Proof of the Collatz Conjecture

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Authors: Y Liu
Cited by: 0

Abstract

The collatz conjecture points out that any positive integer must eventually return to 1 after the iterative operation of "even numbers divided by 2, odd numbers multiplied by 3 plus 1". Based on the operational characteristics of positive infinity positive even numbers, this article deduces through limit analysis that the limit of a positive infinity even number divided by 2 raised to the positive infinity power is 1. This article also proves that the previous digit of the iteration end point 1 must be an even number, verifying the correctness of the collatz conjecture from extreme situations.

Fields of Study & Subjects

Advanced Mathematical Theories Analytic Number Theory Research Mathematical Dynamics and Fractals

Publication details

Publication date
14 January 2026
Document type
Preprint