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Wei_Dai comments on Probability Space & Aumann Agreement - Less Wrong
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It was confusing for me too, which is why I gave an imperative definition: first form the union of I and J, then merge any overlapping elements. Did that not help?
It should have. The fault is certainly mine. I skimmed your definition too lightly because you were defining a technical term ("meet") in a context (partitions) where I was already familiar with the term, but I hadn't suspected that it had any other usages than the one I knew.