I would hope this thread could be limited to Bell-mathematical questions and answers concerning just one given Bell paper -- though it may involve many mathematical questions as we follow it to resolution. This thread concerns mathematical questions in one Bell paper and so it should NOT need a lot of words and diversion to resolve it. It is about quantum physics so I think it belongs here --- with help from mathematicians. It might help us more if those helping us could say what level of mathematics and quantum physics they have reached. But I respect privacy. I believe that logic is at its highest development in mathematics and probability theory -- so I should be not too slow in those areas. -------------- Let there be no question here about Bell's assumptions BUT -------------- Question 1. Is there a mathematical error in Bell's theory, as will follow? After starting and following the threads "Understanding Bell's logic" and "Understanding Bell's mathematics", I would like to discuss and resolve a clash of the two in Bell's Bertlmann's socks paper -- which is available to all from CERN on-line -- [PLAIN]http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers [Broken] [/URL] -- the discussion in those threads not appearing to resolve it for me. One of Bell's latest papers on EPR, without excuse it should be one of his clearest? Look at Bell's equations (11) and (12), and combine them to form (Bell 12) = [tex] P(A, B|a, b) = \int d\lambda \rho (\lambda) P_ 1(A|a, \lambda) P_ 2(B|b, \lambda). [/tex] It is Bell's supposition (above his (11)) that the variables [tex] \lambda [/tex] allow this decoupling. Question 2. Are [tex] P_ 1 [/tex] and [tex]P_ 2 [/tex] Probability Functions? Question 3. Is it not the case that Probability Functions map a subset of the sample space to the real interval [0, 1]? Question 4. If [tex] P_ 1 [/tex] and [tex]P_ 2 [/tex] are Probability Functions, how do we apply Bell's [tex]\rho (\lambda)[/tex] to such functions? Question 5. If they are NOT Probability Functions, what are they, please? Question 6. Could you provide an example of the Function that you believe them to be, please? Question 7. Bell has [tex] P_ 1 [/tex] and [tex]P_ 2 [/tex]. Why did he not have also [tex] \lambda_ 1 [/tex] and [tex]\lambda_ 2 [/tex] ? Question 8. If he did the lambda-separation in Question 7 -- which is allowable under his theory -- how would he have written Bell (12) above? Thank you very much.