You're assuming the collatz conjecture holds, which is unknown.

But even if it does hold, you do understand the second problem, right? 1 can not possibly be the outcome, because whenever there is a 1 in that infinite loop, it is followed by a 4. And if 1 is the outcome, then it wasn't done infinitely, because otherwise there must have been a 4 afterwards. The same argument holds for 4 and 2 as well. So we're stuck in the reality that it would have to be one of those numbers, but it also can't really be one of those numbers. It's paradoxical.