On the Union-Closed Set Conjecture

TL;DR

This paper presents a straightforward proof of the longstanding union-closed sets conjecture, which has significant implications across various fields including graph theory, number theory, and order theory.

Contribution

It offers a simple proof of the union-closed sets conjecture, advancing understanding of this open problem in set theory.

Findings

Proof of the union-closed sets conjecture provided

Immediate applications to graph, number, and order theory discussed

Simplifies previous approaches to the conjecture

Abstract

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.