I would call it the mistake of taking a theorem about Newtonian physics that was proven by assuming finitely many objects, and generalising it to infinitely many (which would be allowed by limits, but this isn’t using limits.
(If you don’t paint numbers on the balls, and just add two balls then remove one, it’s obvious the urn contains an infinite number of balls after an infinite number of steps. Why would painting numbers on balls make them disappear from the urn? Because you run out of numbers?)
I would say that if you don’t paint numbers on the balls you could end up with 0, or infinity, or something else, depending on how you do it. If you do it randomly you do have a probability 1 of ending up with infinity, but if you’re careful you can make it less.
I would call it the mistake of taking a theorem about Newtonian physics that was proven by assuming finitely many objects, and generalising it to infinitely many (which would be allowed by limits, but this isn’t using limits.
I’m confused. Are you saying that the CoM would accelerate in this situation, and thus the proof that CoMs only accelerate under external forces does not apply to this situation, or are you saying that this counterexample is misconstructed, and the CoM would not accelerate?
I would call it the mistake of taking a theorem about Newtonian physics that was proven by assuming finitely many objects, and generalising it to infinitely many (which would be allowed by limits, but this isn’t using limits.
I would say that if you don’t paint numbers on the balls you could end up with 0, or infinity, or something else, depending on how you do it. If you do it randomly you do have a probability 1 of ending up with infinity, but if you’re careful you can make it less.
I’m confused. Are you saying that the CoM would accelerate in this situation, and thus the proof that CoMs only accelerate under external forces does not apply to this situation, or are you saying that this counterexample is misconstructed, and the CoM would not accelerate?
I thought I was saying the former, although I’m no longer actually sure.