> So, we can run up to this number and either the machine will stop - and we'll go to the next one until exhaust the whole set - or the machine won't stop, and we'll refute the conjecture
No, you do not refute the conjecture if you run up to this number and a machine does not stop. Finding a machine that runs for more than 47,176,870 steps is easy - there are plenty of machines that run forever. The trick is that it needs to stop.
No, you do not refute the conjecture if you run up to this number and a machine does not stop. Finding a machine that runs for more than 47,176,870 steps is easy - there are plenty of machines that run forever. The trick is that it needs to stop.