Definition talk:Set

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I think it should be also mentioned here that set is distributive (not collective) aggregation of objects (this might be reason for avoiding naming set a "collection" :p). Example: Mars is an element of set of planets but any element of this planet, e.g. rock lying on it, is not an element of the set of planets anymore (distributivity); body is an element of car parts and windshield is an element of the body, so it is an element of the car (collectivity). I belive that this would give proper intuition for the notion. joel talk 19:16, 29 December 2012 (UTC)

Just sounds like overcomplication to me. Never seen these terms used in anything I've encountered. --prime mover (talk) 21:44, 29 December 2012 (UTC)
I've noticed that it is hard to find a decent source about the subject: aim of this distinction is to differentiate distributive set theory (classical) from collective set theory (mereology) of Leśniewski (check also Standford Encyclopedia of Philosophy and Philosophy of Stanisław Leśniewski). if none is introduced (and unknown) then it might be profitable to tell in some words which meaning of the set is intended. All in all it might be, as you said, too complicated—I generally do not insist to incorporate it into this article, all things are ultimately settled by axioms, but thought it would be helpful in some way to give a proper intuition (maybe it'd be enough to say that "belonging relation is not transitive"). joel talk 09:23, 30 December 2012 (UTC)
I don't know about the rest of you out there, but I would fight tooth-and-nail against extending ProofWiki to encompass "philosophy".
A page documenting "belonging relation is not transitive" may be worth adding as a theorem/proof page, which would then be (possibly) linked in via the "Also see" section, but it would not be directly added to this page. --prime mover (talk) 15:42, 30 December 2012 (UTC)
Note that this site is more akin to a dictionary than encyclopedia, and so pages are encouraged to be small and do not include much extraneous detail. --prime mover (talk) 10:32, 30 December 2012 (UTC)