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Standard probability theory does not have a notion of infinitesimals. There have been non-standard attempts at probability theory that do involve such a notion

Standard probability theory does not have a notion of infinitesimals. There have been non-standard attempts at probability theory that do involve such a notion. See [0] (found on a brief search; I have only skimmed). EDIT: Admittedly, the existence of the non-standards analysis is a good indication that this is an artifact of the formalization of probability theory; not of the underlying reality that we are trying to model. Simpson's paradox is probably a better example of a "real" "paradox" of probability. [1] [0] https://lirias.kuleuven.be/bitstream/123456789/551380/1/BenciHorstenWenmackers-BJPS-InfinitesimalProbabilities.pdf https://lirias.kuleuven.be/bitstream/123456789/551380/1/Benc... [1] https://en.wikipedia.org/wiki/Simpson's_paradox https://en.wikipedia.org/wiki/Simpson's_paradox

abecedarius 10y ago
https://www.amazon.com/Radically-Elementary-Probability-Theory-AM-117/dp/0691084742 https://www.amazon.com/Radically-Elementary-Probability-Theo... is apparently another take on this problem.
Retric 10y ago
While I don't disagree with what your saying, I would point out if you want to use specific definitions they don't apply in the general case. Abstractly, there must be some difference between 0.2 and 2 as the first is a valid output and the second is not. Otherwise when you sum [0.2,0.3] vs [2,3] you get the same probability of 0. But, there is a trade off that can make things a little cleaner if you define the probability at 0.2 to be 0.