They prove that no finite amount of training data is enough to extrapolate an adversarially constructed non-continuous function. It's something akin to the no f

They prove that no finite amount of training data is enough to extrapolate an adversarially constructed non-continuous function. It's something akin to the no free lunch theorem (NFL). No one uses the NFL to "prove" that LLMs can't learn to be the best optimizers, because it also proves that people can't be the best optimizers, but we manage somehow, so the theorem is irrelevant. This is a fallacy of proving too much.