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Preprint / Version 7

COLLATZ-HASSE-SYRACUSE-ULAM-KAKUTANI SEQUENCE: CONVERGENCE TO THE TRIVIAL CYCLE PROVED

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DOI:

https://doi.org/10.31224/6063

Keywords:

Collatz-Hasse-Syracuse-Ulam-Kakutani (CHSUK) Sequence, Collatz-Hasse-Syracuse-Ulam-Kakutani (CHSUK) Conjecture, Convergence, Isomorphism, Dedekind-Peano Axioms

Abstract

The convergence of the Collatz-Hasse-Syracuse-Ulam-Kakutani Sequence is proved, thus proving the Collatz Conjecture, which has been an unsolved problem.  The proof is based on the isomorphism established between the set of positive integers and a carefully designed system with a hierarchy (arborescence) of binary exponential ladders defined on the set of positive odd numbers.

 

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Posted

2025-12-21 — Updated on 2026-01-04

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Copyright (c) 2025 Keshava Prasad Halemane

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Version justification

emphasized the irrelevance of the presence of extraneous objects (unbounded and/or closed chains) in the structured system framework - other than the relevant hierarchy (arborescence) that is isomorphic with the set of natural numbers