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Preprint / Version 9

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, Bijection, Isomorphism, Dedekind-Peano Axioms, CHSUK-Theorem, CHSUK-Generative-Parameters

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 bijection 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 2026-01-08

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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

Key-Words updated; Bijective-Isomorphism emphasized; PROOF mentions "DEDEKIND-PEANO AXIOM : Existence of 1 as the invariant base element."