A vital article and a core idea in Mathematics. I'd like advice on how this article could be expanded, and what is needed to bring it to good or featured status. Thanks! CloudNine 18:12, 17 January 2007 (UTC)
There are many ways this article could be improved. Most sections are trivially short. Here are some particular comments in no particular order.
- As it stands, this article is extremely redundant with naive set theory, almost to the point of duplication. This has been a problem for a long time, but someday it ought to be resolved.
- This article is an appropriate place to discuss the philosophical questions associated with sets, which I would be interested in reading and which would not fit into the technical articles. For example, Penelope Maddy is widely rumored to have claimed that sets exist in some "physical sense".
- There is no mention of extenstionality in the article, but this is one of the things that makes sets into sets. Like they say, there are no blue sets.
- The concept of the cumulative hierarchy is missing.
- Can a set be a member of itself? Of course the axiomatic treatment doesn't belong here, but some discussion does.
- The sections on basic operations could be grouped together (union, intersection, relative complement).
- There is no mention of Russell's paradox except as a "see also" link. This is, historically, an important step in the understanding of the technical limits of the natural language term "set".
I gave the article a bit of a copyedit; hopefully, I didn't change the meanings. I think the article works well as a basic introduction to the theory of sets, but needs more background information. There is very little detail on the history of sets, or their application to Mathematics in general (except in the lead, and the lead shouldn't introduce anything that isn't expanded upon later). A bit more background information (with references) would balance the article and provide a more well-rounded look; at the moment, it's more of a textbook than an encyclopaedia article. Trebor 16:45, 18 January 2007 (UTC)
- Thanks. My main worry now, with including the History and Applications section, is that naive set theory will be a duplication of Set (the set theory article already duplicates a lot of information about basic set operations). What do you think? CloudNine 18:00, 18 January 2007 (UTC)
- Hmm, I'm not very knowledgeable on sets so I may end up talking rubbish. But I would say that Set should be a summary of both naive and axiomatic set theory. Then it would include a summary of the history and development of both, describe any features that they have in common and explain how they have been used in Mathematics to do "notable stuff". At the moment, the article is (I think) focused more on naive, which could be seen as POV. But since I don't know which features they have in common (if any), it may be quite hard to write an article that encompassed both. I just think that the general article Set shouldn't focus on a particular definition too much. Trebor 18:49, 18 January 2007 (UTC)
It's a bit simple, isn't it? The content that's there is fine, but it's very elementary - sort of pages 1-5 of an introductory text. I'm only passingly familiar with set theory, but surely there should be something on countability here? The 'history' section is currently blank, and there's not even a link to ZF anywhere. Other more minor issues:
- Images are prime candidates for SVG-ifying.
- Top image is lamely cartoony; it's like Donald Duck's Guide to Sets.
- FA and GA will whack you over lack of inline citations. Most of this stuff is trivially self-verifying, but when you add more background/history and more advanced material, make sure to add references where appropriate.
- While you're motivated to improve articles on this subject, uncountable set is badly disorganized. Opabinia regalis 03:13, 19 January 2007 (UTC)