The Radical Mistakes in the Theories on Calculus of Cauchy-Lebesgue System

TL;DR

This paper exposes fundamental misunderstandings and errors in the traditional theories of calculus by Cauchy and Lebesgue, specifically regarding the concept of differentials and their application in composite functions.

Contribution

It identifies and discusses critical defects in the definitions of differentials and highlights associated mistakes in differentiation within the Cauchy-Lebesgue calculus framework.

Findings

Identified defects in the definition of differentials

Pointed out mistakes in differentiation of composite functions

Clarified misunderstandings in calculus theories

Abstract

The misunderstanding of the concept of differentials in the theories on calculus of Cauchy-Lebesgue system was exposed in this paper. The defects of the definition of differentials and the associated mistakes in the differentiation of composite functions were pointed out and discussed.