I think (and I am no expert here, so correct me if I am wrong) that, when it comes to actually written programs, there is little difference between “actually infinite” and “practically infinite”. This is like saying the probability of any particular real number being given by a float is zero because floats are only countable infinite (practically) rather than uncountable infinite. I don’t know, maybe I am talking out of my ass, tho lol

then you have added nothing to the problem. of course if you run the program and it halts, even if runs until T+heatdeathofuniverse^googleplex (which is a finite time) without an infinite loop, you have not solved the conundrum implied by Turing’s work. Turing proved no algorithm exists that always correctly decides whether, for a given arbitrary program and input, the program halts when run with that input. The essence of Turing's proof is that any such algorithm can be made to produce contradictory output and therefore cannot be correct. He proved it - QED