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May 20, 2011 at 17:38 comment added TMM The most interesting questions related to the $3n + 1$ function (e.g. Are there any other cycles? Do sequences exist that tend to infinity?) are not addressed by this approach. There could be infinitely many cycles or diverging paths, which does not even contradict the convergence of the random process. It only tells us that the set of these counterexamples is (probably) not dense in $\mathbb{N}$.
May 20, 2011 at 16:25 history answered Hauke Reddmann CC BY-SA 3.0