Ding Xiaoping：A Brief Discussion on Incorrectness of Generally-Accepted Rationale for Calculus

Calculus is the foundation stone of mathematics. The Calculus methods are used everywhere. So what’s the reason why the Calculus methods work so well? Headed by Cauchy, mathematicians established the current rationale of Calculus to explain the reason why the methods of Calculus are effective. However, this rationale is flawed and difficult to justify itself in many places.

This paper is part of the research results of Chinese mathematician Ding Xiaoping. This paper reveals the incorrectness in the current rationale of Calculus, including the incorrectness of generally-accepted rationale of differentials and derivatives, problems in generally-accepted rationale for integrals, incorrectness in theory of solving differential equations and the twisted structure of generally-accepted rationale for Calculus.

The article has been translated from Chinese. There are some language problems inevitably. However, the expression of mathematical logic is clear.