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Dominik comments on An Intuitive Explanation of Solomonoff Induction - Less Wrong
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Some algorithms run forever, some do not, and we do not have any way to prove that an algorithm is in the first set and not the latter, that was my interpretation at least.
How do you know some algorithms run forever if you have no way of proving that an algorithm is in the set "runs forever" or not?
You can prove that some algorithms run forever. Similarly, you can prove that some algorithms halt. What you can't do is come up with a procedure that will determine whether an arbitrary algorithm you feed it halts or not.