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Partial Order - Reconciling Definitions by Garling and Goldrei
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[QUOTE="fresh_42, post: 5608980, member: 572553"] Hi Peter, I agree, although I would not call it anti-reflexive, because it is a forbidden reflexivity, while the "anti" in the anti-symmetry has actually to do with symmetry. Let's leave it to linguists ... To be honest I got confused myself each time I read my own statement for linguistic corrections. For some time I even thought Goldrei wanted to distinguish between sets like ##\{1,2,3, \dots\}## and ##\{\frac{2}{2}\frac{4}{4}\frac{6}{6}, \dots \}## but that's too absurd for obvious reasons. I prefer Garling's definition and reserve "strict" as a property of possible inclusions as examples of a partial order, or for progression, comparisons in size and so on. It's fine enough to have partial orders in Garling's sense and distinguish between ##\subseteq## and ##\subsetneq## as examples, if needed. [/QUOTE]
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Partial Order - Reconciling Definitions by Garling and Goldrei
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