Simple proof of Zermelo's theorem

TL;DR

This paper presents a simplified proof of Zermelo's theorem, a fundamental yet traditionally complex statement in the theory of well-ordered sets, aiming to make its understanding more accessible.

Contribution

It introduces a straightforward proof of Zermelo's theorem, reducing the complexity of existing proofs and enhancing comprehension in set theory.

Findings

Provides a simpler proof of Zermelo's theorem

Reduces complexity of understanding well-ordering assertions

Encourages further exploration of simple proofs in set theory

Abstract

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper is to propose a simple proof of this theorem. Please inform us if you ever encountered such a proof.