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Edit:nvm see thread For collatz, the empty input machine loops over all natural numbers and halts if it finds one which doesn’t eventually reach 1. To prove t
by srcreigh 2y ago
Edit:nvm see thread
For collatz, the empty input machine loops over all natural numbers and halts if it finds one which doesn’t eventually reach 1.
To prove that it never halts, you’d have to prove the collatz conjecture. Otherwise you’d have to find the smallest counter example of the collatz conjecture.
- LegionMammal978 2y agoSuppose that there exists a natural number that diverges to infinity under the Collatz map. Then the Collatz conjecture would be false, but your machine would still run forever on that diverging number. As far as I am aware, there is no known machine that halts iff the Collatz conjecture is false.
- srcreigh 2y agoYou are correct, thank you