The last proof of extreme value theorem and intermediate value theorem

TL;DR

This paper presents a unified and simplified proof of the extreme value theorem, intermediate value theorem, and Cousin's theorem, enhancing understanding of fundamental calculus concepts.

Contribution

It introduces a novel, unified proof approach that simplifies the demonstration of key theorems in analysis.

Findings

Unified proof method for multiple theorems

Simplified understanding of fundamental analysis theorems

Potential for broader application in mathematical education

Abstract

The paper gives a unified and simple proof of both theorems and Cousin's theorem.