Math is ridiculous

I've been thinking about this all day since I saw it, mostly about how you would even go about finding a value that disproves the theorem. If you iterated through all the numbers looking for one that doesn't terminate, wouldn't you end up in an infinite loop? Like, if I wrote a class in Python that uses an integer not bound by usual data size limits, and let it iterate, how would I tell the difference between it being stuck in an infinitely growing sequence and just going on like normal?

Like maybe if you find all the numbers that hit [n]-operations, pause them at that number, and then run them again as a smaller set limited to [n+m] operations, if one of them DOES go off infinitely, how would you know?? Like you could raise it again to [n+2*m], [n+3*m], all the way to [n+∞*m] but how would you differentiate it from a number with a really, really high peak value?? You would just end up raising the ceiling over and over again until the vulture pecking out your eyes steps on the keyboard and closes the window. How do you determine whether a value is headed to infinity when the function it's using falls into the definition of randomness???