Incoming links: Collatz cycle
Collatz conjecture failure mode 2025-10-14
There are to ways in which the Collatz conjecture can fail: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.
- 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