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Okay but the Collatz conjecture is a little different in that there can't just be a one-off counterexample: it's a statement about a sequence. The counterexampl
by SilasX 3y ago
Okay but the Collatz conjecture is a little different in that there can't just be a one-off counterexample: it's a statement about a sequence. The counterexample would have to be either a cycle (that excludes 4/2/1), or a sequence of numbers that keep spiraling up indefinitely. And they've proven that any cycle would have to be very long[1]. Either way, it would mean trivially unlocking a sequence of numbers that happens to satisfy a very specific criterion.
[1] https://en.wikipedia.org/wiki/Collatz_conjecture?useskin=vector#Cycles https://en.wikipedia.org/wiki/Collatz_conjecture?useskin=vec...
- timeagain 3y agoRight. So there might be some set of numbers way out there that are like the “sporadic simple group(s)” of the collatz conjecture. Following the same rules as everyone else, you end up with something otherwise unclassifiable.