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Mar 17, 2021 at 22:35 comment added Ryan And that would mean that we are affixing a different definition to the english word impossible than the one that I supplied, which would, of course, change what I wrote. Again the definitions that I supplied for those words were designed to differentiate almost zero probability from zero probability in the reader's mind. Since we, as humans, are bad at reasoning with very small probabilities.
Mar 17, 2021 at 22:26 comment added Ryan That being said in the strictest mathematical sense in a universe of possibilities, i.e. a set of outcomes, it may contain elements that have zero probability, thus they would be technically possible because they are in the set, but never occur because the probability is zero. Which is what I think you are getting at when you say zero probability is not the same as impossible.
Mar 17, 2021 at 22:25 comment added Ryan Technically, I was affixing my own definition to an English word. Therefore, that definition should be considered axiomatic to the discussion that follows. Furthermore, I feel justified that my definition of the word "impossible" is a reasonable definition given that I was trying to emphasize the difference between "impossible" and "you will have to wait long past the heat death of the universe to ever see it happen".
Mar 17, 2021 at 14:08 comment added peterh For example, if you choose a random point on a plane. Then the probability of a single point to be selected, is zero. But the selection of any point is possible. But I feel some... noice in this. I think the probability of a point to be selected, should not be zero, but $\frac{1}{|\aleph_1|}$. Which is zero in all practical senses. Afaik higher math can somehow handle the difference, but not with the ordinary real numbers.
Mar 17, 2021 at 0:15 comment added Sandejo Zero probability is not the same as impossible.
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Mar 16, 2021 at 20:31 history answered Ryan CC BY-SA 4.0