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Kazuo_Thow comments on Book Club Update, Chapter 2 of Probability Theory - Less Wrong
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I did not go through the 9 remaining cases, but I did think about one...
Suppose (AB|C) = F[(A|BC) , (B|AC)]. Compare A=B=C with (A = B) AND (C -> ~A).
Re 2-7: Yep, chain rule gets it done. By the way, took me a few minutes to realize that your citation "2-7" refers to a line in the pdf manuscript of the text. The numbering is different in the hardcopy version. In particular, it uses periods (e.g. equation 2.7) instead of dashes (e.g. equation 2-7), so as long as we're all consistent with that, I don't suppose there will be much confusion.
Could we standardize on using the whole-book-as-one-PDF version, at least for the purposes of referencing equations?
ETA: So far I've benefited from checking the relevant parts of Kevin Van Horn's unofficial errata pages before (and often while) reading a particular section.