A somewhat popular variant I've seen of this problem of the infinite limit versus the real physical reality is people calculating the probabilities of some even

A somewhat popular variant I've seen of this problem of the infinite limit versus the real physical reality is people calculating the probabilities of some event occurring in some game with a fixed seed, as was popular in old games. Someone might start computing the probability that this monster has its rare variant AND the boss gets the maximum HP roll AND the awesome sword gets its lowest damage variant AND so on and so on... but if the game has a 32-bit seed that determines everything and the resulting probability is, say, one in a trillion, then the real probability is likely a straight zero, because none of the finite number of seeds will have the calculated outcome, even if a hypothetical variation of the game with a large random state space could. Similarly, if you use a psuedo-random number generator and start trying to calculate how long it will be before it produces some string substantially larger than the side of its internal state, your answer will likely be incorrect as the answer is it will never produce the longer string, a flat zero. Not consequential errors in most cases because it's fairly rare to exhaust the entire state space of a random number generator and be concerned about the result. (Unless you're a speedrunner. Or in the case of one recent YouTuber, just insane, in that good ol' hacker way: https://www.youtube.com/watch?v=jNMWkD5VsZ8 https://www.youtube.com/watch?v=jNMWkD5VsZ8 "Beating every possible game of Pokemon Platinum at the same time")