into three categories;analyzes in detail the logic errors inherent in the definitions of three types of differential, and appeals to the academic circles to re-examine the current calculus system and reveal the true. The principle of calculus is developed and the calculus method is developed.