Henri Lebesgue and the End of Classical Theories on Calculus

TL;DR

This paper introduces a new calculus framework based on 'werden', correcting foundational errors in classical calculus and demonstrating its roots in Newton-Leibniz theories through historical analysis.

Contribution

It presents a novel calculus system founded on a new quantity-figure model, redefining core concepts and exposing flaws in traditional theories.

Findings

A new calculus system based on 'werden' is established.

Theories on calculus are corrected and redefined.

Historical verification links the new theories to Newton-Leibniz calculus.

Abstract

In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the theories on current calculus were exposed. A new quantity-figure model as the premise of mathematics has been formed after the correction of definition of the real number and the point. Basic concepts such as the derivative, the differential, the primitive function and the integral have been redefined and the theories on calculus have been reestablished. By historical verification of theories on calculus, it is demonstrated that the Newton-Leibniz theories on calculus have returned in the form of the novel theories established in this paper.