"I aimed to show that all claims like yours were unsuitable for a proof of the Collatz conjecture, because either they could not be iterated or they could not s

"I aimed to show that all claims like yours were unsuitable for a proof of the Collatz conjecture, because either they could not be iterated or they could not show a decrease for all inputs." I'm not sure I addressed your criticism fully. Earlier you noted: "For starters, that would only work if your argument applied to the entire set of outputs that you'd feed back in again as inputs." That is precisely the case I am describing. I begin with a universal property of any sequence, then proceed to show that all sequences beginning with an even terminate. I then note that the earlier property requires that all sequences beginning with odd numbers immediately follow this pattern after at most one iteration. A sequence that terminates after a finite number of steps + 1 still terminates after a finite number of steps. I have summarized this in a post above. The abmiguity you describe in the set of proofs you are disqualifying is not present in my arguement. I begin at the first value for all sequences (evens, and then odds, which is exhaustive of inputs, and outputs, as you note is necessary) and that is exhaustive of sequences. Is it a variation on the most naive approach that pretty much everyone would start with? Sure, and that's reason enough to be skeptical. But, does it work? It seems to...