Proof of the Collatz Conjecture
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