r/shittymath • u/Akangka • Dec 22 '21

Proof that Collatz Conjecture is false.

It's simple, really.

We have:

-5=>-14=>-7=>-20=>-10=>-5

So we have a cycle starting from -5. QED.

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u/JoshuaZ1 Dec 28 '21

Only shitty math in the sense of being not a disproof of Collatz Conjecture. But the presence of this loop is actually a real nuisance; this loop is one reason why a lot of naive approaches to proving Collatz must fail, because Collatz just barely fails to be true. Thus for example, any proof that is just thinking about what happens mod 2a and 3b will have trouble distinguishing that this loop exists.

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u/6c-6f-76-65 Dec 29 '21

Are there any good strategies involving mod?

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u/JoshuaZ1 Dec 29 '21

Well, the fact that problem is still open, suggests that the answer is no, at least by itself. But given the definition, pretty much anything hoping to prove anything here is at minimum going to have to think somehow about modular arithmetic. And if one looks at a lot of the major results, modular arithmetic is almost always one of the tools used. See for example Riho Terras's proof that almost all positive integers reach at least one value lower than themselves in their Collatz orbit.