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harrylin said:It appears to me that it is just that point that is stressed in the section following the section that you think to be wrong. Their disagreement with Bell is about which kind of physical models can match which distributions. I don't know if they are right but I'm pretty sure that they agree with the point that you try to make.
Once more, I interpret their assertion that a requirement for the inequality to hold is "that the random variables are defined on the same probability space" as referring to the equation that Bell referred to with similar phrasing. That happens to be your first equation here above, which you also assert to be required for the inequality to hold.
I'm sorry, I don't know how to say clearer that when one person says 1+1=2 and another says that instead 2-1=1, that they say the same thing...
That's perfectly clear, it's just completely wrong. They are not saying the same thing. The authors say:
Summing up: Theorem (1) proves that Bell’s inequality is satisfied if one takes as hypothesis the negation of his “vital assumption”. From this we conclude that Bell’s “vital assumption” not only is not “vital” but in fact has nothing to do with Bell’s inequality.
I'm saying exactly the opposite of that, that Bell's "vital assumption" is necessary to prove Bell's inequality.
I don't know why you think we are saying the same thing, when we are saying exactly the opposite.