 Collatz conjecture failure mode

ID: collatz-conjecture-failure-mode

There are to ways in which the Collatz conjecture can fail:

Collatz cycle: there is a cycle that loops forever and never reaches 1
Unbounded Collatz trajectory: there is a sequence that grows without bound without looping

These are the only two options because if any sequence has an upper bound, it must sooner or later repeat an element, leading to a cycle.

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