Talk:Naive set theory/Archive 1

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Archive This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

"Set-theoretic difference" redirects here, but is nowhere mentioned in the article. I assume it's another term for "relative complement". The symbol for that doesn't show in my browser -- I'd like to suggest A \ B , which is how I've always seen it written. Tarquin

That is the symbol being used — that is, an ordinary backslash. Internet Explorer has some trouble displaying that backslash for me as well, but I doubt that we can fix that here. -- Toby Bartels, Sunday, June 9, 2002

Testing... A \ B ... that shows. A \ B ... that shows... yet the same markup in the article doesn't show in Mozilla 1.0 Win98 OR Mac IE. Weird... Tarquin

It appears to be a bug in the Wikipedia page cacheing, since backslashes display properly the first time the page is loaded. It doesn't make any difference what browser you use, since it's not a browser problem. --Zundark, Sunday, June 9, 2002

Backslashes used to work, but don't any more. The backslashes disappeared from the urethane formula. File a bug report. --phma

Actually, one has been filed — been there for a few days now. It doesn't mention this page, but it seems to be the same bug. — Toby Bartels, Tuesday, June 11, 2002

The following comes from Talk:Basic Set Theory:

Beginning of discusssion on FallenAngel..

I see you removed the note about "first article".

Anyway, seems to me to be a fine job, introducing what is to many a difficult subject. This presents the info that is needed to even begin the axiomatic approach.

I saw somewhere a comment that this article is a duplication of effort. Not so. Both this and the set article (whose title is very ambiguous) are needed for different levels of study. --Buz Cory

I did indeed, for two reaons: firstly, until yesterday no comments were forthcoming so I decided it wasn't working; secondly, I was worried that it sounded a little proprietary and unwikian, something like " If there's anything you don't like ask me and I might change it." Certainly the deletion was not intended to discourage comments or commentary, for which I remain grateful

I think what was meant was the set theory article, but nobody seems to be brave enough to refactor it. :-) -- JanHidders
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Thats what I meant, and I also did not mean to disparage this one, rather that the two should be merged, with the strengths of this one added to the old, rather than presented as an alternative. -- GWO
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Basic Set Theory should remain as a separate article. For historical reasons at least...:))). ZFC is pretty new. -- Damas

The above is old talk, but it reminds me of an idea that I had.

First, ZFC is not all that new compared to set theory in general, as a mathematical concept; that is, we've had ZFC for most of the time that we've had sets, by now. But the fact remains that ZFC is an obscure subject of interest only to logicians, philosophers, and what we now call "set theorists" (and anybody else that wants to poke their heads into these people's subjects, of course, which includes most mathematicians at some point in their lives but certainly not every time that they use sets). Sets themselves can be used without ZFC: without worrying about foundational issues if you simply avoid certain (now well known) constructions, and with alternative foundations if you want to worry about such things.

So we should have two articles. But we should arrange them so that they're about what mathematicians would recognise as mathematical subjects. In particular, the article Basic set theory is not simply a more elementary introduction to the concepts in the article Set theory. Basic set theory is about what mathematicians call "naive set theory", while Set theory is about what we call "axiomatic set theory", and I argue that the articles should have those names. The introductions should also be rewritten to explain what these terms mean as the names of areas of mathematics (but the bulk of the articles require no change for this purpose).

I wasn't going to mention this soon, since I'm not sure that I'm ready to do that right now. Of course, it'd be great if somebody else did it instead, but it's unreasonable of me to expect that; if you want something done on Wikipedia, you have to do it yourself ^_^. So the real reason for saying this now, for no better reason than that the old talk reminded me of it, is to see if anybody objects to this as screwing up a really good present organisation. If not, then I'll do it when I get around to it.

— Toby 14:29 Oct 28, 2002 (UTC)

Wow! I just have to suggest something and it happens. I have such power ^_^! — Toby 17:00 Oct 31, 2002 (UTC)

I can't get the intersection symbol to show up. I am using IE 5.5 -- [[user:GABaker|GABaker] 15:15 Oct 28, 2002

IE 5 has some weird bugs where it will show a symbol sometimes and not others. I don't really know of a way around it. — Toby 17:00 Oct 31, 2002 (UTC)

In IE5.5 the symbols dont show up in my browser. As a suggestion, in the Dutch wiki I am using:

  • Ì for subset
  • Î for subset
  • Ç for intersection
  • È for union

Should show up pretty well in any browser with the Symbol font installed. I think this font comes default with most versions of windows, dunno about unix/linux.TeunSpaans 09:59 Dec 5, 2002 (UTC)

It turns out the symbols on this page do not turn up on IE6 either. Though I had started to convert the dutch wiki pages to the system used here, I am gonna change them bck to the symbol font. 90% of the browsers used is IE5.0, 5.5 or 6.0.

They display properly for me with IE 4.0 (except the union sign, for some reason). I'm sure they work in later versions of IE too - you just need a Unicode font installed. --Zundark 16:04 Dec 6, 2002 (UTC)
Without any reason or change, some symbols are now showing up in Ie5.5 at home, others still don't. TeunSpaans 20:09 Dec 6, 2002 (UTC)

Well, the symbols show up for me as "Ì" and "Î", "Ç", and "È". The real solution is to avoid using these symbols, prefering words in simple situations and texvc displays in complicated ones. -- Toby 01:29 Mar 12, 2003 (UTC)

"The name is perhaps derived from the title of Paul Halmos' book Naive Set Theory."

I'm not so sure about that. "Naive" is a general shop term used by mathematicians when talking about anything in general. The term means roughly "non-rigorous" (or at least not completely rigorous), informal heuristic arguments, or just general thinking out loud without worrying about justifying precisely every little detail. Thus, "naive" as opposed to "axiomatic" set theory. Revolver

I was surprised by this also. I had thought that Halmos's book was called Naïve Set Theory because it was about naïve set theory, not the other way around. -- Dominus 20:29, 9 May 2004 (UTC)

Is it really necessary to switch all the spellings to "naiive" (I don't even know how to get the double dots)? I know it's the original French, but I think it looks awkward to most eyes, it's listed as a "variant" spelling in every American and British dictionary I found, and it's harder to render. Revolver 02:30, 13 Mar 2004 (UTC)

Agreed. Widespread use of the term derives from Halmos, and his book was published in English as "Naive set theory". "Naïve set theory" is in use, but a Google search turns up many fewer hits than "naive set theory", and it doesn't help that WP floats to the top of the list. I'm inclined to revert to "naive". Wile E. Heresiarch 16:37, 4 Aug 2004 (UTC)