TL;DR
This paper explores the 3x+1 conjecture through an innovative approach involving quotient spaces and invertible maps, transforming the problem into equivalent forms that could be easier to analyze.
Contribution
It introduces a new framework using quotient spaces and invertible maps to reformulate the 3x+1 conjecture, offering fresh perspectives for its investigation.
Findings
Equivalent problems derived from the original conjecture
New mathematical structures related to the accelerated Collatz function
Potential pathways for future proof strategies
Abstract
In this paper, we discuss the well known 3x+1 conjecture in form of the accelerated Collatz function T defined on the positive odd integers. We present a sequence of quotient spaces and an invertible map that are intrinsically related to the behavior of T. This approach allows to express the 3x+1 conjecture in form of equivalent problems, which might be more accessible than the original conjecture.
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Taxonomy
TopicsBenford’s Law and Fraud Detection · Digital Media Forensic Detection · Computability, Logic, AI Algorithms