A Proof for the Collatz Conjecture

Abstract

Jerome Chauvet

This proof addresses the Collatz conjecture and relies on the quantitative evolution undergone by the densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system, from which we deduce the final cyclic attractor, hence proving the conjecture.

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