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by concreteblock
1904 days ago
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I agree with the first 3 statements. Just to confirm, I am using 'almost surely' in the technical sense, which means 'with probability 1.' Consider the following statement: If you keep flipping a fair coin every day, it is almost sure that after some day you will have gotten a tails. This is the same 'almost surely' that I am referring to. |
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The point was that you didn't specify "almost surely" previously, that's why I asked for a proof to understand what did you mean exactly when you said that "everyone goes bankrupt and will never recover" and "or "there is a finite time after which no-one ever passes above $0.0000000000000001".
The mean of a random variable that is close to zero is close to zero, the mean of a random variable that is almost surely close to zero can be anything.