Zorn's Lemma- An elementary proof under the Axiom of Choice

TL;DR

This paper provides an elementary and simplified proof of Zorn's Lemma under the Axiom of Choice, making the proof more accessible and detailed compared to the original by Halmos.

Contribution

It offers a more straightforward, detailed proof of Zorn's Lemma under the Axiom of Choice, enhancing understanding and accessibility.

Findings

Simplified proof of Zorn's Lemma presented

Detailed explanation improves comprehension

Historical context provided for Zorn's Lemma

Abstract

This article presents an elementary proof of Zorn's Lemma under the Axiom of Choice, simplifying and supplying necessary details in the original proof by Paul R. Halmos in his book, Naive Set Theory. Also provided, is a preamble to Zorn's Lemma, introducing the reader to a brief history of this important maximal principle.