Proof of the Collatz Conjecture

TL;DR

This paper claims to provide a proof of the Collatz Conjecture by defining key functions and demonstrating that all numbers eventually reach 1, addressing a long-standing mathematical problem.

Contribution

It introduces a characteristic function for Collatz sequences and uses it to prove that all numbers reach 1, aiming to resolve the conjecture.

Findings

Proposed a formula for the characteristic function of Collatz sequences

Proved that every number eventually reaches 1 under the Collatz process

Addresses a long-standing open problem in mathematics

Abstract

Collatz Conjecture is one of the most famous, for its simple form, proposed more than eighty years ago. This paper presents a full attempt to prove the affirmative answer to the question proposed by the conjecture. In the first section, we propose a number of definitions utilized later on the proof. In the second section, we discover the formula for a characteristic function. This formula describes the functionality of the paths taken for each number based on the Collatz Sequence. In the last section, we prove that every number will eventually reach 1, using the characteristic function.