Talk:Naive set theory/Archive 1

message: "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
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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
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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)
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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)
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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)
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"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)
replies: text: 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)
thread_title:  Discussion 2002&ndash; 2004 

message: "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 (25:05, October 24, 2003 (UTC))
: 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)
replies: text: I could be wrong. I remember having a prof in grad school tell some students their approach to a problem was "naive", and them getting a bit offended, until he explained he explained it meant roughly the above. Revolver 06:39, 21 May 2005 (UTC)
thread_title:  Origin of the term "naive"

message: 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)
replies: text: 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)
replies: text:  I have moved this article back to naive set theory and within the text reverted "naïve" to "naive" (except in a quotation). (1) "Naive set theory" is much more widely used on the web (about 4000 Google hits for "naive" compared to about 1000 for "naïve"). (2) Within WP, almost all links to this article are from "naive" instead of "naïve". (3) Halmos's influential book was "Naive set theory". (4) "Naive" is the ordinary English spelling. Happy editing, Wile E. Heresiarch 06:04, 6 Aug 2004 (UTC)
replies: text:  Not just to make things difficult, but to set things right, I'm warning you that I will soon change the spelling on this page from naive to naïve unless you can give valid reasons. I will not accept that you don't want the correct spelling simply because it hurts your eyes. And as for you seeing naïve listed as a variant in every American and British dictionary, such lies. Most English Wikipedia pages regarding spelling look to The Oxford English Dictionary, the most comprehensive dictionary of the English language. Their main variant is "naïve" because it's the number one spelling, not naive a cheap knock off. Simply because Google turns up the most spellings as naive, does not mean it is right. Google can search for anything, including spelling errors from illiterate users. Let's stick with what is correct, not what we've stolen from another language and murdered by removing it's orthography. --Speakslowly 06:43, 17 December 2006 (UTC)
replies: text: The OED lists "naive" as the principal spelling, with "naïve" as a variant.    Dominus 07:01, 17 December 2006 (UTC)
replies: text: Before action is simply taken, let us get a firm grasp of WP:CON - Sam 07:18, 17 December 2006 (UTC)
replies: text: Yes quite. Paul August ☎ 16:46, 17 December 2006 (UTC)

text: Apparently you don't read the New Yorker, which even spells coöperate with a trema, and has meticulous copyediting.  Nevertheless, naive is a perfectly standard spelling, and there is no need to justify it.  If the article is moved, it is simple to move it back. CMummert 14:06, 17 December 2006 (UTC)
replies: text:  The ï is not a letter, but instead the letter i with a diaresis to distinguish the pronunciation from its antecedent. --Speakslowly 05:32, 18 December 2006 (UTC)
replies: text: If I read Diaeresis correctly, that means that "naive" is to be pronounced "na" followed by "ive" as opposed to sliding from the "a" to the "i". But once again. In English, it is not normal to include such information in the spelling outside special contexts such as dictionary pronunciation guides and linguistics. JRSpriggs 09:07, 18 December 2006 (UTC)
replies: text: The point of the trema is that naive doesn't rhyme with maize.  But I agree that the title of this article should not have one. CMummert 13:07, 18 December 2006 (UTC)

text:  There's really no point in discussing this any further.  Speakslowly did not address any of Wile E. Heresiarch's arguments in favor of "naive", and presented only one cogent argument of his own, namely, his claim that the preferred spelling given in the OED is "naïve".  As I pointed out above, this claim is false.  So what we have here is not even an discussion; none of the earlier arguments has been seriously challenged, and no new arguments have been presented.   The issue should not have been re-opened at all. -- Dominus 14:17, 18 December 2006 (UTC)
replies: text:  Yes, naïve helps distinguish the pronounciation as in na-ive, so it's not pronounced "nave". It's not normal to include such information? I guess we might as well throw out the alphabet because pronunciation does not seem to matter anymore. As for Dominus, you're wrong about the OED listing "naïve" as the variant, according to the The Oxford English Dictionary [Second Edition] Volume X, naive is the variant. I of course would not state such things without proof, so follow the links to see a photo of the page for yourself. If you'd like a full sized version I'd be more than happy to send it to you. №1 №2 I think the issue should have been re-opened, especially since the first argument said the spelling was ugly. As for Halmo's book, I would love to see further proof and other authors who have spelled it likewise. --Speakslowly 20:12, 18 December 2006 (UTC)
replies: text: I think your information is out of  date.  The OED Second Edition was published in 1989.  The entry for "naive" was revised in 2003 to list the headword "naive", not "naïve".  As for "further proof that others have spelled it likewise", you might try reading the OED entry.   It currently provides citations for "naive" (with that spelling) as far back 1614, and the photograph you posted includes a citation to Dryden from 1673.  Hope this helps.  -- Dominus 21:20, 18 December 2006 (UTC)

text: Speakslowly, concerning Halmo's book, you mention you "would love to see further proof". Further proof of what? Paul August ☎ 21:53, 18 December 2006 (UTC)

text: JRS, that really wasn't very helpful. Paul August ☎ 14:51, 20 December 2006 (UTC)

text:  It's a shame that my information could be out of a date, disgusting to replace an original word with a common mistake. To Paul, I believe the quote you have is very self explanatory, it's simply asking for further proof and examples of "Naive set theory." But don't fret too much, I'll let you rest. To JRSpriggs, you were convinced that ï was a letter, not a diacritic, and didn't even know how to pronounce the word. You're welcome for removing some of your ignorance. Now you can somewhat consider yourself educated because you know what a diacritic is, how the English alphabet works, and how to pronounce naïve. Your mind also learned that it is in fact normal to include accents in words because it's part of spelling! But don't feel too proud just yet, you felt the need to label someone a "troll" because it made you feel bigger. I hope it make you feel really smart, if even for a minute. By the way next time don't be so ignorant and assume you know a person's gender. It could be that I'm not a he. Makes you think doesn’t it? But don’t hurt yourself, we wouldn’t want that.  --Speakslowly 06:06, 20 December 2006 (UTC)
replies: text: Sorry to be dense but I still don't know what in the way of further proof you want concerning Halmo's book. If you doubt that the title is really "Naive Set Theory" without the  diaresis, see this link. Paul August ☎ 14:51, 20 December 2006 (UTC)
replies: text:  I meant as in other books, but it's ok. I had actually already seen the link you posted, but thanks. --Speakslowly 17:00, 20 December 2006 (UTC)
thread_title: "naive" vs. "naïve" 

message: This is in response to Fropuff's remarks a few paragraphs up:
:...I think there is a very important category that is being overlooked here. That is, set theory as used by mathematicians that are not working directly on the foundations of mathematics. I think 95% of the time that mathematicians, physicists, etc. use set theory they don't need to worry about the rigorous formulation.
Well, neither do set theorists, really, as you say 95% of the time. But non-set-theorist mathematicians do use the results of foundational researches, and know more about them than they think they do (though less, of course, than they ought to :-). For example, they know how to apply Zorn's Lemma, and they know to expect that any set of reals they can actually define, will be Lebesgue measurable. So I think set theory as used by mathematicians fits just fine into what I foresee as the general set theory article, into which axiomatic set theory should be merged. Naturally it would be near the top of the article, whereas axiomatizations and advanced techniques would come later. --Trovatore 23:52, 30 January 2006 (UTC)
replies: text: I guess as long as the set theory article had a prominent link to the naive set theory article and the set article is kept pretty basic, I don't having any major objections to merging axiomatic set theory in with set theory. Modern set theory is, after all, axiomatic; whether we choose to think about it or not. Perhaps we should continue the discussion at Talk:Set theory. -- Fropuff 02:03, 31 January 2006 (UTC)
thread_title: Set theory as used by mathematicians

message: Here is an example of a naive presentation which will do everything naive consumers probably want and which will not lead to paradox (all formalizable in ZFC).
As in the existing article, say that everything we do initially is carried on in a universe of discourse U.  It is reasonable to stipulate that any set in U also has all its elements in U (we don't need to use the word transitive when we say this).  (It might also be reasonable to stipulate that any subset of an element in U is also in U, but that is optional, and we certainly won't even whisper supertransitive).
Then say that for any property of elements of U, there is a subset of U consisting of everything with that property, which lives in the larger universe P(U)).  If we stipulated that all subsets of elements of U are in U, then we would have \{x \in A \mid P(x)\} in the universe U if A is in U, which is an advantage; otherwise subsets of elements of U get promoted to P(U).  Notice that I said "property"; not a word about formulas of first-order logic!
We can say that the process of construction of power sets can be repeated any desired finite number of times (any property of elements of Pn(U) determines an element of Pn+1(U)).  The resulting world satisfies all the axioms of Zermelo set theory (as long as it is implicitly understood that everything is in some Pn(U).  Any instances of replacement that are not satisfied are the result of recursion on the universe-constructing machinery, which is not a naive application of set theory.
The specific recursion leading to the natural numbers can simply be presented and it can be asserted that such a set is provided. An easy way to do this is to close U under the construction of finite sets.  This gives us each natural number in U and the set of natural numbers in P(U) (if we don't just provide it in U itself). 
It's not that this is easy; some of these ideas are hard.  But it is easy to avoid paradox:  restrict all comprehensions to sets already formed or power sets of sets already formed (and allow construction of finite sets of previously constructed objects).  No sophisticated logic needed. Randall Holmes 17:58, 30 January 2006 (UTC)
thread_title: semi-formal naive set theory, or, why it isn't difficult

message: I corrected the ascription of the paradoxes to Cantor's set theory (this is unclear, while Frege was definitely implicated).  I remarked that naive set theory is not always the inconsistent set theory anyway:  Halmos's book is about ZFC with all the axioms listed.  Further, I removed the statement that axiomatic set theory is abstruse and has no bearing on mathematics; this simply isn't true (it's not that abstruse -- witness Halmos -- and it has some definite bearing). Randall Holmes 22:24, 29 January 2006 (UTC)
thread_title:  various corrections 

message: * JA: The meaning of the word "naive" in this context is synonymous with "native" and "natural", as in "native intuition" and the "natural light of reason" (Galileo's il lume naturale).  It refers to that distributed but diverse intuitive conception of bunchiness that nature's evolution gave us at birth and that we nurture through comparative and critical reflection on the available panoply of provisional formalizations.  The word was used this way in philosophy generally long before Halmos and others wrote the mathematical books on it.  Though prior in time, the issue of (naive) set (folk) theory is perfectly analogous to the issue of the Church?Turing thesis about the eternally empirical and ever-intuitive notion of "what's a computation, anyway?"  Thus, it is a pragmatic matter that cannot be resolved solely by considerations of deductive, exact, formal reasoning.  The manifesto is ended ? Go in peace.  Jon Awbrey 14:08, 30 January 2006 (UTC)
replies: text: * I don't really disagree with what you say here at all.  Naive set theory is by definition not formalized (though the usual exact reference of this term is to a formal theory extracted from Frege by later workers; Extensionality + unrestricted Comprehension). But most naive set theory done nowadays is the sort which if formalized would end up in some relative of ZFC. Randall Holmes 15:30, 30 January 2006 (UTC)

text: * Though I do have a specific opinion about this:  I think that most "folk set theory" is either mereology or (folk) second-order logic (theory of universals).  I don't believe that there is any folk set theory in the true sense of set theory, in which there are sets of sets (or if there is it is of very recent development), and this is one of the reasons that teaching set theory is hard. Randall Holmes 15:34, 30 January 2006 (UTC)
thread_title:  On being naive 

message: To do set theory without risking paradox (in particular, to do set theory in a style which is formalizable in ZFC) is not especially difficult.  Thus I eliminated the language which says it is a "much more difficult development".  Perhaps the complaint is about logical technicalities about infinite axiom schemes?  Of course, thinking about set theory is hard, but this is because it is quite abstract, and the difficulties  about level of abstraction already exist in a "naive" treatment. Randall Holmes 15:27, 30 January 2006 (UTC)
thread_title:  Moderating propaganda against correct set theory 

message: Halmos's Naive set theory is actually a rigorous presentation of all the axioms of ZFC; it is axiomatic set theory.  Every axiom, including the scheme of Replacement (which he calls Substitution) is presented quite precisely. Randall Holmes 22:35, 30 January 2006 (UTC)
replies: text: Thanks for that report—I don't have Halmos's book available and have only barely glanced at it in the past. Part of the problem then seems to be his idiosyncratic naming. Set Theory from an Informal Perspective would have been a better name. The book may be a fine resource, but I think we don't need to ape his nomenclatural choices. --Trovatore 22:43, 30 January 2006 (UTC)
thread_title:  False impressions of Halmos 

message: One might find the now more refined semi-formal naive set theory amusing. Randall Holmes 17:51, 31 January 2006 (UTC)
thread_title: Semi-formal naive set theory

message: Google exact phrase search data:
 Basic set theory       -- 22,100 hits
 Casual set theory      --      3 hits
 Elementary set theory  -- 18,200 hits
 Informal set theory    --    273 hits
 Naive set theory       -- 32,100 hits
 Naïve set theory       -- 34,700 hits
 Prêt à Porter Set      --     28 hits
 Semi-formal set theory --      0 hits
* NB.  Google is using fuzzy search even on exact phrases these days, so pretty much ignores fussiness over diaereses, except that it works disjunctively to bring in extra hits.  Conclusion:  I think we have a real opportunity to get in on the ground floor with that semiformal set demographic. Jon Awbrey 03:14, 1 February 2006 (UTC)
thread_title: Usage data

message: ===Devlin (1993)===
* Devlin, K.J., The Joy of Sets:  Fundamentals of Contemporary Set Theory, 2nd edition, Springer-Verlag, New York, NY, 1993.
Zermelo–Fraenkel set theory, which forms the main topic of the book, is a rigorous theory, based on a precise set of axioms.  However, it is possible to develop the theory of sets considerably without any knowledge of those axioms.  Indeed, the axioms can only be fully understood after the theory has been investigated to some extent.  This state of affairs is to be expected.  The concept of a 'set of objects' is a very intuitive one, and, with care, considerable, sound progress may be made on the basis of this intuition alone.  Then, by analyzing the nature of the 'set' concept on the basis of that initial progress, the axioms may be 'discovered' in a perfectly natural manner.
Following standard practice, I refer to the initial, intuitive development as 'naive set theory'.  A more descriptive, though less concise, title would be 'set theory from the naive viewpoint'.  Once the axioms have been introduced, this account of 'naive set theory' can be re-read, without any changes being necessary, as the elementary development of axiomatic set theory.  (Devlin, p. 1).
* JA: Apparently the distinction betwen naive and otherwise is in the eye of the beholder, the outlook that develops in the exercise thereof.  Jon Awbrey 03:48, 1 February 2006 (UTC)
thread_title:  Uniformedly at random reading 

message: * Devlin, K.J., The Joy of Sets:  Fundamentals of Contemporary Set Theory, 2nd edition, Springer-Verlag, New York, NY, 1993.
Zermelo–Fraenkel set theory, which forms the main topic of the book, is a rigorous theory, based on a precise set of axioms.  However, it is possible to develop the theory of sets considerably without any knowledge of those axioms.  Indeed, the axioms can only be fully understood after the theory has been investigated to some extent.  This state of affairs is to be expected.  The concept of a 'set of objects' is a very intuitive one, and, with care, considerable, sound progress may be made on the basis of this intuition alone.  Then, by analyzing the nature of the 'set' concept on the basis of that initial progress, the axioms may be 'discovered' in a perfectly natural manner.
Following standard practice, I refer to the initial, intuitive development as 'naive set theory'.  A more descriptive, though less concise, title would be 'set theory from the naive viewpoint'.  Once the axioms have been introduced, this account of 'naive set theory' can be re-read, without any changes being necessary, as the elementary development of axiomatic set theory.  (Devlin, p. 1).
* JA: Apparently the distinction betwen naive and otherwise is in the eye of the beholder, the outlook that develops in the exercise thereof.  Jon Awbrey 03:48, 1 February 2006 (UTC)
thread_title: Devlin (1993)

message: * JA: One of the things that we are supposed to have acquired an appreciation for in mathematics is the distinction between what we can prove and what we can merely imagine or wish to believe.  In that regard, when it comes to horses and wishes about the consistency of any future axiomset that could stand up and be counted as a set theory, or claims about the equivalence of several different axiomsets for sets, well, about the most that I've ever seen any careful person claim for his or her pet system is that "it's free from the more obvious contradictions ..." (Kelley, more or less, I think).  So let's try to keep that in mind.  Jon Awbrey 05:06, 1 February 2006 (UTC)
replies: text: Um—keep it in mind when doing what, exactly? --Trovatore 05:15, 1 February 2006 (UTC)
replies: text: Yes, that's a point, but a bit of a side issue, and I doubt Paul was claiming actual apodeictic knowledge of the consistency of any particular formal theory. --Trovatore 05:29, 1 February 2006 (UTC)
thread_title: Contradiction freedom's just another word ...

message: I edited this section removing the set of imaginary numbers \mathbb{I}. I'm graduating in math and I've never seen such a notation; purely imaginary numbers are denoted as i\mathbb{R}. Wikipedia artcle on numbers does not mention them either, so I don't think they deserve to appear in this article.192.167.204.9 15:24, 25 November 2006 (UTC)
thread_title: Some important sets

message: Several of the special math characters used in this article show up as squares in IE 7.  Can someone substitute the TeX math characters?  Bubba73 (talk), 05:06, 15 February 2007 (UTC)
replies: text: There are too many articles with too many such symbols. Why do you not do what I finally did -- switch to Mozilla Firefox. JRSpriggs 08:51, 15 February 2007 (UTC)
replies: text:  Firefox has a different set of problems.  I need to set a minimum font size for it to work well, and then it chops off the descenders on the tabs, etc.  Bubba73 (talk), 19:32, 16 February 2007 (UTC)
replies: text: The problem is that Wikipedia uses some GNU software. I notice that it works great with Linux, no matter which browser I use (I have three browsers on Linux). Windows is a whole different story. Firefox definitely works better than IE (6.0) when I'm running Windows, but neither one works as well or looks as nice as any of the browsers running under Linux does.  DavidCBryant 21:07, 16 February 2007 (UTC)
thread_title:  special characters 

message: Presenting naive set theory as the first set theory developped by Cantor may lead to the impression that all elementary mathemetics are based on a contradictory theory. The amendments I proposed today are aimed at a better dissociation of inconsistent Cantor-Frege theory from naive set theory, in accordance with french version of this article.
CBerlioz 16:04, 21 May 2007 (UTC)
thread_title:  Is naive set theory necessarily contradictory? 

message: Substituted at 06:33, 7 May 2016 (UTC)
thread_title: Assessment comment