# Wikipedia talk:WikiProject Mathematics/Archive 28

This is the archive file "Wikipedia talk:WikiProject Mathematics/Archive 28". It is for August 2007.

 Archive 25 Archive 26 Archive 27 Archive 28 Archive 29 Archive 30 → Archive 35

This is my first foray into this WikiProject, and I'd like to have a rant. I know a lot of work has been done on maths articles on Wikipedia, and I really appreciate the effort. However, I don't recall the last time I came away from a maths article less confused than I started. This is English Wikipedia, and at the risk of sounding like an arrogant Western tourist in the Japanese country side, can you (authors of maths articles) please write in ENGLISH? I'm not asking for a whole article without mathematical notation, nor for formal, rigorous mathematical definitions to be translated perfectly into English (although that would be nice too)...

What I am saying, is that me, as a layman, like the many others who read Wikipedia, would find the maths articles a lot easier to digest if you (the authors) would at least include an opening short paragraph without any mathematical symbols whatsoever. None at all. The empty set. For a whole paragraph. I can't stress this enough. Wikipedia is not Wolfram's world of maths and Wikipedia's readers are not all mathematicians. Please write introductions (at least) for a general audience. The only assumption you should be making is that your reader knows English.

Hawking refrained from using more than a single equation in a brief history of time*; surely you can refrain for a single paragraph. To labour the point, here's a quote from the WP:Manual of Style (mathematics) which also encourages informal introductions: (* e=mc²)

It is a good idea to also have an informal introduction to the topic, without rigor, suitable for a high school student or a first-year undergraduate, as appropriate. For example,

In the case of real numbers, a continuous function corresponds to a graph that you can draw without lifting your pen from the paper; that is, without any gaps or jumps.

The informal introduction should clearly state that it is informal, and that it is only stated to introduce the formal and correct approach. If a physical or geometric analogy or diagram will help, use one: many of the readers may be non-mathematical scientists.

Imagine trying to read any of these opening paragraphs with no knowledge of any mathematical notation system. They are mostly simple concepts.

Opening paragraph examples:

In mathematics, a domain of a k-place relation LX1 × … × Xk is one of the sets Xj, 1 ≤ jk.
In the special case where k = 2 and LX1 × X2 is a function L : X1X2, it is conventional to refer to X1 as the domain of the function and to refer to X2 as the codomain of the function.
• Image (mathematics) (here the opening paragraph is in English, but it makes no attempt to define the term. ugh.)
In mathematics, image is a part of the set theoretic notion of function.
Let X and Y be sets, f be the function f : XY, and x be some member of X. Then the image of x under f, denoted f(x), is the unique member y of Y that f associates with x. The image of a function f is denoted im(f) and is the range of f, or more precisely, the image of its domain.
• indicator function (not terrible, but still no need for symbols in the first sentence).;
In mathematics, an indicator function or a characteristic function is a function defined on a set $X$ that indicates membership of an element in a subset $A$ of $X$.
• Lambda system (this introduction leaves me wanting to yell "DO YOU SPEAK ... ENGLISH ???")
In mathematics, a λ-system on a set Ω is a class L, consisting of certain subsets of Ω, such that: the set Ω itself is in L;
• Hermitian adjoint (A counter example, perhaps. I have no idea if it's possible to make this readable, even with its lack of symbols. But I'm giving the example here as food for thought..)
In mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator. Adjoints of operators generalize conjugate transposes of square matrices to (possibly) infinite-dimensional situations. If one thinks of operators on a Hilbert space as "generalized complex numbers", then the adjoint of an operator plays the role of the complex conjugate of a complex number.
The adjoint of an operator A is also sometimes called the Hermitian adjoint of A and is denoted by A* or A (the latter especially when used in conjunction with the bra-ket notation).

...

Please opening maths articles with an informal introduction. I'd go on to ask for equations to also be given captions or explanations, much like other illustrations, but that might be stretching it.

Thanks to all contributors, and especially those who have been endeavouring already to make Wikipedia readable by all. Thanks for reading this far. end rant

Pengo 08:30, 3 August 2007 (UTC)

You are right that these are not good. (However, there is not a single of your examples that are not written in English; the trouble is not the language but the content, i.e. the lack of an informal introduction that provides context - for example, what does this concept generalize, or what is it used for). You hereby have permission to start fixing them. :-)Henning Makholm 09:37, 3 August 2007 (UTC)

## Help clean up these weird links to "expectation"

The article titled expectation seems to be about a weird mixture of psychology, economics, and the supernatural.

The article titled expected value is about the mathematical concept.

Lots of mathematics articles link to expectation when expected value is clearly intended. Changing [[expectation]] to [[expected value|expectation]] would fix those links. Go to expectation and click on "what links here" and find cases that look as if they should link to expected value and go from there. Michael Hardy 19:32, 3 August 2007 (UTC)

Sounds like a plan. I've been doing the same with the bizarre and probably not salvageable article Infinity, replacing with links to Infinite set. Unfortunately this doesn't work in all cases, but I'd rather delink (or better, link to Extended reals or the like) than keep a mathematical article's link to the psychological/historical/supernatural/revisionist OR-mismash that is Infinity. CRGreathouse (t | c) 19:55, 3 August 2007 (UTC)
I agree about expectation, which is now a little better as I've removed some of the more spurious see also links. Less convinced about Infinity/Infinite set. Infinite set fails the layman test mentioned above, its also less encyclopaedic than Infinity as the reader may be interested in other aspects of the term, such as its treatment in computing. Infinity probably also explains a little better its most common usage as bounds in integrals, summations. Extended reals is not the right link in these context as the infinity symbol is more a notational convenience than an actual element of a set being considered. --Salix alba (talk) 21:58, 3 August 2007 (UTC)
In the course of helping to clean up the erroneous links to expectation, I ran across this article. For a moment I was tempted to start a new article about indiscreet mathematicians – the list to be headed by Evariste Galois, of course. But then I came to my senses.  ;^> DavidCBryant 00:51, 4 August 2007 (UTC)
Make sure that you put Gian-Carlo Rota into the indiscrete crowd ^-^ Arcfrk 20:53, 4 August 2007 (UTC)
Just in case, just in case: Let us not forget that discreet, with two consecutive "e"s, and discrete, with a final "e", are two different words that mean two different things. Evariste Galois might indeed be called "indiscreet", considering the way he died. Gian-Carlo Rota could be considered "indiscrete" considering the title of one of his books. Michael Hardy 21:24, 4 August 2007 (UTC)

## Homogeneous linear equation

I didn't find anything on WP about homogeneous linear equations: $\mathbf{A} \mathbf{x} = \mathbf{0}$ where $\mathbf{x}$ is a vector and $\mathbf{A}$ is a matrix or linear transformation. I want to write a definition and say something about the characters of the solution with links to SVD and to null space, etc. Q: should this be an article of its own or put somewhere, for example, in the linear equation article since it can be seen as a special case of a linear equation? --KYN 17:15, 5 August 2007 (UTC)

Possibly this should go into the system of linear equations article. It already has some information on this topic. Jim 17:38, 5 August 2007 (UTC)

Thanks for this reference. I will move my case to that Talk page. --KYN 18:40, 5 August 2007 (UTC)

## Copyeditor needed

The current FAC for Orion (mythology) recommends a copy-edit. I really cannot do this myself; I'm too close to the article to see it clearly. Also, the FAC has brought out some very useful additions to the article, and I may be too respectful of my helpful colleague's prose.

Why here, though? Because a large number of intelligent and literate editors hang out here, and while I've asked the appropriate project, it is largely deserted. More importantly, this article has the same problem as many mathematics articles: those who would naturally edit it know the subject, and it's hard to tell what it looks like to readers who don't. What the article needs is a detailed read-though, to check that it is clear and grammatical everywhere. Please help. Septentrionalis PMAnderson 20:17, 5 August 2007 (UTC)

## Infinite monkey theorem in popular culture

Infinite monkey theorem in popular culture was improperly deleted and I have restored it. A regular AFD nomination was begun at Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture and someone deleted the article in the early stage of discussion. User:Kurykh and User:Sr13 appear very very hostile to Wikipedia's conventional norms and procedures. The latter's edit summary when he deleted it was dishonest, stating that it was done "after discussion". Michael Hardy 02:53, 6 August 2007 (UTC)

I've commented on Wikipedia:Administrators' noticeboard/Incidents#Infinite monkey theorem in popular culture. Let's keep the discussion there. -- Jitse Niesen (talk) 03:24, 6 August 2007 (UTC)

### Please express opinions on this proposed deletion

Please express opinions at Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture. Michael Hardy 05:41, 6 August 2007 (UTC)

### No, let's keep the discussion here, where it belongs

It is not proper to speedily delete when the discussion is just getting underway and people disagree on whether to keep an article.

The AfD system is badly broken. In this case, Wikipedia talk:WikiProject Mathematics and Wikipedia talk:WikiProject Probability were never told the article exists, let alone that it was nominated for deletion. It was spun off from another article, and never tagged with [[Category:Probability]] that would have caused the appropriate bots to pick it up.

Most people on Wikipedia are good people.
Most people who opine on AfD are good people.
Most people who spend all their time on AfD are bad people, full of hatred. I've said this before over the past couple of years. Something in the system encourages this.

Tomorrow I'll open a deletion review and suitably notify this project and that other one. Michael Hardy 06:59, 6 August 2007 (UTC)

Most people who spend all their time on AfD are bad people, full of hatred What the hell? That is the worst accusation of bad faith that I think I have ever read on Wikipedia. Note that I am not one of those "bad people, full of hatred", as can be verified by examining my contributions (I haven't edited an AfD in a long while). I am nonetheless disturbed by your comments. Please go read Wikipedia:Assume good faith, and reconsider your rhetoric. --Iamunknown 07:05, 6 August 2007 (UTC)
When I saw your post at AN/I, and examined the posts at the relevant WikiProjects, I noticed your post here. I now see that you posted comments similar to the above at AN/I. I have posted in more detail there. I would like to remove any argument related to non-mathematics topics which might crop up from the Mathematics WikiProject, so as to not disturb this talk page, and so I have stricken my comments. --Iamunknown 07:44, 6 August 2007 (UTC)

Infinite monkey theorem in popular culture was deleted in an irregular way when this WikiProject had not been notified of the proposal for deletion. Please express opinions here: Wikipedia:Deletion_review/Log/2007_August_6#Infinite_monkey_theorem_in_popular_culture. Michael Hardy 22:56, 6 August 2007 (UTC)

man, these bureaucrats are something else, eh, Mr. Hardy? :-) Mct mht 01:36, 7 August 2007 (UTC)

## Bibtex for Wikipedia, the third

Following several people's encouragement, I pursued the aim of a database for easy referencing of WP articles.

See http://zeteo.info for the results of these efforts.

• It essentially consists of 4 databases: for references (i.e. books or journal articles), authors, journals and publishers. These databases are intertwined, e.g. linking from a certain reference to its author and vice versa etc. It is possible to add references from scratch, i.e. inputting all necessary information concerning the book.
• It is also possible to parse a text (for example a Bibtex file, or a file containing {{Citation}} or related templates). The procedure is semi-automatic, i.e. the program tries to recognise reference items in the text. In good cases, when the author, journal, publisher of a reference is already existing in the respective database, no further action is necessary. Otherwise the user will have to confirm the correctness of the input. I've tried to make this as quick and comfortable as possible. Adding some hundred references (from your BibTex-file, say) will take no more than 3 minutes.
• One can export all items into the {{Citation}} template.
• There is a little search engine template (the ones Firefox shows at the top right corner), so one can comfortably look for a book while typing a WP article. (To install it in Firefox, open the above URL and add the engine by clicking at "add 'zeteo search'" in the list of existing search templates).
• A slightly more complete documentation is here.
• At the moment there is no user managment, nor are there "flagged items" (showing the correctness of the information of some item).
• For now, the use of the database will smoothly work only for editors on the English Wikipedia, but enhancing the functionalities to other ones won't be a big deal.

Obviously, the database will fulfill its purpose only if there's enough information in it. So, how do we get it in there? In roughly decreasing order of reliability, there are the following options:

• As said above, it is pretty easy to include information of your personal Bibtex files. Other sources of BibTex-style information are MathSciNet and Zentralblatt MATH. However, they publish the stuff under copyright (see e.g. [1]), so I'm not sure whether it is legally OK to copy the BibTex information they provide and parse it, especially if more than a small amount of data is transferred this way.
• Another option, suitable for single items, is Google Scholar (e.g. [2])
• Also possible is User:Diberri's tool, which retrieves information on books, if you have the ISBN. (In fact, this is already incorporated: if you look for a book via its ISBN and nothing is found, the database will propose to look up the information using this tool).
• Finally, suggested by User:CBM, admins are apparently able to retrieve all citation templates in Math WP articles. One could then parse them and add the information to the database this way. After trying some hundred test items provided by CBM, it seems that this will work, too. However, WP contributors seem quite creative in formatting these templates, e.g. mixing up journal and publisher, misprints in the author's name and so on.

So, please tell me your ideas/impressions about it. I hope the engine will help making a decisive step towards more accurately/completely referenced articles.

Some other thoughts/questions:

• Does anybody in Math use EndNote as a referencing tool?
• Given the (as far as books are concerned) apparently pretty complete database of [3], it may also be an idea just to ask them whether they are willing to include an export option using Wikipedia templates. However, they don't seem to have any journal articles.

Jakob.scholbach 01:51, 6 August 2007 (UTC)

I tried it out and imported about ten references. The interface is intuitive, so that's good. I do have some comments though:
1. If it doesn't recognize the author, it asks the user to check. That is good. However, there are different spellings of a name ("Arnold" and "Arnol'd", to give a simple example), sometimes wildly different. I think it would be good if you could browse the author names in the database alphabetically. Does the system warn you if a similar name exists (like it does for publishers)?
2. Searching for "Arnol'd" gives some errors. You should be very careful with user-supplied data. See for instance the PHP manual for details.
3. Search for "Golub" indeed gives one of the books that I imported. However, the reply is {{Citation | last1=Golub | first1=Gene H. | author1-link=Gene H. Golub | last2=Van Loan | first2=Charles F. | author2-link=Charles F. Van Loan | title=[[:en:Gene H. Golub|Matrix Computations]] | publisher=Johns Hopkins | edition=3 | isbn=978-0-8018-5414-9 | year=1996}} The link in the title field is wrong.
4. Searching for "golub" does not yield any results; apparently the search is sensitive to case. I would make it case-insensitive.
5. I find the list of references that you get when you go to http://zeteo.info/ rather confusing. Start with an empty display.
It's a good start, but we'll have to see whether it will prove to be useful. But I've bookmarked the page.
I don't know of anybody in maths using EndNote, except for students who don't know latex and write their reports in Word. -- Jitse Niesen (talk) 03:07, 6 August 2007 (UTC)
Thanks for the comments. In order not to overwhelm everbody's watchlist, you can also report bugs which are probably not so interesting here: User:Jakob.scholbach/zeteo/bugs.
3.-5. are fixed. 2. is partly fixed (I need to test it further)
Ad 1: When adding a reference, the query for the author is sharp, i.e. not allowing merely similar names. There is no warning if a similar author exists. Both is on purpose (otherwise, as the database grows, it will likely yield unwanted results). If it happens that someone adds a reference with author="Arnol'd" and another one with "Arnold", it is possible to redirect one author to another one (similarly with publishers and journals). This way you can handle different transcriptions, typing errors etc. After setting the redirect, only the "correct" name (of the author which gets the redirect) will be shown. As for looking up the authors alphabetically, you can do that in the author's view, sort it by name by clicking at the "Name" column. Jakob.scholbach 05:05, 6 August 2007 (UTC)
By the way, it isn't that admins have some special ability to pull out citation info from articles - I have a small parser that I wrote that does it. — Carl (CBM · talk) 02:57, 7 August 2007 (UTC)
OK. So, can you run your script once to retrieve all the information? If possible, include the leading {{ and }}. (The zeteo parser needs these to recognize the format).
It seems to work very well! Is it stable enough to add this to Wikipedia:WikiProject Mathematics/Reference resources?  --Lambiam 08:01, 7 August 2007 (UTC)
Yes, perhaps we wait a little bit how everybody likes it? especially when populating the database with the above information.Jakob.scholbach 23:30, 7 August 2007 (UTC)
Another question: Is it possible to automatically replace LaTeX by this Latex-derivate we are using here? This would be handy for titles like On the asymptotic distribution of the eigenvalues of pseudodifferential operators in $\bf R\spn$ (replaced to ...$\mathbf R^n$) Jakob.scholbach 00:58, 8 August 2007 (UTC)
Great progress; thanks! I'll have to experiment more to comment in detail, but here's one quick observation: One standard date format, advocated for some citation templates, is yyyy-mm-dd. It is not among the three formats listed as acceptable for the form. --KSmrqT 02:47, 8 August 2007 (UTC)

## proposed merger of axiomatic system and formal system

This is a pointer to the discussion at Wikipedia_talk:WikiProject_Logic#Merger_of_Axiomatic_system_and_Formal_system. — Carl (CBM · talk) 22:42, 7 August 2007 (UTC)

Actually that's a pointer to a pointer. Probably better to comment directly at talk:formal system. --Trovatore 22:44, 7 August 2007 (UTC)

## iff

I'd just like to bring to people's attention that blackboard shorthand notations such as "iff" and "wrt" are not really in the right linguistic register for an encyclopedia article. To avoid repeating "if and only if" over and over again, you might try substituting some handy synonyms, such as "just in case", "exactly when", "necessary and sufficient". --Trovatore 22:04, 7 August 2007 (UTC)

I also disfavor iff, although Halmos was fond of it. I would immediately replace wrt if I saw it in an article. — Carl (CBM · talk) 22:45, 7 August 2007 (UTC)
I'm sorry – I can't resist. Wrt wrt, I'd immediately replace it iff I saw it in an article.  ;^> DavidCBryant 01:24, 8 August 2007 (UTC)
you're getting outta control, Dave. Mct mht 02:19, 8 August 2007 (UTC)
This issue has been raised and discussed before: Wikipedia_talk:WikiProject_Mathematics/Archive_1#About 'iff', Wikipedia_talk:WikiProject_Mathematics/Archive_14#Use "iff", not "if", in definitions!. Should we add some text to Wikipedia:Manual of Style (mathematics)#Writing style in mathematics to encourage authors to avoid this and other jargonistic abbreviations (e.g. "wlog"), and in general to keep the mathematical jargon at a low level?  --Lambiam 23:43, 7 August 2007 (UTC)
Yes. Paul August 00:34, 8 August 2007 (UTC)
if and only if with a link seems sensible to me. iff redirects to if and only if, but some readers will not know iff and not follow the link. I prefer to write out if and only if. When there are many in an article, iff could be used with the first occurrence saying "iff (if and only if)". PrimeHunter 00:47, 8 August 2007 (UTC)
Honestly I'm against linking it at all. I'm not convinced there should even be an article on "if and only if". No, I don't agree with using "iff" just because there are a lot of them -- if you want to do elegant variation, as I said, there are synonyms. --Trovatore 00:55, 8 August 2007 (UTC)
I don't want to do elegant variation here. I want to use consistent notation, but "if and only if" may get a bit annoying if it's repeated 20 times in an article, so I suggested 20 iff for brevity with the first occurrence explaining the meaning. PrimeHunter 01:11, 8 August 2007 (UTC)
No, I don't agree with that. No matter how many times it's repeated, it's still blackboard shorthand, which doesn't belong in an article. If it's repeated that many times, it may be an indication that some material could be rephrased as a list of equivalent conditions. --Trovatore 01:14, 8 August 2007 (UTC)

I added a paragraph to the math manual of style about this (diff) with an appropriate edit summary. — Carl (CBM · talk) 18:24, 8 August 2007 (UTC)

### Periods at the end of displayed formulas

As long as we're on stylistic points -- Giftlite is going around adding periods to the ends of sentences, even when the "sentence" finishes with a formula in displayed math mode. I think these look very odd (see this diff for an example). Does anyone else have an opinion on these? --Trovatore 18:32, 8 August 2007 (UTC)

I always use these, on the interpretation that a displayed formula, like a displayed quotation in a humanities paper, is part of the sentence that precedes it. Similarly, if the part of the sentence following the formula is a parenthetical phrase, I would end the formula with a comma. Like so: Euler's identity is
$e^{i\pi} = -1,$
where e is the base of the natural logarithm. A quick random selection of books from my shelf shows this style is very common. I have noticed that even algebra and category theory books often end their commutative diagrams with a period when the diagram ends a sentence. — Carl (CBM · talk) 18:47, 8 August 2007 (UTC)
(edit conflict) Everything I have ever read says that this is standard mathematical style when the formula is actually part of the sentence (and not just a "stand-alone" formula). At first, it looked weird to me to, but once I started doing it my own writing, I got used to it, and now I prefer to see the periods. VectorPosse 18:51, 8 August 2007 (UTC)

And here's a technical complication:

Right:

$f(x) = \begin{cases} 1 & \mbox{if }x = 2, \\ 2 & \mbox{if }x = 1. \end{cases}$

Wrong:

$f(x) = \begin{cases} 1 & \mbox{if }x = 2 \\ 2 & \mbox{if }x = 1 \end{cases}.$

I've seen this happen a number of times. Someone just puts the period at the end of the TeX code without thinking of what it will look like, rather than putting it where it makes sense in light of the appearance. Michael Hardy 18:56, 8 August 2007 (UTC)

I still think the whole idea is weird. Yes, at a certain abstract level, it makes sense, but from a practical point of view punctuation is meant to separate ideas, and a displayed math formula is already about as separated as you can get. The eye wants to find a mathematical meaning for the punctuation rather than an English-typography one, and it isn't there. --Trovatore 19:00, 8 August 2007 (UTC)
(edit conflict again. Carl is always quicker than I am.) Well, let's put it this way: if it weren't for the fact that your attention was drawn to it by someone going around adding them, would you have noticed? In fact, look at some of the standard books or journals you use on a regular basis and check to see if the periods are there. Have they ever bothered you before?  :) VectorPosse 19:12, 8 August 2007 (UTC)
When writing about TeX in the 80s, Knuth was adamant that professional typesetting with TeX still needs professional editors to do well. Things like the poor punctuation above are just the tip of the iceberg... — Carl (CBM · talk) 19:11, 8 August 2007 (UTC)
Generally, math text with formulas should read as a complete English sentence, including punctuation. Jmath666 23:51, 8 August 2007 (UTC)
Per Jmath above. Virtually all math books and publications put a period at the end of a formula if the formula is a the end of the sentence. This is also written in the math style manual (admittedly, by yours truly). This is the accepted style, and I believe it makes a lot of sense. Oleg Alexandrov (talk) 23:55, 8 August 2007 (UTC)
Well, OK, if everyone thinks so. I still don't like it myself. The "practical" style seems to me to leave off the period, whereas the truly "logical" style would be to put the period at the start of the next line. Actually I like that latter suggestion a lot -- if I'm ever in charge of a publishing house I'll suggest it. --Trovatore 00:12, 9 August 2007 (UTC)
If[f] ... :) Oleg Alexandrov (talk) 05:47, 9 August 2007 (UTC)
(edit conflict) Publishing houses and journals sometimes create their own manuals of style - nothing is fixed in stone, of course, and there is no math writing police. I do not like the periods and commas after a formula sometimes myself, they may get confused with a part of the formula, but that's what the current usage is. At least in math written in English. A good way to put it to test would be to submit an article with the alternate way of punctuation to a major math journal and see what would happen - how much the referees and then the copy editor object. Of course the math would have to be good so that the process would get to that point. Jmath666 06:00, 9 August 2007 (UTC)
Emotionally, I'm still on the fence; in practice, I've begun to include punctuation. Carl's example, where Euler's identity has a trailing comma, seems compelling. Michael's horribly-placed-period example is a warning to take care. As another example, if punctuation is included, it must be inside the $brackets. Incidentally, I appreciate seeing the "good" Michael Hardy; excess Sturm und Drang we do not need. --KSmrqT 06:39, 9 August 2007 (UTC) In LaTeX, comma in inline formula should be outside of   so that the spacing is handled correctly as part of text) while in displayed of course inside to avoid comma on the next line. Why it should be here different? A related problem, people keep replacing inline math by italics, which is just a workaround for lousy rendering (hopefully temporary problem) and logically wrong in any case. Jmath666 06:56, 9 August 2007 (UTC) So the "logical" way is definitely punctuation outside the [itex],$ pair (the punctuation certainly not being part of the math formula). So if it's neither "logical" nor practical, what exactly is the point of having it at all? It strikes me as being like the American punctuation-inside-quotes, which, Yank though I be, I simply refuse to use, because it's obviously just wrong, much as I prefer American usages and spellings in most cases. --Trovatore 07:15, 9 August 2007 (UTC)
I don't understand this last remark. Punctuation inside math tags is practical, at least in some circumstances. For instance, "$a = e^{x^2}$." with the full stop outside the math tags is rendered as
$a = e^{x^2}$.
That looks wrong; the full stop is too high. On the other hand, "$a = e^{x^2}.$" yields
$a = e^{x^2}.$
That looks fine; at least, it is as good as we are going to get. -- Jitse Niesen (talk) 07:51, 9 August 2007 (UTC)
If the Wikipedia TeX worked like normal TeX, there wouldn't be this problem. So we have to resort to putting the period inside the $tags to get the rendering to work correctly. In TeX, one would never put a period inside the math environment. So this raises the important question: why the heck does Wikipedia's TeX function so differently than real TeX, and how do we change it so that it functions as it should? VectorPosse 07:58, 9 August 2007 (UTC) Not quite true: one must put punctuation inside displayed math environments (like  or ). One should never put punctuation inside inline math environments. One of the difficulties with the wikipedia tex system is that it does not distinguish between these. — Carl (CBM · talk) 12:16, 9 August 2007 (UTC) TeX outputs dvi files, which gives it complete control over the exact position of every glyph on the page. In contrast, MediaWiki's TeX engine outputs separate image files, which are then embedded in HTML for the ordinary text. HTML provides only crude control over the vertical position of inlined graphics with respect to the surrounding text. –Henning Makholm 09:26, 9 August 2007 (UTC) Which is not exaktly true, it is only texvc that does not return baseline information for the proper placement of the graphics. For a counterexample, see meta:Blahtex. It will be introduced into mediawiki surely before the hell freezes over, but long after the release of Duke Nukem Forever, which, as is widely known, will happen shortly after the stable version of the GNU/Hurd system is released.--LutzL 11:51, 9 August 2007 (UTC) If the period is outside of the formula, it sometimes gets rendered to the next line, which looks awful, an empty line only with a period at the beginning. Period and comma should always go inside of the math tags. Oleg Alexandrov (talk) 16:32, 9 August 2007 (UTC) It may look awful to have a blank line with just a period at the beginning, but it is precisely what makes sense. Which is why, to avoid it, my intuition is just to drop the period altogether. It's not as though anyone is likely to think the next sentence is a continuation of the one containing the formula. --Trovatore 16:43, 9 August 2007 (UTC) It's more important to have formatted articles that make sense than to have markup that makes sense. My view (and I think it's the conventional one) is that you should be able to read a sentence containing math out loud and have it make sense as a sentence. That means punctuating math properly, not treating it as some out-of-bandwidth unpunctuated thing like a figure. And to punctuate it properly, in this markup system, you sometimes need to put the punctuation inside the math markup. It's a flaw in our markup system, not a flaw in our conventions for math typography, but it's a flaw that's easily worked around. —David Eppstein 16:58, 9 August 2007 (UTC) It's not a question of the markup making sense, it's a question of the format making sense. Including punctuation, which is a part of the containing sentence, in a displayed math formula, which is supposed to be only math, does not make sense. It's like moving the comma inside the close-quote. --Trovatore 17:00, 9 August 2007 (UTC) I shall try to correctly answer some of the questions raised; I cannot promise you will like the answers. Mathematics on the web gets little respect. (This is hardly different from word processors.) The W3C standard markup language is MathML; but despite the age of the standard, only the Mozilla family of browsers has native support. Still, plugin support is available for Internet Explorer. So what does Wikipedia use, and why does it not use MathML? The MediaWiki software allows projects to choose how (if at all) they will handle mathematics. While some wikis use other mathematics systems, Wikipedia relies on texvc. This is not TeX. Full TeX is a powerful, flexible, programmable system, designed as an integrated whole. What we get instead is a somewhat arbitrary subset of the basic abilities, with images (and no baselines) as output. No surprise; the entire infrastructure of MediaWiki software is an ugly undisciplined misuse of tools. Most blogs use cleaner and more sophisticated software. (Did you ever look at what the wiki software generates for lines starting with colons, semicolons, and asterisks? It's list items!) Which brings us to why we don't have MathML here. While old-style web markup was "tag soup", MathML lives in the new disciplined world of strictly valid XML, and the MediaWiki software is out of control. The browsers that handle MathML reject the rest of the page that it's on as invalid markup. This ought to be fixed for its own sake, but who knows when that will happen? In light of the underlying morass, it is ludicrous to nit-pick fine points of notation markup. Jmath666 mentioned italics inline. Every time I replace an inline • [itex] y = x^2$
with wiki
• ''y''&nbsp;= ''x''<sup>2</sup>
it disgusts me. Every time I fight to format a wiki table without the benefit of full HTML and full CSS, I want to scream. But I do it anyway, for the sake of the readers.
Let's face it, a great deal of Wikipedia wastes our time and energy, whether it's fighting vandals and bad edits instead of using a check-in system, or clawing our way through the bizarre maze of markup. And over a span of years, I see almost no change in any of this, and no impetus to do so from those who could.
If you choose to edit Wikipedia, you choose to cope with it, both the good and the bad. We want to make good, and good-looking, articles for our readers. Given our tools, that sometimes means we must resort to ugly-looking markup. I don't like it; it violently offends my sense of aesthetics.
Yet there is a magic to Wikipedia. It draws people to contribute. The process is flawed, the product is flawed, many editors are flawed; and despite all that, look at the good that has been accomplished. So I try to treat the flaws like gravity: either get off the planet or get used to it. --KSmrqT 19:07, 9 August 2007 (UTC)

From a posting to the usenet newsgroup sci.math.research on November 17th, 1994 by Paulo Ney de Souza, approved by moderator Greg Kuperberg:

I am looking for a good reference (preferably a textbook) for the Gaussian integral invariance under isotopy. That is the fact that the integral

${\ell}k(\kappa_1,\kappa_2) = \frac{1}{4\pi} \int_{\kappa_1} \int_{\kappa_2} \frac{\langle dv_1 \times dv_2, v_1 - v_2 \rangle}{\left| v_1 - v_2 \right|^3}$

is an integer and invariant unnder isotopy of the components of a link and of metric choices.

One would hope that this would be all over textbooks in Diff. Topology and some text in Knot Theory, but apparently it is NOT! The only one where I could find it stated [DFN] they wave hands to early and makes it difficult for an undergraduate to unnderstand.

If anyone knows a good referencec I would like to hear about it.

[BG] Berger, M. & Gostiaux, B., Differential geometry: manifolds, curves, and surfaces. Springer-Verlag, 1988
[DFN] Dubrovin, B. A., Fomenko, A. T., & Novikov S. P. Modern geometry--methods and applications, vol 2, Springer-Verlag, 1992

Paulo Ney de Souza
desouza[at]math.berkeley.edu

[mod note: The proof that I know that is it invariant unnder isotopy is that, if you let F(v1) be the result of integrating over v2 in κ2, then F(v1) is curl-free except that it is singular on κ2. The line integral of F(v1) is therefore the same by Stokes' theorem on κ1 and κ1′ as long as there is an annulus connecting κ1 and κ1′ that does not cross κ2. The annulus can even cross itself; the linking number between κ1 and κ2 does not change if you make κ1 cross itself. Switching κ1 and κ2, it's also constant as you vary κ2.

The proof that you get an integer is similarly asymmetric. Imagine an annulus that connects κ1 and κ1′ that does cross κ2. The surface integral on this annulus, which is the difference between line integrals on κ1 and κ1′, is the integral of a bunch of delta functions at the places where it crosses κ2. The surface integral does not depend on the surface, of course; putting it in favorable position, namely perpendicular to κ2, it is easy to see that these delta functions have integral integrals.

However, this is not a reference. Maybe the best place to look is an E&M physics book, since the theorem is just the same as Ampere's law - Greg.

Is this information somewhere on Wikipedia? How much has knot theory been applied to the physics of electromagnetic fields? Michael Hardy 17:08, 1 August 2007 (UTC)

The article Linking number (to which Linking integral currently redirects) has this formula in it, but Linking integral ought to have its own article with some kind of explanation like the above. VectorPosse 21:42, 1 August 2007 (UTC)
The linking integral section of the linking number article already contains a proof of this fact -- the linking integral is isotopy invariant because it is the degree of the Gauss map. The problem is that this proof requires familiarity with the concept of degree, which mostly limits the audience to specialists in topology or geometry.
There are two ways this situation could be improved. First, a separate article on the linking integral could contain both proofs, as well as a proof that the integer computed by the linking integral is the same as the topological linking number. Second, the article on degree of a continuous mapping should be rewritten to be accessible to a more general audience. It needs more pictures and examples, and a clear explanation of how to calculate the degree for a differentiable map between surfaces. Jim 18:27, 5 August 2007 (UTC)
Hmm, our concern with proofs should be with 'interesting' or 'notable' proofs. I think improving the degree article sounds good. But the invariance could be left with the note that it follows from the characterisation by degree, surely. Charles Matthews 18:52, 12 August 2007 (UTC)

## Will "infinite monkey theorem in popular culture" ever get restored

The discussion is continuing, and it's been moved to Wikipedia:Deletion review/Infinite monkey theorem in popular culture. So far 16 favor "relisting" the article, which could result in restoring it, and 16 endorse its deletion.

The predominant argument for endorsing deletion, as nearly as I can tell, is that since Wikipedia's math community irresponsibly neglected to offer its assistance in the deliberations originally, it should be punished by being forbidden to help later. POV: Frankly, I think that argument disregards the actual intended purpose of the process, which is to serve the interest of improving Wikipedia. Punishing the math community for not helping originally but forbidding it to help later is being made the purpose of the process instead. Michael Hardy 05:03, 10 August 2007 (UTC)

(edit conflict) I read the opposition differently. One line of argument says "Wikipedia has no place for popular culture articles". A less strident line says "The deleted article was a load of rubbish"; for some this may be the previous sentiment in disguise. Some have coldly said, "The process was correct; case closed". Many editors have said "Michael Hardy acted in ways unbecoming an admin, and should be punished by rejection of this DRV". (I have phrased it more politely than they.) Finally, the closest to your characterization are the heated remarks to the effect that no project has special standing or reason to expect to know about an AfD; if you missed it, tough luck. Some of these comments may again be motivated by animosity towards you, and some of the "process correct" remarks may also hide this view.
The level of emotion and the dearth of reasoning based on the merits is shocking. --KSmrqT 07:02, 10 August 2007 (UTC)
As I read the discussion at DRV, the main argument for endorsing the deletion is that no convincing argument has been offered for why the article should be restored. -- Jitse Niesen (talk) 06:27, 10 August 2007 (UTC)
Topics without secondary sources are frequently deleted (per WP:N), and in my opinion rightly so. As I see it, that's what happened here, but for some reason Michael ascribes other motivations to the people involved. -- Jitse Niesen (talk) 06:31, 10 August 2007 (UTC)

Yeah. Look, I voted to overturn the deletion and re-debate it at AfD, mainly because I'm not in love with the idea that AfDs should be final unless some procedural flaw is discovered, but let's keep this in perspective -- it was never really a math article in the first place. Even its parent article, infinite monkey theorem, was only tangentially a math article; the "popular culture" spinoff is definitely not, as Realpolitikers would put it, one of the vital interests of this project (in fact my main reason for wanting such articles to exist is to provide a low-visibility dumping ground for trivial content that would otherwise cruft up more important articles).

So bottom line, anyone who wants to comment at DRV, please be polite. I think we've already lost a lot of political capital over this, and in my opinion it's not even close to worth it. --Trovatore 06:38, 10 August 2007 (UTC)

I think reading through the comments in the AfD might cause some to sympathize a little more with Michael. "Another list -- delete!" "Culture again? Delete!" Michael seems to invest a lot of time on mathematics articles, if not this one in particular. Trashing a much-developed article without a second glance understandably may upset those who voluntarily bear the responsibility of writing them. It's a lot easier to delete articles than to create them, and arguably too many editors are taking advantage of that. — xDanielxTalk 08:09, 10 August 2007 (UTC)

After reading the DRV discussion, I cannot say that I am too shocked. It's not a secret that (a) many people hate maths (if only subconciously) and (b) it is a common trait to become entrenched especially when one feels the weakness of his position and/or senses having committed an error. Being polite is a good course to follow in any circumstances; however, my firm impression is that there are special interest groups who want the present decision to stand regardless of the merits. No volume of politeness is capable of overcoming that attitude. Unfortunately, it also appears that there are people, let us call them "wikivermin", who are more interested in loudly expressing their indignation at … (anything?) than in engaging in constructive editing. Arcfrk 17:45, 10 August 2007 (UTC)

They hate math, so they delete an article about things like Simpsons episodes? Come on now. I agree that they're arguing for AfDs to stand regardless of the merits provided they were performed correctly procedurally, and that's a position I don't much like, which is why I voted to overturn. But let's dial back the math-against-the-world stuff. It's making us enemies, over a silly piece of fluff. --Trovatore 18:18, 10 August 2007 (UTC)

I have a bunch of lecture notes from my college years, besides I have prepared a number of lectures myself. I based my lectures on textbooks, and I believe that the old lecture notes were also based on some books at a time. I believe that is a quite common practice among teachers. Now my question is: if I make contributions to the Wikipedia based on these notes, do I infringe on the copyright of the textbooks? That is why when I contribute something, I am struggling to rephrase the sentences to distance from the books/papers. Yes, in some trivial cases there is no copyright on the fundamental knowledge, but some cases may be tricky, right? For example, what if some of the lectures were given by a professor who is writing a new book? He probably would not like to see it on Wikipedia before the book gets even published. Or the lectures are automatically in the public domain? (Igny 03:49, 11 August 2007 (UTC))

As long as you paraphrase the content so that you are using your own words rather than someone else's words, it would not be a copyright infringement. The real issue regarding lecture notes is whether they violate WP:V or WP:NOR — is it verifiable from a peer-reviewed source? JRSpriggs 04:00, 11 August 2007 (UTC)
There were cases when I trusted my professors more than the peer-reviewed sources. We even had a seminar where we discussed math papers in very respected journals and had quite a few laughs. (Igny 04:08, 11 August 2007 (UTC))
As JRSpriggs said, verifiability and reliable sources is the real issue. You can't cite your lecture notes (well, unless they were published, I suppose) as a source for things. On the other hand, I think that wikibooks might be a good place for contributing based on your lecture notes. I don't really do much with it, so I can't provide any detailed advice, but it seems like the right place to me. --Sopoforic 04:20, 11 August 2007 (UTC)
Still, the lecture notes were probably based on published sources. I would recommend starting small, introducing changes conservatively. After a while, you will get a feel for what we require explicit references for and what we do not. In particular, if you expand stub articles to longer articles based on your lecture notes, other people can help fill in the references. — Carl (CBM · talk) 01:44, 12 August 2007 (UTC)
Actually, Igny has been making some substantial contributions already, with articles like Glivenko-Cantelli theorem. Were the lectures in English or in Russian, Igny? If they were in Russian, then I don't think there's any problem at all, because translating your notes into English will give you the opportunity to paraphrase the stuff in the notes. And we have a few people here who like articles about probability and related topics, so we can probably chip in to help provide references when those are necessary. DavidCBryant 04:24, 12 August 2007 (UTC)
Wikipedia has high visibility on the Web, so cranks find it an attractive target for their pet theories. In reaction, Jimbo Wales insists on a peculiar standard that is called verifiability. Nobody can be completely sure what it means, because everyone interprets it differently. After meeting some rather extreme and unpleasant interpretations, science and mathematics editors got together and wrote up a guideline for our articles, the scientific citation guidelines. (Better still, we have a project page of editor resources, and one specifically devoted to reference resources.) But let's assume that you can cite at least one journal article or book for any non-obvious and unfamiliar claim.
Sensibly, your question was not about "verifiability", but about "intellectual property" infringement. Already that makes you an exemplary editor, because we get some contributions (images, even complete articles) that are copied from elsewhere without permission. However, it is difficult to give guidance that is both precise and general.
I would begin with a standard of courtesy. If there was a reasonable expectation that the ideas were for private use only, it might be considerate to seek permission to promulgate those ideas. (Also, Wikipedia insists that unpublished results must not be used.) If the class notes were handed out to you, then the default assumption would be that you do not have the right to publish them on Wikipedia. (Yet you might have the right to make copies for a class you teach.) However, if you are comfortably sure that you are welcome to share the ideas, then the usual academic standards of plagiarism are a reasonable guide. Would the author look at what you wrote and see a word-for-word transcription of the handouts, save for minor changes or substitutions? If so, you need explicit permission; if not, copyright probably does not apply.
Please be aware that intellectual property law can be weird stuff, and nothing I say has any standing in a courtroom. The standard disclaimer is IANAL ("I am not a lawyer"), and if you need a legal opinion you need a lawyer. (But even that is no guarantee that another lawyer won't argue differently!)
Finally, you need to be aware that anything you contribute to Wikipedia is covered by the GNU Free Documentation License, and that it may (and probably will) be mangled by some other editor(s), and you have agreed to allow it to be redistributed for profit by others. --KSmrqT 09:55, 12 August 2007 (UTC)

I have both Russian and English notes (I got Master's in Russia and the PhD in USA). There are two issues for which I need clarification. Usually when I make contributions, I also look into books to double check the material. I found out that some of the stuff in the notes is nearly word for word taken from some particular textbooks. I cannot blame the teacher since it is common practice to base the lectures on books. But this creates a difficulty for me as a contributor to Wikipedia. In some cases I managed to find a different book with similar ideas and I mixed the content, so I don't think I infringed on anyone's copyright. (my probability contributions were a mixture of ideas from books by Dudley, Billingsley, Vapnik). Another issue is verifiability. For example I have in my notes a bunch of examples of VC classes, for which we calculated VC dimension as an excersise. Some examples were trivial, some were covered in books, but some were not so trivial and I don't have a reference ready for them. Do the latter constitute original research? (Igny 15:08, 12 August 2007 (UTC))

The question of original research has to be decided on a case by case basis. But a complex (not trivial) derivation that doesn't appear in any texts is likely to be considered original research even if it wouldn't be suitable for publication in a research journal. In practice, simple derivations and examples are usually considered OK, even if not directly sourced to references, as long as they are sufficiently clear to other editors. But these are also kept to a limited number since the encyclopedia isn't meant to be a textbook or a set of lecture notes itself.
Regarding copyright, by the time you rearrange material in an appropriate manner for an encyclopedia article and rephrase it into your own words, unless you are trying to make a copyright violation you are unlikely to do so accidentally. — Carl (CBM · talk) 18:30, 12 August 2007 (UTC)

## infinite monkey process continues....

Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture (second nomination)

The long process continues. Now it is necessary for everyone who has an opinion on whether the article should be kept, to post their views at Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture (second nomination). Click on that link and write either

• Keep for this reason and this reason and this reason...
or
• Delete for this reason and this reason and this reason...
Michael Hardy 04:44, 11 August 2007 (UTC)
A good deal of the significance of the monkey theorem is in how the idea gets applied "philosophically" to our, possibly infinite, universe – whether infinite in spatial or in temporal extent. The reception and reflection in popular culture is an important aspect of that, and therefore I'm actually not entirely unhappy that the section has returned to and been accepted in the bosom of the main article. The challenge is to raise this above the level of a mere list of trivia and give it an appropriate encyclopedic treatment, without resorting to writing an essay on the topic.  --Lambiam 05:29, 11 August 2007 (UTC)

### Update

By my quick count, 17 "keep", 25 "delete" so far, plus various gradations such as "trim" or "merge" or "trim and merge", etc. And several people have changed their minds based on the spate of recent edits to the article. Anyone with an opinion should speak up now before this closes. Michael Hardy 22:44, 15 August 2007 (UTC)

### Bottom line

Another half-dozen-or-so "keep" votes showed up, and then the AfD was closed as "no consensus". The article underwent considerable improvement, much of it even after I posted the remarks above, and someone has suggested nominating it to be a Featured Article. Michael Hardy 15:29, 17 August 2007 (UTC)

For those new to the AfD process, the practical effect of "no consensus" is to keep the article
I assume at this point Michael will receive a flood of apologies for the nasty comments about his request for further consideration. ;-)
But seriously, while I supported the review and supported keeping the article, next time such an issue comes up could we try to have less inflammatory language? And if passion does overcome prudence, as sometimes happens, can we more quickly get back to dealing with progress rather than personalities? Assuredly we see problems with the AfD process, and with various editors; equally assuredly, an extended name-calling contest won't fix those problems. --KSmrqT 00:18, 18 August 2007 (UTC)
I will second this. Oleg Alexandrov (talk) 01:46, 18 August 2007 (UTC)

And here is a related question: how to deal with the following situation. An article is deleted after seven confused people comment in the AfD discussion in language that says they want to be disrespectful to those who disagree with them, then the AfD is closed with a comment that says it was treated as a speedy deletion---clearly forbidden---then the person who wrote that comment responds to complaints by participating in the reopening of the discussion, having said such irregular reopening would be "fine", then it turns out his use of the word "fine" was dishonest---his only intention was to reopen it for a few minutes so that others could post comments saying the article is "bilge" or "garbage" but avoiding any attempt at giving reasons.

Well, I guess I should avoid inflammatory language in response to such abuse. But those dishonest people should not. So I'm told, emphatically, repeatedly. Michael Hardy 02:00, 18 August 2007 (UTC)

As far as I could tell, the original AfD discussion was closed only a few hours shy of the 5 day official period. That is rather normal practice for uncontroversial debates like this one (where the vote was almost unanimously for deletion). The right approach would have been to go to DRV rather than misusing one's administrator privileges and using improper language towards the dedicated people who close deletion requests. Oleg Alexandrov (talk) 02:25, 18 August 2007 (UTC)
As far as you can tell. But I now see from following your link that the record's been altered. I hadn't noticed that before. The person who closed it wrote "speedy close", and that's not there any more. Michael Hardy 16:45, 18 August 2007 (UTC)
I looked again at the page history, and indeed, as far as I can see, the discussin was open for almost five days indeed. Oleg Alexandrov (talk) 21:46, 18 August 2007 (UTC)
The discussion was opened and closed more than once, but the original close is still in the brief edit history. As well, the DRV opens with these lines: 'This article sat on AFD for almost five days and was then deleted on 31 August. The discussion was closed without intervening comment about 16 hours later as "speedy close, already deleted", with the deleting admin apparently indicating he/she intended to close the discussion then.' So the language is hardly concealed, unless in the sense of The Purloined Letter (hidden in plain sight).
Which is beside the point. Some of the advocates for deletion, especially Calton (talk · contribs), made repeated inflammatory posts. So did you. Neither were helpful. --KSmrqT 21:06, 18 August 2007 (UTC)
Let's assume the abuse is unfair and infuriating, and the provoking actions are indefensible. Why should the good guys act with restraint when the bad guys don't? Two reasons: (1) it is generally more effective, and (2) we are the good guys. (Similar arguments explain why most civilized nations refuse to use torture.) A rare brief display of anger may be effective, and is likely to be excused; an extended tirade becomes tiresome and undermines credibility. Remember what George Bernard Shaw said:
• I learned long ago, never to wrestle with a pig. You get dirty; and besides, the pig likes it.
Let the "pigs" rant and make fools of themselves; if we try to behave reasonably then their unreasonableness should be more apparent. Besides, many of these opponents are visibly immature; shall we stoop to their level?
I don't claim equanimity is easy to project; I don't claim it is fair to demand. I claim we should try anyway. (But I'm open to other alternatives, if anyone has them.)
When we review this episode, I assume your aim was to give the article a better AfD, and perhaps we may also assume your preference was to keep the article. Both were accomplished, but if anything your angry behavior seemed to make the process more difficult and less likely to succeed. Also, it may have tarnished the reputation of the mathematics community, making it more difficult for us to reach desired outcomes in future conflicts, some of which may be of much greater import.
I very much support your willingness to challenge poor decisions, and your right to feel angry; I just wish you could focus more energy on the desired outcome and less on the drama. --KSmrqT 11:18, 18 August 2007 (UTC)
Yes, a Jedi's strength flows from the Force. But beware of the dark side. Anger, fear, aggression; the dark side of the Force are they. Easily they flow, quick to join you in a fight. If once you start down the dark path, forever will it dominate your destiny, consume you it will (Yoda) -Weston.pace 14:06, 18 August 2007 (UTC)

## WAREL

WAREL's primary IP is vandalising Copeland–Erdős constant, up to about 9RR. Until he's blocked, could we have a few more eyes there? — Arthur Rubin | (talk) 22:11, 13 August 2007 (UTC)

Make that 14RR. Aren't there any uninvolved admins? I may have hit 5 (if you count partial reverts of nRR, where n>8), but then WAREL is up to 14 in the past 4 hours. — Arthur Rubin | (talk) 23:22, 13 August 2007 (UTC)
The IP was blocked (not be me) about a quarter of an hour ago. -- Jitse Niesen (talk) 00:17, 14 August 2007 (UTC)
While this was going on, I spotted two instances of WAREL's nonsense, and got an edit conflict when I went to revert it – someone else was quicker than I was both times. So it seems that there may have been plenty of eyes on the article. DavidCBryant 00:56, 14 August 2007 (UTC)
Why did one wait until 9 reverts? The recent history of the article is a sorry thing to look at. :) Oleg Alexandrov (talk) 02:46, 14 August 2007 (UTC)
I started sending it to 3RR at 5 reverts (4 clear), but he kept reverting. As an actively participating admin, I didn't think I could block. — Arthur Rubin | (talk) 16:41, 14 August 2007 (UTC)

## "proof"

I introduced a version of the article proof that 22 over 7 exceeds π on Citizendium. Someone wrote on the talk page: "there is a certain position that proponents of this statement ('There is proof that', 'I have proof'.. etc) always take and I don't think we should cater." Obviously that is imbecilic nonsense. Has anyone here ever seen this particular flavor of nonsense before? Does anyone have any idea what he's referring to? He was not willing to be specific. Michael Hardy 06:18, 16 August 2007 (UTC)

I read the talk page on Citizendium, and I looked at the author's user page. I think he's a student of psychology, and he's just trying to mess with you. You should drop the subject, in my opinion. All he wants is to get you excited. In other words, his "criticism" is meaningless. Oh – he probably doesn't understand calculus. DavidCBryant 10:55, 16 August 2007 (UTC)
The discussion is at [4]. Maybe he refers to people who claim to "prove" things in non-mathematical areas where the alleged proofs are often loose arguments, e.g. "Proof that God exists" (Google hits). Such terminology would violate our NPOV but mathematics is different, and apparently outside his area of expertise. PrimeHunter 13:01, 16 August 2007 (UTC)

### Original research on CZ

I found it interesting that several people in the discussion on CZ linked above were concerned about original research. Could someone more familiar with CZ provide a link to CZ's original research policy? The main benefit of verified credentials, I thought, was to allow experts to rely on their credentials in ways that would be considered original research here on WP. Perhaps I was mistaken. — Carl (CBM · talk) 19:20, 19 August 2007 (UTC)

## Request for comment at Partially ordered set

There is a discussion at Talk:Partially ordered set about the merits of using logical quantifiers ($\forall$, etc.), versus plain words, and on whether the $\scriptstyle\preceq$ notation is preferrable to ≤ for the partial order.

Things are not made simpler by an editor who has not made any edits to the talk page but keeps on reverting in the article with odd edit summaries and no explanation. Anyway, comments welcome. Oleg Alexandrov (talk) 06:47, 19 August 2007 (UTC)

This is not a direct answer to your question, but I think if someone says "Every even number greater than 2 is the sum of two primes", the plain words are an instance of a universal quantifier. The terse quantifier symbols like $\scriptstyle\forall\,$ are not the only things that should be called "logical quantifiers". Michael Hardy 20:13, 19 August 2007 (UTC)

## Code2000 AfD (yes, again)

We have a new AfD for Code2000, again by Ptcamn (talk · contribs), who claims that the DRV "failed to actually demonstrate that the subject was in fact notable." Could some admin speedily close this nonsense AfD and explain to the nominator that the DRV (barely a month ago) resulted in an overwhelming consensus that Code2000 is notable? And keep an eye on this loose cannon. --KSmrqT 10:55, 19 August 2007 (UTC)

Outcome was speedy keep, closed by Carl. (Thanks.) --KSmrqT 23:43, 19 August 2007 (UTC)

## Non-math articles in the list of mathematics articles

Sometimes the articles in the list of mathematics articles are not quite mathematical. This is partially because since when Wikipedia was starting it was considered good to add to those lists even articles that are more physics and computer science. Another source of not quite math articles is the bot updating the lists nowadays, since sometimes non-math articles are categorized in math categories (although I keep a close eye on those).

Yesterday I removed over 200 articles which are not quite math from the lists. The list of removed articles is available for review at Wikipedia:WikiProject Mathematics/Current activity (see the "Removed articles" section there for August 18 -- thanks to Jitse's bot for maintaining that very useful page), in case anybody wants to take a look (I can put back any of them at any time). Oleg Alexandrov (talk) 21:35, 19 August 2007 (UTC)

Helix jumped out at me as an article that should be considered as being not "not quite math". -- Dominus 00:02, 20 August 2007 (UTC)
The bot removed a bunch of helix articles, like 3 10 helix. It removed Helix too. But now that I think about it, perhaps helix itself can be added back as math, it has a formula after all. :) Oleg Alexandrov (talk) 01:07, 20 August 2007 (UTC)

## Mersenne number definition

Reliable sources use two different definitions, discussed at Talk:Mersenne prime#New Mersenne number definition. I have reverted many (unrelated) good faith edits by User:PhiEaglesfan712 on prime number articles and would like input before doing it again. PrimeHunter 23:07, 19 August 2007 (UTC)

I have restored the old definition and made a number of other changes, please, post your comments at the talk page of the article. Arcfrk 02:33, 20 August 2007 (UTC)

## Update on the PlanetMath Exchange project

As a reminder (or news, it depends for whom), our math wikiproject has been involved for two and a half years in copying articles from PlanetMath to Wikipedia (PlanetMath uses GFDL, so copying material as allowed, provided a note specifying the source of the material is added). This subproject is at Wikipedia:WikiProject Mathematics/PlanetMath Exchange.

We have a tool that greatly helps in copying/merging new material (it generates wikicode and suggests categories). In the last year and a half or so, PlanetMath has gone from 4802 articles to 6940 articles, so the harvest is plentiful. :)

The articles to be copied/reviewed, are arranged by subject matter, which also helps in copying.

You can see more details (and join the project) at WP:PMEX. Oleg Alexandrov (talk) 02:36, 20 August 2007 (UTC)

## AfD

Square root of 5 is up for deletion at Wikipedia:Articles for deletion/Square root of 5. Maybe you should have a deletion sorting page dedicated to Mathematics or do you expect to find them in the Science deletion sorting page? There are tools now that make it easy to add deletion discussions to the deletion sorting pages and I would certainly add any mathematics article as I scan through AfD. --Bduke 23:06, 11 August 2007 (UTC)

They usually show up automatically in Wikipedia:WikiProject Mathematics/Current activity, though a note here as well doesn't come amiss. —David Eppstein 23:19, 11 August 2007 (UTC)
That is a great tool. It could have uses elsewhere. I see it is written by Jitse, who I know from WP meetups here. I'll talk to him about it. --Bduke 00:40, 12 August 2007 (UTC)
This article is in List of mathematics articles and so it should be picked up on the automatic update this evening. The problem with another recent AFD was that the article was so poorly categorized that it wasn't in the list of mathematics articles. — Carl (CBM · talk) 23:21, 11 August 2007 (UTC)
Right; as I understand it the reason infinite monkey theorem in popular culture didn't show up at "Current activity" is that it wasn't in any math categories, so the bot didn't find it. (And really, why should it have been in any math categories? It's not about mathematics except in a very tangential way.) --Trovatore 23:24, 11 August 2007 (UTC)
For the record, this AfD was closed as a speedy keep. --KSmrqT 04:05, 21 August 2007 (UTC)

### Examples

In its present incarnation, square root of 5 contains such items as these identities of Ramanujan (which I put there):

${1 \over {1 + {e^{-2\pi\sqrt{5}} \over {1 + {e^{-4\pi\sqrt{5}} \over {1 + \cdots\qquad\qquad}}}}}} = \left( {\sqrt{5} \over 1 + \left[5^{3/4}(\varphi - 1)^{5/2} - 1\right]^{1/5}} - \varphi \right)e^{2\pi/\sqrt{5}},$

$4\int_0^\infty\frac{xe^{-x\sqrt{5}}}{\cosh x}\,dx ={1 \over 1 + {1^2 \over {1 + {1^2 \over {1 + {2^2 \over 1 + {2^2 \over {1 + {3^2 \over {1 + {3^2 \over{1 + \cdots \quad}}}}}}}}}}}},$

...and also the fact that √5 is the "best possible" constant in Hurwitz's theorem of Diophantine approximations. (In other words, it doesn't rely on any policy of having an article about every irrational number; there are some assertions of notability.) Michael Hardy 01:03, 13 August 2007 (UTC)

## Fuchsian model and Kleinian model

Hello, both pages Fuchsian model and Kleinian model contain a considerable amount of inexact information. Is anyone interested in discussing this? Katzmik 08:14, 20 August 2007 (UTC)

From a review of the two pages' history, it's clear that Linas started both articles. So it might make sense to ask him directly, at his talk page. He's a nice guy – I'm sure he'd be glad to hear from you. On the other hand, you clearly know a lot about this sort of stuff, and I don't think Linas was overly impressed by his own efforts on these particular articles – look at the edit summary on this edit to see what I mean.  ;^> I'm pretty sure you've got the green light to improve either article, or both, in other words. DavidCBryant 11:21, 20 August 2007 (UTC)
Both pages can be deleted, I think. Whatever is correct in them, can be found in other pages, and whatever is not, will be automatically taken care of. Katzmik 13:37, 20 August 2007 (UTC)
If the relevant content should be merged into other pages, you don't need to delete the articles. Just merge the content and make the two pages into redirects to the new location(s). There is a fine line between making stubs versus making redirects to existing articles, which I have often found to be a difficult decision. The benefit of stubs, no matter how short, is that they encourage other editors (like you) to improve them, but there is no so much temptation to replace a redirect with an article. In other words, bad stubs are part of the "wiki process" for content writing. Of course factually incorrect or misleading stubs should always be fixed immediately when discovered. — Carl (CBM · talk) 14:41, 20 August 2007 (UTC)
P.S. After looking briefly at the two articles, I don't think they should be merged, just improved. — Carl (CBM · talk) 14:43, 20 August 2007 (UTC)
Certainly they should not be merged into anything until the errors are corrected. Katzmik 14:49, 20 August 2007 (UTC)
Well, the merging process could include correcting/leaving out the errors. The key point is that simply deleting the pages is not a good idea if they are topics that could be expected to have an article or even be searched for. At the very least, replace them with redirects to articles where the material is covered, alternatively, replace any errors with something better. JPD (talk) 15:47, 20 August 2007 (UTC)

Just picking up on the point above from Carl about "there is not so much temptation to replace a redirect with an article" - one way to address this is to categorise the redirect in a suitably named "redirects with possibilities" category. This can also apply to sections within an article that look like they might be about to burst forth and flower into their own article. There is a much under-used Category:Redirects with possibilities category, but for a better example of how this works, have a look at Category:Middle-earth redirects with possibilities. It should be simple to create something like this for the Mathematics WikiProject. Carcharoth 01:42, 21 August 2007 (UTC)

## Fathers and mothers of branches of mathematics

Can someone who knows about math history add to the "reason" sections of this table: fathers of mathematics? Thanks: --Sadi Carnot 18:52, 19 August 2007 (UTC)

Sorry, I did the opposite: subtracted two claims of priority for Indians over arithmetic (!) and calculus, sourced only by web sites. Many other entries in that table are as badly sourced. Anybody can be called the father of something on a web site; to make a real claim for a title on that list, I think you need multiple textbooks or other scholarly works. —David Eppstein 19:01, 19 August 2007 (UTC)

What a deeply flawed idea for an article. The mathematics part is pathetic in its wordings, inclusions and omissions, but ultimately, not salvageable, therefore, in my opinion, should not even be "fixed". OR by synthesis, unencyclopaedic, et cetera. Apparently, this list was rescued from multiple deletions by a very small group of enthusiastic supporters. Arcfrk 20:18, 19 August 2007 (UTC)

I have removed the whole math section from that article, and I will leave my reasoning on that talk page. Further discussion belongs there, instead of here. — Carl (CBM · talk) 22:48, 19 August 2007 (UTC)
This page would benefit from the attention of a few more people - it's very hard to determine consensus with only a few editors working on the page. — Carl (CBM · talk) 18:05, 20 August 2007 (UTC)
It's getting more attention than timeline of mathematics (see below)... Carcharoth 09:43, 21 August 2007 (UTC)

### Timeline of mathematics

• What is relevant here is a need for better sourcing for things like timeline of mathematics. At the deletion review for the "founder/father/mother" article, I suggested that this sort of thing is better dealt with in timelines. Could the members of this project help source the entries at the timeline? A note at the bottom says "This article is based on a timeline developed by Niel Brandt (1994) who has given permission for its use in Wikipedia." - but the timeline has been edited since then, so it is unclear which bits are from Brandt's timeline, and which have been added later. I am sure Brandt wouldn't want his work damaged by others trying to extend it (which is something I don't think people explain enough when asking for permission to use text written by others). Also, the talk page has a comment asking for a compact timeline. I agree that a separate, shorter version, or splitting into eras, is needed. Does anyone here want to work on that? Carcharoth 12:05, 20 August 2007 (UTC)

## Tracking the recent changes to math articles

First a note. A recent feature of watchlists and recent changes (which is tweakable via preferences) makes it possible to collapse several consecutive changes to an article into a single diff. I find that a very useful time saver when checking the watchlist.

Second, as most people know, one can view the recent changes to the math articles by visiting the list of mathematics articles. There one gets separate lists of changes for articles starting with 0-9, A-C, D-F, ..., because it is not possible to put all math articles into one single page (as they are too many).

I wrote a small tool that combines all the pages of changes mentioned above into a single list (and it uses the feature mentioned above of having just one diff for all the recent changes to any given article). The tool is available here. In effect, it works as if having all the math articles on one's watchlist. I hope this tool could be useful in monitoring the math articles. Oleg Alexandrov (talk) 01:58, 21 August 2007 (UTC)

This is sweet! Can your tool do the same thing for specific categories or groups of categories? I may not want to view all math articles, but I might want to keep tabs on topology articles, for example. VectorPosse 10:15, 21 August 2007 (UTC)
The tool does not keep track of categories, but of lists. If you have a list, one can keep track of it as shown in the list of mathematics articles (this tool only merges the recent changes from those lists).
Of course keeping track of all the math articles is too much work for any person. My hope is that it will help against vandalism. Oleg Alexandrov (talk) 14:56, 21 August 2007 (UTC)

## FYI: Competence self-assessment

I just came across an old article that might be of interest in the context of Wikipedia:

Incompetent People Really Have No Clue, Studies Find: They're blind to own failings, others' skills

This may help explain the phenomenon of editors who don't know what they don't know, who boldly blunder where angels fear to tread. Of course, the article offers little help for us in knowing what to do about it. Anyway, enjoy. --KSmrqT 09:05, 21 August 2007 (UTC)

It seems as if you consider yourself competent. Right? Bo Jacoby 09:15, 21 August 2007 (UTC).
As a matter of fact, KSmrq could easily put together an actual consensus of editors who agree he is competent. VectorPosse 10:21, 21 August 2007 (UTC)

## Inspiration or lunacy: help decide

I was talking with an editor about how to promote the concept that an article should include at least one citation, when an idea popped into my head (perhaps others have thought of it as well):

That is, when an article is created, include a {{citation}} template to be filled out. (This template is the best choice, because it works uniformly for books and journal articles and every other source.) Unlike with image licenses, we cannot force a multiple choice among acceptable alternatives, so we may get junk citations. Nor does it directly improve the large number of existing articles. Still, it might have more impact than all those tags that editors ignore.

Before I propose the idea where someone might implement it, I thought I should ask for feedback. Especially, could this turn into a disaster? Are we handing a loaded weapon to a child? --KSmrqT 23:51, 17 August 2007 (UTC)

What we could do it watch the "new articles" on the daily activity list for the math project, and add references to the ones that don't have them. In general the "wiki process" for writing an article has been assumed to often begin with an unsourced stub that grows into a mature article; requiring too much too soon breaks that assumption. — Carl (CBM · talk) 19:24, 19 August 2007 (UTC)
I also think that putting a emtpy template may look intimidating to somebody who never used one. However this tool could stimulate including references. Last time I announced this, I didn't get that much response, though. Can you, Carl, provide the list of reference templates in Math articles, please? (You mentioned that everybody could do it, but I'm myself totally illiterate about the inner technical mechanisms :-( ). Thanks. Actually, if it is possible, could you also retrieve the categories the references belong to, e.g if you parse algebraic geometry and find the references on Hartshorne's book etc., retrieve that this book belongs to the categories Category:accuracy dispute (which would be irrelevant here) and Category:Algebraic geometry. This would later help to suggest references to editors when writing articles. (Compare to Amazon, where you are always helped/bothered by getting some related books to existing ones). Another possibility is the information used in the rating process (in this case, the field "Geometry"). The latter and sometimes also the former are pretty coarse, though. We could refine this by assigning to articles more precise (and unique) content-id's (possibly multiple ones) like the classification numbers (e.g. 11B65) the AMS is using. PlanetMath does this, for example. I figure, if someone could write a little template, we can get this done pretty easily. Jakob.scholbach 01:23, 22 August 2007 (UTC)
Sure, I can do whatever. Please leave a detailed request of exactly what you want on my talk page. — Carl (CBM · talk) 02:03, 22 August 2007 (UTC)
As Ksmrq pointed out above, the danger in pressing people to provide references is that they may supply irrelevant, or in any case, suboptimal, citations. This would clearly be worse than having none at all! "Amazon model", based on automated suggestions, would exacerbate this problem. Arcfrk 03:08, 22 August 2007 (UTC)
OK. I certainly don't want to press anybody to provide references. I hope that nobody would add random references he/she does not have read or at least looked at before. But in any case, having the information is better than not having it. (Likewise I don't buy every [actually almost no] book Amazon proposes me). This is also somewhat parallel to KSmrq's "Still, it might have more impact than all those tags that editors ignore.": why do people ignore the tags? (I did so, too): when writing about something off your head or something you know pretty well, adding a ref would take you only a second, namely thinking of your favourite references on this/that topic. Instead of this second, it takes at least a minute, first to get a somewhat complete information somehow, then to turn it into a reasonable format etc. Decreasing this tedious and I believe, partly pretty stupid work will help achieving better referencing, that is in terms of quality and quantity. So, I'm just striving for a reference collection as formatted as possible. Jakob.scholbach 06:12, 22 August 2007 (UTC)
Absolutely! For me, typing in and formatting a reference takes considerably more than one minute and can be quite distracting. So anything that simplifies this tedious task (and provides more uniform structure at the same time!) is greatly appreciated. Arcfrk 23:46, 23 August 2007 (UTC)

OK, thanks everyone for the comments. I don't think I'll be proposing a citation form for new articles any time soon.

As for mathematics, if we can get Jakob.scholbach's tool filled with existing citations, incorporate validation stamps, and then lead by example, I believe a realistic goal is at least one citation per mathematics article within six months.

I have said many times: citations for me are not about Wikipedia's bizarre fantasy that they make an article reliable; citations are a service to the reader. For example, suppose I told you about a fabulous meal at a restaurant, but did not tell you the name or location of that restaurant; or suppose I told you of a discovery that could add twenty good years to your life, but did not tell you where to find the details of what to do. That's my view of articles with not one citation. And let's face it, since we will never satisfy the begging to make articles into tutorials, a citation gives us an easy out.

Besides, filling in citations can be pleasurable. I get special enjoyment from reading the original words of master mathematicians, and many of these historic works are increasingly available online, without cost. In the past, only a really good university library could provide access to such materials. So, enjoy. --KSmrqT 12:08, 24 August 2007 (UTC)

## List of triangle topics

I just added Ono's inequality, Pedoe's inequality, and Hadwiger-Finsler inequality to the list of inequalities. And it occurs to me: list of triangle topics is a red link, and I no of no such list under any other title. We have a list of circle topics. The collection of Wikipedia articles about triangles is huge and many of them are quite impressive (maybe not always the article itself, but often the result that it reports). When I'm less busy, I'll create that. UNLESS someone beats me to it. So would some eager beaver get on it? Michael Hardy 04:15, 18 August 2007 (UTC)

Why do we need a list when we have Category:Triangles? —David Eppstein 14:27, 19 August 2007 (UTC)

Oh god...not this again. Categories are far far far inferior to lists. The last couple of dozen times someone's said "why do we need list of X when we already have Category:X?" I've assumed it was some kind of fluke that someone thought that, but now I'm beginning to suspect this horrible disease may not be so rare. I'm going to gather up the evidence in one convenient place so that I can just copy-and-paste and do a few small adaptations in answer to each such occasion. This may take a few days, then I will rescue those benighted infidels..... Michael Hardy 20:08, 19 August 2007 (UTC)

That's a completely unhelpful and unneeded reply Michael. Anyways, lists can help explain the connection between things and group things with a little more structure. Take a look at List of North American birds for a good example. -Weston.pace 12:41, 20 August 2007 (UTC)
Well, I was rushed and didn't have time to make the whole case and I didn't want any several-day delay in my reply to be construed as recognizing the wisdom of David Eppstein's views, so this terse boilerplate notice was indeed helpful. To be continued.... Michael Hardy 21:04, 20 August 2007 (UTC)
Fwiw, I've started to compile a list (no structure yet) at User:DavidCBryant/List of triangle topics. Anyone who wants to work on it is welcome to do so.
I'm approaching this particular list with some trepidation, because triangles pop up everywhere. In geometry itself you've got divisions among Euclidean, hyperbolic, and spherical triangles. In solid geometry you get to see equilateral triangles in combination (tetrahedron, octahedron, icosahedron, and God only knows how many of those stellated monstrosities). In number theory you get ideas as diverse as triangular numbers and the Eisenstein integers. Triangles find applications in analysis as well – should results like Hurwitz's automorphisms theorem and the Cauchy-Goursat theorem be included in such a list? (These don't mention triangles explicitly, but the notion of a triangle, or a network of triangles, is essential to the proofs.)
All these examples come from mathematics. Should we also aim to include stuff from other fields (such as the musical instrument called a triangle, or the role of triangles in civil engineering, or various mystical concepts based on triangles, etc?)
I'd be glad to hear what other people think of the way such a list should be structured, and what the criteria for inclusion ought to be. Thanks! (A benighted infidel ;^>) DavidCBryant 15:41, 20 August 2007 (UTC)
One small suggestion with regard to Hurwitz's automorphisms theorem that you mentioned above: a closely related page is the (2,3,7) triangle group where triangles are more explicit. Katzmik 15:48, 20 August 2007 (UTC)

Judging by the current early state of his list, David Bryant does not seem so benighted at all. Some (definitely not all) of the advantages of lists over categories can already be seen in his list even in its current preliminary state. The fact that they pop up everywhere is a good reason for such a list to exist. Soon we should add the list to the list of mathematics lists. Michael Hardy 21:15, 20 August 2007 (UTC)

...OK, now it's a red link at list of mathematics lists. Michael Hardy 21:18, 20 August 2007 (UTC)

Yet another one of the many many many ways in which lists are better than categories manifested itself when user:tosha decided to create Category:Triangle Geometry instead of Category:Triangle geometry. You can't move a category just by hitting a button, the way you can with a list. Now that mess will need to get cleaned up. Michael Hardy 23:14, 23 August 2007 (UTC)

## allowing unconverted metric units in scientific articles

I'm seeking consensus at MOSNUM talk for a change in the wording to allow contributors, by consensus only, to use unconverted metrics in scientific articles. Your opinions are invited. Tony 15:19, 25 August 2007 (UTC)

## Horrible font mismatches are no longer a necessary evil

We have \text now! See this edit summary. Michael Hardy 13:47, 26 August 2007 (UTC)

Eh? We've had that for quite some time; I even mentioned it in examples in this very forum over a year ago. Nor does it cure all our font mismatch ills.
This may be an opportune time to mention the latest update from the STIX Fonts project:
The packing of the OpenType version of the STIX Fonts is almost complete. We are resolving a few dozen final corrections and hope to be ready to release the fonts within the next two weeks.
This site was last updated on August 20, 2007. The next update will occur during the week of 27 August.
While this probably does mean the fonts will be available Real Soon Now, the deadline slippage on this project reminds me of the celebrated (?) rule of thumb for interpreting time estimates: double the number and convert to the next higher unit of time. --KSmrqT 14:25, 26 August 2007 (UTC)

Somehow I missed this a year ago. I must be getting quite elderly in Wikipedia terms, since I've been here for almost five years now, so to me a year ago isn't so long. Michael Hardy 01:39, 27 August 2007 (UTC)

## Request for comment on small set / large set

I would like to request comment on the matter of the articles small set and large set. Another editor determined that "large set" and "small set" cannot share a disambiguation (I don't see why not), and split them up into two articles (I don't see why). I thought this was terribly redundant (just look at the two pages) and completely unnecessary. Maybe I'm wrong, but I propose that one ought merge them back together, so that people looking for large/small sets will find what they're looking for regardless. The two can (and have) coexisted in a disambig together for quite some time, and there's no reason they can't continue to do so. Do others have input on this? It would be greatly appreciated Thanks in advance. --Cheeser1 06:04, 24 August 2007 (UTC)

The problem is not as much with sharing a disambiguation as it is with listing Large set (Ramsey theory) as a possible meaning of small set. I suggest merging the two pages into Small and large sets with content along the lines of:
In mathematics, the term small set is used to refer to any set that is small in some sense. A large set is one that is not small. The terms have specialized meanings in the following contexts:
-- Meni Rosenfeld (talk) 06:45, 24 August 2007 (UTC)
See, but if large set redirects to small set, then large set (Ramsey theory) is not a specialized meaning of "small set," it's a specialized meaning of "large set," because the article (at that point) would cover both. That might require new wording, but I don't know if the title has to be changed to accommodate that. We have plenty of articles with multiple titles, and the content is allowed to reflect that multiplicity of titles. --Cheeser1 16:44, 24 August 2007 (UTC)
I had put together a page for this purpose User:CRGreathouse/Large and small sets, although as I recall Trove didn't like it much. CRGreathouse (t | c) 17:26, 24 August 2007 (UTC)
Seems OK to me. Such a thing could become over-extended, but that's a bridge to cross when we come to it. Charles Matthews 19:42, 24 August 2007 (UTC)
I don't see any problem with having separate disambiguation pages for "small set" and "large set" disambiguation pages, like redirects, are cheap. Paul August 19:49, 24 August 2007 (UTC)
That's the way I see it. I don't want to see an OR-ish exposition of all the various ways "small set" or "large set" might be used as nonce terms, under these titles. Our articles on ideals and filters and measures are the proper place for most of that content, and the disambig pages can have see-alsos to those articles. --Trovatore 03:31, 25 August 2007 (UTC)
But that requires double-duty for maintenance/upkeep of varying definitions of small/large. The "exposition" and see-alsos are not the matter in question, in any way (although "OR-ish" is a bit of a stretch). Small and large set often are the same thing (or rather, they describe the same notion). Combining the pages, as was the case previously, saves people trouble of looking for one or the other and getting different results. The exposition is unnecessary in the disambiguation, yes, and it could easily be removed. But that doesn't change the fact that the two topics can easily and sensibly be in the same disambig together. (This excludes the proposal by CRGreatehouse that we make it into a page with content, where exposition becomes necessary, of course.) --Cheeser1 08:09, 25 August 2007 (UTC)
The OR part is the idea of abstracting a commonality from the disparate ways in which the terms "small set" and "large set" are used. This we should not do. And that includes abstracting the notion that a small set is a set that isn't large, or is the complement of a large set, or anything of the sort. Your own objection to the term "small set" in Ramsey theory reinforces this point (quite possibly, that line item should be removed from the small set disambig page).
The upkeep issue is not terribly convincing -- all we need to do is make sure that the articles remain disambiguation pages in the strict sense, with zero exposition. That's fairly minimal upkeep, well worth it to avoid any suggestion that "small set" or "large set" has some general mathematical meaning apart from their particular meanings. The closest thing to such a commonality is the concepts described at ideal (set theory) and filter (set theory), but these are not standardly described using the terms "small" and "large" in any technical sense, so they are properly dealt with by listing them in the "see also" section without further comment. --Trovatore 19:26, 25 August 2007 (UTC)
All of that is about the exposition you're concerned about, not about whether or not the articles should be split up. Like I sad a week ago on the article's talk page, if you had an issue with the exposition, you should have removed the exposition, not split up the articles. The fact is, it's perfectly sensible to combine the two and link to the appropriate uses of the term (large or small). When the terms have specific meanings, they often mean opposite things. This is mentioned in this devilish exposition, when it appears in the content of each article. Nothing prevents us from disambiguating to them from one page, instead of two, by combining them as they had been combined up until a week ago. --Cheeser1 19:43, 25 August 2007 (UTC)
There is no sigificant cost to having the two articles disambig pages, and it's cleaner that way. Should have been done that way from the start; all I did was correct the original mistake. As I say, assuming you're right about the Ramsey theory issue, the small set (Ramsey theory) entry should probably be removed from small set. --Trovatore 20:17, 25 August 2007 (UTC)
There's also no reason to have two articles either (your points about exposition aside - exposition is an unrelated concern to be resolved at another time). As such, there was no reason to change it, and it seems that on Wikipedia, if there is no reason to go one way or the other, you leave it as it was first done (e.g. BC vs BCE). You keep referring to it as a "mistake" or "problem" that you need to "fix" but you've never presented an honest-to-goodness policy or reason why we can't have two things in one disambig. "Small set or large set may refer to: ...(list)" In fact, I'm relatively sure we can. I'm not convinced that having two pages wouldn't require extra upkeep and wouldn't be more difficult to navigate - even if we assume you're right and they wouldn't make things worse, the only reason you've given in their favor is the one about exposition - a point that isn't related. --Cheeser1 20:45, 25 August 2007 (UTC)
And the exposition would be simpler with one article; unless someone can give an example of a "small set" which is not a "not-large set". Septentrionalis PMAnderson 21:32, 25 August 2007 (UTC)
There is no such example, as far as we know. There is a "large set" here where "small set" is not used, but the only problem that could arise would be if there were a "small set" of this type (Ramsey theory) that is different in its definition from "not a large set." This is highly unlikely (I'd wager impossible), since I can't imagine terminology being accepted where "large set" and "small set" in a particular context are both defined but completely unrelated. --Cheeser1 22:16, 25 August 2007 (UTC)

Let's clarify our terms here. Disambig pages are not "articles". They are navigational tools, intended to get the reader to the article he/she is looking for. We should not have any article whatsoever about "small set" in general or "large set" in general, because there is no such mathematical concept. To the extent there's a mathematical concept to be extracted, it is that of an ideal or a filter (though I don't know whether "large sets" in the Ramsey-theory sense form a filter; I'd be interested in seeing that clarified, but just as a point of curiosity irrelevant to the discussion at hand).

Since the dab pages are purely tools to map search terms to real articles, and not real articles themselves, it is appropriate to have separate ones for separate search terms, even if they wind up mapping to the same collection of articles. --Trovatore 07:28, 26 August 2007 (UTC)

First of all, drop the filter stuff. It's irrelevant, and is obfuscating the fact that you have yet to address the question at hand. You continue to make points about how this is a disambig. Therefore it can't be an "article" or have too much "content." That's fine. That is not what we are discussing. It's perfectly reasonable to have two disambigs. It's also perfectly reasonable to have one. The two terms are often indistinguishable, and as a "navigational tool" either configuration works just as well as the other. You felt the need to throw your weight around by asserting that you're "fixing" the "problem" but you aren't. There is no guideline, policy, or reason (that you've given or that I've ever seen anyway) that tells us we can't have left it the way it was. If changes were unnecessary, as I believe they were, you should have left things as they were. So, tell me we can't have exposition or an "article" or how filters are really great, but I still feel like there's a perfectly reasonable solution: until there's a good reason to split the articles (a problem that doesn't just require cutting down on the exposition or whatever), don't split them. --Cheeser1 04:06, 27 August 2007 (UTC)
I find the analogy with filters, and the question of how sharp it is, to be very relevant here. Among regulars of this page, discussing the actual mathematical content while deciding how to arrange our description of it is common practice. There's no reason I can see that the discussion about filters obfuscates anything. If anything, it helps to clarify what's going on. — Carl (CBM · talk) 14:07, 28 August 2007 (UTC)
Cheeser, you started the whole thing by asserting -- quite incorrectly -- that redirects should be replaced by direct links. You were just wrong about that, but you wouldn't give up on uglifying the small set dab page by putting in a "large set" line item. It's reasonable to allow small variations on the basic search term as line items in a dab page, but antonyms, IMHO, are going too far.
I cut the Gordian knot by making the second dab page, which is an inherently better solution anyway, since it lets you (you personally, if you like, or you generically, otherwise) take out the "small set (Ramsey theory)" link, which we have your word is an unused term, and leave the "large set (Ramsey theory)" link in a dab page where it would be naturally found. --Trovatore 05:49, 27 August 2007 (UTC)
First of all, accusing me of anything, based on I "started the whole thing," is completely irrelevant, inflammatory, and a ridiculous side-point. You're twisting my words, taking things out of context, and trying to ignore my points, which are about the current discussion, not the one from three weeks ago. I inserted "large set" because there is no such "small" analog in use. That is the reason it was there. That is all that's relevant to this discussion, and I'll thank you not to dredge up old nonsense to try to obfuscate this issue.
I'm glad you think you've solved everything by taking bold decisive action. However, the only reason you've come up with is that it's "ugly" and that you seem to think that antonyms are not allowed on disambiguations. Now, I think it makes more sense there, and that's how it was, and until you find me a policy for this "it's ugly to have an antonym" opinion of yours, you've got neither policy nor consensus on your side. And yet you think your edits should stand because, what, you've decided you're the fixer and I'm the bad guy? Sorry, saying that you're "fixing" the "ugly" "problems" I add to pages doesn't make it so. --Cheeser1 06:41, 27 August 2007 (UTC)

Because there is no compelling policy-reason either way, and because there is consensus both for and against a merge, I suggest that we follow Wikipedia's general policy whenever two things are both perfectly good - keep it the way it was. In light of this, I suggest we merge them, like they used to be (although perhaps with slightly different content), since that's how they were in the first place. Does anyone object to following this widespread precedent for disputes without consensus? --Cheeser1 06:47, 27 August 2007 (UTC)

Cheeser, "the way it was" was with the link to small set (Ramsey theory) in small set, not to large set (Ramsey theory). There's no policy either way on that either (though there definitely is a guideline against replacing redirects with direct links). If we go back to the status quo ante, it should be back to that version. But this way makes more sense altogether. --Trovatore 16:30, 27 August 2007 (UTC)
"Small set" is not used in that sense. There is a policy on that, it's called WP:V. There's no such thing as "small set (Ramsey theory)" in this context. If you want to violate WP:V to prove some petty point about how you want to split it and I don't, be my guest. Otherwise, we will continue to discuss the issue at hand - whether or not to split the articles. There is no policy or consensus either way. I would like to proceed in a manner consistent with widespread precedent and collapse them back into two articles. If you'd like to stick to your guns, that's fine, but unless you have a policy you'd like to cite, no version is better than the other and you changing things just because you feel like it isn't a good way to work in a community of editors. --Cheeser1 18:55, 27 August 2007 (UTC)
So start a new section and make a straw poll. I'd like to see just what the consensus is -- or if, more likely, few really care. CRGreathouse (t | c) 20:35, 27 August 2007 (UTC)
That's what I just tried to do when Trovatore jumped back in to pick up the discussion (notice my: "does anyone object ...?"). It's already pretty clear, as far as I can tell, that consensus (among those who care to comment) is mixed. Unless an overwhelming consensus pipes up one way or the other, or unless some policy is dug up that clears any of this up, I'm inclined to believe that the do-it-the-way-it-was-done method is the way to go. I'll try again, with a new heading. --Cheeser1 07:13, 28 August 2007 (UTC)

The status quo ante had all the line items in small set as some small set (foo), which obviously makes sense for someone looking for the search term "small set". Cheeser1 wants to consider these issues separately, but they are in fact linked, and if it's to go back "the way it's always been" then the link should go back to small set (Ramsey theory). If as Cheeser1 claims, that's an unused term, then fine, let people looking for the search term "large set" see a disambig page where the articles are called "large set", and contrariwise. --Trovatore 07:26, 28 August 2007 (UTC)

The status quo had large set redirecting to small set, and thus this page served as disambiguation for both terms. The fact that someone inserted the unsourced and irrelevant commentary/exposition and formatting (use of "small set (subject)" throughout) based on the false assumption that all "large sets" are defined as "not small sets" is irrelevant. This is plainly obvious. You yourself argued that such exposition needed to be removed. --Cheeser1 08:36, 28 August 2007 (UTC)

### "Straw poll"

In order to assess more succinctly if there is a consensus in this matter, please comment below with "split" "merge" or "no opinion" and, if you'd like, a sentence explaining your position (what policy, guideline, or personal opinion might be motivating your "vote"). Please keep discussion above, where it belongs. Thanks. --Cheeser1 07:13, 28 August 2007 (UTC)

• Merge - no policy, guideline, or (apparent) consensus either way, so keep them together like they always have been. --Cheeser1 07:13, 28 August 2007 (UTC)
• Leave as is. The status quo ante had all the line items in small set as some small set (foo), which obviously makes sense for someone looking for the search term "small set". Cheeser1 wants to consider these issues separately, but they are in fact linked, and if it's to go back "the way it's always been" then the link should go back to small set (Ramsey theory). If as Cheeser1 claims, that's an unused term, then fine, let people looking for the search term "large set" see a disambig page where the articles are called "large set", and contrariwise. --Trovatore 07:26, 28 August 2007 (UTC)
• Further philosophical comment. Disambig pages are kind of like redirects to multiple pages, with one big exception: Whereas redirects are semantical, based on the expected meaning, dab pages are inherently syntactical -- you're looking for a particular search term. The least surprise principle suggests that people looking for the search term "large" should not be dumped into a disambig page titled "small". Then when they actually follow the links, that's different; it's normal to be redirected to an article and have to find the search term there; that's semantical. --Trovatore 07:26, 28 August 2007 (UTC)
• No opinion between merging and keeping split. I had proposed exposition (see User:CRGreathouse/Large and small sets for an example) but Trovatore doesn't want exposition here, and I'm unwilling to oppose his wishes without some serious consensus. CRGreathouse (t | c) 13:36, 28 August 2007 (UTC)

### Why are we having a poll here?

Why are we having a poll here? There aren't nearly enough people involved to expect to get a resolution from it. — Carl (CBM · talk) 14:07, 28 August 2007 (UTC)

In order to conclude more concretely the fact that there is no consensus on this matter. I suppose a poll isn't necessary, but someone suggested it, and I would feel remiss if I did not heed such a suggestion and instead acted in a way that might be interpreted as unilateral. I'm certainly of the opinion that the lack of the consensus is fairly evident, but I would not want to presume that it is until is more explicitly so. After a day or two more, I believe consensus or lack thereof will be determined clearly enough. --Cheeser1 17:25, 28 August 2007 (UTC)
That would not, of course, be sufficient for you to make your preferred change; at best your wikilawyering would get you back to the status quo ante (with all line items being "small set"). There's no consensus for your change either. --Trovatore 01:07, 29 August 2007 (UTC)
Sure. Unfortunately, I have WP:V on my side. "Large set" is the appropriate term, and if lack of consensus (which we obviously have) leads us to revert to the "status quo" we will have a disambiguation page for both terms together. WP:V leads us to change "Small set (Ramsey theory)" to "Large set (Ramsey theory)" to avoid original research. Stop mincing words. Why are you so obsessed with splitting these pages? There is no policy or consensus in favor, just your personal preference, albeit shared with some people. Without consensus, things should stay the way they are. The fact that you want to revert my unrelated contribution which has to do with WP:OR violations is irrelevant. Stop making a fuss. I know you want to "fix" the "ugly" "problems" so that Wikipedia is exactly the way you want, but you don't own Wikipedia. --Cheeser1 01:48, 29 August 2007 (UTC)
It really isn't appropriate to make any further changes to the pages' names until we find some consensus to go forward. Pushing towards "no consensus" isn't a productive strategy. Many editors here have long experience with WP and are not particularly vulnerable to wikilawyering. I recommend that you work towards finding some compromise. — Carl (CBM · talk) 01:54, 29 August 2007 (UTC)
First of all - are we changing pages' names? I don't recall that being proposed by anyone (maybe I misunderstood or missed something). Regardless, when somebody swoops in and makes a huge unilateral change to an article, I expect a reason besides "I like it better this way." And I'm not pushing for no consensus - there's already no consensus, this should be evident. The fact that I'm trying to move on from there is apparently counting against me. Either the article is split, or it isn't. There was no (objective) reason to split it, and no consensus to do so. So we should un-split it. I'm perfectly happy compromising by cutting the exposition and so forth - nowhere did I expect that to go back in, and I'm just as opposed to it as anyone else. What more compromise could I give, but to concede entirely to Trovatore just because he insists that his version is "better" because it "fixes" "ugly" "problems" in the article. This is the most compromising version one could use, without conceding entirely to Trovatore (hardly a compromise) or violating WP:OR by abusing/inventing terminology. --Cheeser1 02:47, 29 August 2007 (UTC)
Not a chance, not gonna fly. The only thing you can get with the "no consensus" version is back to the status quo ante. I will admit that I wouldn't have my back up about this if it weren't for your seriously substandard manners and comportment in the original discussion at talk:small set combined with the colossal gall then to lecture me about mine. But that's the way we stand; if you're going to play wikilawyer, the best you can get is back to where we were before your change. --Trovatore 03:27, 29 August 2007 (UTC)
The no consensus version should not violate WP:V, and as such, should include only verifiable mathematical terminology. If you want to give me the "pipe down whippersnapper" lecture, you can hold your proverbial tongue because I'm not interested. You accuse me of Wikilawyering - at least what I'm trying to do (include "Large set") is based on policy (and consensus, I might add), instead of an irrelevant personal preference that requires sweeping and unsupported changes to the article structure. I've given you everything except exactly what you want - I've agreed to reduce exposition, agreed to link only to valid mathematical terminology, agreed to avoid expanding it into any sort of article, all of which we've come to terms with - but when I still don't give you the split that you want (for no supportable reason), what? You refuse, and insist that we revert to a version that violates policy?? This is crazy, and if you're going to use my "manners" as motivation for refusing to compromise, I'd say you're the one who's out of line. I'm merging the articles, per the status quo, based on lack of consensus, policy, or other means to determine whether or not to split them. I will not include content that violates WP:V. If you want to reintroduce that content without splitting up the articles, feel free, but I will not be the one to reintroduce the WP:OR term "Small set (Ramsey theory)." How's that for compromise? --Cheeser1 05:22, 29 August 2007 (UTC)
There was no consensus to expand the small set dab page to include the search term large set. You work out how readers are going to find large set (Ramsey theory), without the large set dab page. --Trovatore 05:27, 29 August 2007 (UTC)
I'm afraid you'll find that before you split them up, this page functioned as the disambig for both. Hence it was the disambig for both terms in per the status quo. We've been over this 100 times. I don't want to have to repeat such a plain and obvious thing again. --Cheeser1 05:31, 29 August 2007 (UTC)
This "I don't want to repeat myself" when you're wrong is the single most offensive aspect of your comportment and manners. It was not the disambig page for both terms; it didn't mention "large". "Large" just redirected there. Redirects are semantical; disambigs are syntactical. For obvious reasons. --Trovatore 05:33, 29 August 2007 (UTC)
Fine. Since you've stooped to continually attacking my "conduct" (asking you not to make me repeat myself), why don't you take your snooty self-righteous attitude out of my face? "Redirects are semantical; disambigs are syntactical." Tthat's all well and good, and I'm glad you remember your SAT words, but this mythic "status quo ante" you keep referring to made explicit, unverifiable claims that "large" means "not small". The only reason it was not explicitly the disambig for both search terms is because of this completely false presumption. It was still implicitly the disambig for both. If not for those misguided assumptions, it would been (correctly) the disambig for both search terms. You were far more adamant than I about removing this "exposition," as you called it. Why can't you cope with the consequences of removing it?? --Cheeser1 05:39, 29 August 2007 (UTC)
The natural consequence is the split. Apparently they never should have been combined in the first place, since there's no uniform relationship between "small set" and "large set" in different contexts. --Trovatore 05:44, 29 August 2007 (UTC)
Ah, so apparently you're in charge of natural consequences. Good to hear that you've appointed yourself mother nature. There is an obvious uniform relationship: when the two exist, they are opposites. This clearly allows for them to remain together (in a natural way). But you'd rather presume that your idea of "natural" is best. Because it's what you prefer, even if it requires sweeping unilateral changes. If you think your idea of best is actually best, then I'm done talking to you. If there's one thing I've learned on Wikipedia, it's this: when someone doesn't know the difference between their completely subjective (in no way superior) preference and "the best possible way to do it," there's really nothing to discuss. --Cheeser1 05:48, 29 August 2007 (UTC)

Cheeser has promised not to respond, but I submit these Facts to a candid world: "small" and "large" are opposites, but "opposite" can mean a number of things. In the current case there are, a priori at least, two obvious possibilities: A large set might be simply not a small set (that is, a positive set in the relevant ideal), or it might be the complement of a small set (that is, a set in the ideal's dual filter). So we can't confidently predict any uniform relationship between the two terms that holds necessarily across all possible contexts ("intensionally" as opposed to "extensionally"). Not that that matters too much anyway, since disambig pages are based on finding a particular search term, and "small" is not the same sequence of letters as "large", nor even any similar sequence of letters. --Trovatore 06:11, 29 August 2007 (UTC)

And while I refuse to respond to Trovatore, I submit these facts (without being pompous or arrogant enough to capitalize "facts"): both articles on small sets explicitly define large sets as sets that are not small. Just like I said. I would ask that other editors disregard his absurd and inappropriate obfuscation of these issues and the related minutia he's using to distract us from the main issue here: There was a perfectly good "status quo" version with one very minor WP:V problem. Trovatore decided to make sweeping changes despite lacking support of consensus or policy, because he likes to have things his way. Since not everyone has rolled over and let him do whatever he wants, he has actually stooped to making the article worse, rather than have a version that he does not like. And keep in mind, I'm only ignoring him because he's explicitly stated that his refusal to compromise is based on some personal issue he's decided to have with me. I'd be happy to continue to discuss this with anyone else. --Cheeser1 06:24, 29 August 2007 (UTC)

Just for the record: I have not seen a single instance yet where Trovatore has made anything on wikipedia worse, and I have seen innumerous places where he has made great contributions. I did witness, on the other hand, basic lack of understanding of the meaning of consensus, cockish and inflammatory edit summaries, edit warring, Neanderthal manners in general, and bizarre insistence on "an administrator thinks that I am right, hence I AM RIGHT!", all of the above by Cheeser1 at Calculus, not even three months ago. Arcfrk 06:13, 31 August 2007 (UTC)
Yes, let's make this an issue about my "manners," especially pertaining to events from months ago. God forbid we discuss the issue at hand. If this is what I get for coming to WPM, I'd rather not come back here. Trovatore admitted to refusing to compromise because he didn't like my attitude, and I'm getting the same crap from someone else to? Forget this. --Cheeser1 11:58, 31 August 2007 (UTC)

## Negation of definitions

I noticed that the following articles have been created:

In general, it seems strange to me to have an article that only serves to negate the definition of another article. — Carl (CBM · talk) 16:51, 28 August 2007 (UTC)

They are there now for no other reason than their absence previously. Certainly feel free to merge or otherwise place these. They do not seem to correspond exactly to the others in Mathematical relations. I do not know the reason for the discrepancy. I don't think these are different "in logic" and "in mathematics." I'm pretty sure they are the same concept. I have a high degree of confidence in their accuracy because I looked into it extensively at the time I took notes. The one I am NOT sure of is Antitransitive. If anyone can enlighten me on that one I would be grateful. It was in searching for that one I learned about the others. Gregbard 17:06, 28 August 2007 (UTC)
BTW, they are not strictly the negation of their base word as the use of a-, non-, anti-, and counter-, etc. are possible. Have a wonderful day. Gregbard 17:09, 28 August 2007 (UTC)
Do you know where you got these definitions from? The definitions given on these "non" articles are not the negations of the corresponding terms. Typically "non" is used to indicate a negation, while "anti" is used to indicated something stronger than negation. For example a nonsymmetric relation just isn't symmetric, while an antisymmetric relation fails to be symmetric to the greatest extent possible. — Carl (CBM · talk) 17:12, 28 August 2007 (UTC)
I didn't write down the sources at the time. I have an extensive collection of index cards with all kinds of logic (over 3000) on them. One that is different is "reflexive" vs. "totally reflexive." In my notes Reflexive is:
(x)(($\exists$y)(Rxy$\lor$Ryx)→Rxx)
Totally reflexive is:
(x)Rxx
Gregbard 17:27, 28 August 2007 (UTC)

(edit conflict)These articles (which apart from anything are too short and technical to be decent articles) seem slightly confused. Why is it "the nontransitive relation", rather than "a nontransitive relation" (implying that "nontranstivity" defines scissors paper rock)? I have never heard "nonsymmetric" mean anything other than "not symmetric", yet the article equates it with "partimsymmetric", which apparently means "neither symmetric nor asymmetric", where asymmetric means antisymmetric and irreflexive. The nonreflexive article equates nonreflexive not with "not reflexive", but with "partimreflexive" (ie neither reflexive not irreflexive), giving partimreflexive examples but actually giving a definition for irreflexivity. At any rate, simple negations would not deserve an article of their own. Stronger concepts may, but even irreflexive relation is a redirect to reflexive relation. JPD (talk) 17:42, 28 August 2007 (UTC)
(I also echo the queries about syntax at Talk:Nontransitive relation JPD (talk) 17:52, 28 August 2007 (UTC))
We need reliable sources for these defnitions. Unfortunately "an extensive collection of index cards" does not constitute a reliable source. Until we can find such, I think the best thing would be for Greg to ask that they deleted. Is that ok with you Greg? Paul August 17:59, 28 August 2007 (UTC)
I think that just redirecting them to the definition articles, and adding the bolded negated term to the definition articles, would be enough. So for example into Reflexive relation we would add "A relation that is not reflexive is nonreflexive." What would need a source, in my opinion, is a claim that nonreflexive means something else than "not reflexive". — Carl (CBM · talk) 18:02, 28 August 2007 (UTC)
I agree. Paul August 18:32, 28 August 2007 (UTC)
Mergers/redirects appear to be in order. Notice, though, that a phrase like "not transitive" is ambiguous. The current article intransitivity covers this thoroughly. If there are no transitive triplets, the article says the relation is antitransitive (and also not transitive). OTOH, if there are some transitive triplets a>b>c, but there are also some exceptions to this rule, the relation does not define a partial order, or, as Gregbard would have it, the relation is nontransitive. DavidCBryant 23:28, 28 August 2007 (UTC)

I'm trying to talk some sense into this incredibly confused reader who's creating a rather large number of articles on these topics. See User talk:Gregbard. Can anyone else help bring him to his senses? He doesn't have a clue about the correct use of quantifiers. Quite possibly he understands the correct definitions of all these types of relations, but his ways of attempting to express them are horribly incorrect. Michael Hardy 17:56, 29 August 2007 (UTC)

Michael, on the nontransitive relation talk page you state
"If by "nontransitive" you mean simply "not transitive" then the way you've written it is utterly wrong. When you write ($\exists$x)($\exists$z)¬Rxz) you're necessarily referring to an "x" and a "z" that are not the same as what you called "x" and "z" earlier; you're just saying there exist two elements such that one is not related to the other. You're NOT saying there exist elements x, y, and z such that x is related to y and y to z but x is not related to z. In the notation your using, that would say \exists x\exists y\exists z(Rxy & Ryz & ¬Rxz. Those preceeding (x), (y), and (z), meaning for all z, etc...., should not be there at all."
No they are NOT "not the same." It says for all xs, ys, and zs there exists a particular x, and a particular z which don't have the relation. You are incorrect in thinking that they are not the same. The x, y, and z quantifier binds the whole expression in parentheses. The $\exists$x, and $\exists$z are particular members of those sets x, and z respectively. So I understand the use of quantifiers perfectly, and you already admit that I understand the relations (thank you for the concilliatory). Be well, Gregbard 23:15, 29 August 2007 (UTC)
You've quantified x twice, in two different ways, within the same sentence above: "for all xs" and "there exists a particular x" — although you wrote it in English rather than formal logical notation, those still look like quantifiers, but the double quantification makes it impossible to make sense of your statement. That does not suggest to me that you are skilled in the correct handling of quantifiers. —David Eppstein 23:21, 29 August 2007 (UTC)
I just want to make sure I understand perfectly clearly: YOU find it impossible to make sense of a precisely crafted expression, but that suggests that I don't know what I'm doing. Well, um, not really. Gregbard 00:15, 30 August 2007 (UTC)
You know, most reasonable people, when confronted with an error in their mathematics, would apologize and correct it. It's not a subject in which the greater ability to bluster will win the day. —David Eppstein 00:50, 30 August 2007 (UTC)
Do you think perhaps he's trying to say something like:
$(\forall y) \left(\left(\exist x)(\exist z)\left (R x y \and R y z \right)\right) \rightarrow \left((\exist x)(\exist z)\left (R x y \and R y z \and \lnot R x z \right)\right)\right)?$
In any case, all clearly not-standard (yes, I meant "not standard", rather than "non-standard") terms (i.e., I don't recognize them ) should be proposed for deletion unless a reference can be provided. — Arthur Rubin | (talk) 23:37, 29 August 2007 (UTC)
Well I'm not going to put them up for deletion, for one; I assume that Gregbard put them up in good faith. But I'm having as much trouble as the rest of you making sense of the expressions. Gregbard, would you be so kind as to convert each of these (here on Talk) into prenex normal form? I think then we'd be better able to discuss the terms. Right now we all seem to be talking past each other.
CRGreathouse (t | c) 01:16, 30 August 2007 (UTC)
The disposition of an article should depend on whether its inclusion, after such improvements as may be needed and can reasonably be expected to be executed with our limited means, increases the value of the encyclopedia – a consideration that is independent of the assumption it was created in good faith. The article Such that was undoubtedly created in good faith, and yet you (CRGreathouse) recommended its deletion, I suppose.[5]  --Lambiam 07:16, 30 August 2007 (UTC)
I do draw distinction between putting an article up for deletion, as Trovatore did for that one, and participating in the discussion on the AfD. Even on these articles, I don't think I'd 'vote' to keep them, depending on what else was suggested. But I'd rather wait until at least the discussion settles before voting them down.
Perhaps it was too fine a distinction, and perhaps I was inspired, at least in part, by a desire to keep the peace with Gregbard: he seems to have had a rather rough time with our project.
CRGreathouse (t | c) 12:02, 30 August 2007 (UTC)

## relations redux

What have we learned? CRGreathouse was the first to raise the question about the definite article, and he was absolutely correct. The relation I stated was incorrect in that regard for certain. The negation of transitivity is the one stated by Michael Hardy and I think Dr. Rubin:

$\exists x\,\exists y\,\exists z\,(xRy \text{ and }yRz\text{ and not }xRz).\,$

I never denied this fact onced faced with it. My further concern was that there may be degrees of nontransitivity, and that the statement I had origianlly thought was the nontransitive relation was still more general than this one stated above. That isn't so wild a thought. After all, the most general form will "screw up" the transitive relation as little as possible and that would seem to only require the participation of two variables. I was shown to be incorrect in this belief by Carl directly. Now I understand. Think about it: there is no such game as rock paper! It requires three. However "grossly incorrect" would be a dramatization.

Carl provided a counterexample that shows that my stated formulation permits for the existence of at least one (and I think we can see intuitively an infinite number) of transitive relations. However the relation I stated may still be some form of weakened nontransitivity, with a name begining with some strange prefix appended to -transitive. I do not know what.

I agree that everything in Wikipedia should have a reference if possible. However I do not agree that it should be deleted altogether, but rather improved and merged appropriately. My intention from the outset was that this would be a noncontroversial relation, and therefore survive to see other editors' contributions.

So everyone is more esteemed in my eyes because I learned from it. Everyone was fairly kind and I was a bit exasperating on the points I was sticking to. However, the low point was when David Eppstien said it looked like I didn't know what I was doing, while stating "the double quantification makes it impossible to make sense of your statement." That statement looks as if he doesn't know that one may put more than one form of quantification on a variable in a formula (that isn't prenex normal form, but still a formula). One can do that, and I know that, but it LOOKS as if he doesn't know that. So I think I played it pretty cool for everyone telling me how much I don't know.

He also said "You know, most reasonable people, when confronted with an error in their mathematics, would apologize and correct it. It's not a subject in which the greater ability to bluster will win the day." This I agree with 100%. So this is the conciliatory note you were waiting for. It hadn't been shown by Carl at that point that I was incorrect, David. Furthermore you hadn't said anything to disprove my claim AT ALL. Maybe someday I'll have a peanut gallery cheering me on instead of sandbagging me. It's okay David, like I said, I see that I was exasperating.

I'm not too worried about nontransitivity. Eventually, there will be plenty of information on it, even though right now there is a redirect to an article with NO information on it at all. I don't know how we are better off. What were you saying about increasing the value of the encyclopedia Lambiam? I agree with that too. Be well, Gregbard 10:09, 30 August 2007 (UTC)

see you in the talk pages...

Hi, Gregbard. I was surprised to see Weak order missing, and for the moment I made it a redirect to a section in an existing article which is devoted entirely to weak orders (there called total preorders). I think there's reason enough to make this its own article; it's quite important in social choice theory and more broadly in economics for the study of preferences.
If anyone's around, your new article Homogeneous relation could use another pair of eyes.
CRGreathouse (t | c) 12:36, 30 August 2007 (UTC)
Well I appreciate that these topics are getting some consideration. I think that's wonderful. However, I don't see that it is a lot of progress to just put a redirect without actually giving the reader looking for that topic something to read about it. I guess it's a little progress. I think I am going to put some material in my userspace and take it from there. You guys are too hypercritical for me. For all that discussion no one has anything useful to contribute to the entry on nontransitive? I really am not here for the debate club aspect. Gregbard 01:04, 31 August 2007 (UTC)

biorder, interval order, semiorder, and almost connected order can all also be defined axiomatically as relations. E.g. biorder: for all x,y,z,w, (xRy and zRy and zRw) imply xRw. Interval order: irreflexive biorder. I added them to the list.—David Eppstein 14:23, 30 August 2007 (UTC)

Am I missing something? Let R be an irreflexive biorder, and assume aRb and bRc. Irreflexivity tells us that ¬bRb. Applying the above defn of biorder with the substitution (w,x,y,z) := (b,b,c,a) tells us that (bRc and aRc and aRb) imply bRb, which can be simplified to ¬aRc. So R is totally antitransitive, and therefore not a partial order; on the other hand, interval orders are supposed to be partial orders.  --Lambiam 16:11, 30 August 2007 (UTC)
Sorry, there was a little bar in the definition of biorder that was too small to see clearly in the font size I was using to read the reference, but makes a big difference in the definition. The proper definition of biorder is: for all x,y,z,w, (xRy and ~zRy and zRw) imply xRw. The reference I was reading is unpublished, but if you want a published one, I think this material is in J.-P. Doignon and J.-Cl. Falmagne. Well-graded families of relations. Discrete Mathematics, 173:35–44, 1997, and C.W. Doble, J.-P. Doignon, J.-Cl. Falmagne, and P.C. Fishburn. Almost connected orders. Order, 18(4):295–311, 2001. —David Eppstein 16:18, 30 August 2007 (UTC)

Greg, you still seem slightly confused. "The nontransitive relation" implies that there is only one relation that is nontransitive, which you have conceded is wrong, yet you still talk about "the relation I stated" as though the property which makes relations nontransitive is itself a relation. As for generality, yes, negation of a condition X definitely gives the most general form of being non-X. It gives everything that is not X. Anything more general must include relations that are X and so could hardly be called "non-X" In my experience, "non-X" is used to mean "not X", the general lack of X-ness, and things like "anti-", etc. are used for stricter conditions, but with the way terminology works, I wouldn't be surprised to find a counterexample.

You also insist that your double quantification was ok. However you understand your formula, it doesn't mean what you said it means. At the very least using the same variable with two different thigns in mind is likely to cause confusion, so the simpler formulations would be better for an article even if you were right. As for the nontransitive article, you say it is now a redirect to an article with no information at all. What do you mean by this? The article intransitivity covers the correct version of everything that was in the nontransitive relation article, in a broader context. The only thing that could possibly be added is the word "nontransitive" as an alternative to "intransitive". JPD (talk) 18:18, 30 August 2007 (UTC)

No, intransitivity is a different thing than nontransitivity. I thought we all agreed on that. The entry was to be redirected to intransitivity and that article would touch on the difference. Think of intransitive as the ongoing pervasive condition of always avoiding transitivity among x, y, and z. Nontransitive is merely the existence of just one counterexample. The article is redirected but has no information that reflects this. Gregbard 01:19, 31 August 2007 (UTC)
the formula I designated uniquely describes a statement of predicate logic. So it wasn't ambiguous. If anyone else didn't understand it then we at least have to SHARE the blame (what do you say) Gregbard 01:19, 31 August 2007 (UTC)
Yes, the formula you designated uniquely describes a statement of predicate logic, assuming we defined the double-bond quantifiers correctly. However, it seems to mean the relation is not universal. — Arthur Rubin | (talk) 02:16, 31 August 2007 (UTC)
It's universal among all x, y, and zs if it begins with (x)(y)(z) Gregbard 05:50, 31 August 2007 (UTC)
For all xs, ys,and zs, it is true that(blah blah blah). If among the "blah blah blah" we have "there exists an x such that..." that's a particular x from among the set that x denotes. It's like saying for all cities, counties, and states there is a city which is its seat of government. (In this case it is trivially true that every city has itself as its seat of government). So like I said not in Prenex normal form, but an unambiguous formula nonetheless. (In these particular cases it's easier to understand and see directly when it is not in PNF). Gregbard 05:50, 31 August 2007 (UTC)

Is a separate article for each of the many red links above contemplated? Maybe some of them warrant individual articles, but if the articles are to be little more than dictionary definitions, perhaps it is better to put those that don't warrant more than a short paragraph all into one long article. Michael Hardy 02:45, 31 August 2007 (UTC)

I think they are called redirects with possibilities. Gregbard 05:50, 31 August 2007 (UTC)

Greg, please read the article intransitivity before claiming that the article has no information reflecting either version of nontransitivity/intransitivity. It starts by defining and describing "intransitivity" as the simple negation of transitivity (i.e. the existence of a single counterexample to transitivity), and then goes on to say that "a more common mathematical definition" is the anti-transitivity notion, where every chain of length 3 is a counterexample to transitivity. In other words, the article clearly states that "intransitivity" is used with more than one meaning, one of which is the most general possible.

As for your formula with double quantifiers, I didn't say it was ambiguous. I said it doesn't mean what you said it did (as Arthur says, it is equivalent to something without any universal quantifers), and that it would be easier to understand if it were written without double quantification. The very fact that you have misunderstood the formula suggests that in this case it is not "easier to understand and see directly when it is not in PNF". I am not sure what to make of your attempt at explanation by example. (x)(y)(z) means "for all choices of x, y and z", not "for any choice from any of three sets denoted by x, y and z". The x doesn't denote a set.

More importantly, what about these red links/articles. I agree with Michael Hardy that many would be better combined in one article. The resulting redirects may have possibilities, but I (and others) don't see what the possibilities could be. JPD (talk) 10:52, 31 August 2007 (UTC)

The article is saying that we use the same name for both, and I am saying that they are different. If there is a strong culture out there that uses the terms that way fine. However, it should still be noted that they are different and that there is a different name for it out there.
The example of the city which is the seat of government is an excellent example of the mixed use of quantifiers. I don't know off hand what the PNF form of that would look like, but I doubt it would be clear immediately that it was that simple a connection. I could be wrong.
($\forall$city)($\forall$county)($\forall$state)($\exists$city)
However I likewize cannot make anything of your statement "(x)(y)(z) means "for all choices of x, y and z", not "for any choice from any of three sets denoted by x, y and z". The x doesn't denote a set."
(x)(y)(z)(blah blah blah) means "for all xs, ys, and zs 'blah blah blah' is the case." This is more specifically understood as that idea that you can choose a member from each of the three sets and "blah blah blah" will be true of them. x, y, and z are particular members of sets. "(x)" corresponds to some set of values for x which is a set.
Be well, Gregbard 11:18, 31 August 2007 (UTC)
The article says the terms are used with different meanings in different places, including the meaning of intransitive that you advocate. As I said earlier, the only thing that is possibly missing is the "different name" "nontransitive". The fact that the meanings are different is already noted. You may be right to question whether the word "intransitive" is actually used in the way the article describes, but the article does cover both notions, and point out how they are different.
No, "($\forall$city)($\forall$county)($\forall$state)(blah)" means "For any choice of city, county and state, blah holds" (that is, any choice of a triple (city, county, state)). For the seat of government example, you seem to be saying it means "For any choice of (a) city, (a) county or (a) state.", which is wrong. I am not familiar with this idea of using variable naming only to tell us which sets are being considered, but it is not relevant in the original case of hommogenous relations, and seems to only make more room for confusion, as demonstrated by your incorrect formula. For your example, we can simply write "$(\forall x\in A)(\exists y\in B)Gxy$", or more formally, "$(x)(\exists y)(Ax\rightarrow(By\wedge Gxy))$", where A is the set of cities, counties and states, B the set of cities and G the relation "x is the seat of government of y". I fail to see how your style helps understanding at all, especially since you haven't actually produced a full formula for your statement. Restricting ourselves to cities, we may say that all cities have a seat of government, "$(x)(\exists y)Gxy$". However, if we wish to say all cities are their own seat of government, no existential qualifier is needed "$(x)Gxx$". JPD (talk) 12:29, 31 August 2007 (UTC)
(edit conflict) I read the city/county/state example as
$\forall x\in X, y\in Y, z\in Z \exists w\in X (Gwx \vee Gwy \vee Gwz)$ (X the set of cities, Y the set of counties, Z the set of states, Gab the binary relation "a is the seat of government of b")
or more simply
$\forall x\in X\cup Y\cup Z \exists w\in X (Gwx)$
While I agree that PNF isn't ideal for everything, and in fact I don't generally use it myself (I just wanted something unambiguous), I don't think it's hard to do for any of these transitivity relations or this example. In fact it's already in sloppy PNF, where set memberships for the quantified variables is allowed; to move those out, you'd just have
$\forall x\exists w (x\in X\cup Y\cup Z \wedge w\in X)\rightarrow(Gwx)$
As for the comment you didn't get anything from, Greg: $\forall xyz$ (as I've been writing it), $\forall x, \forall y, \forall z$ (as a formal system might have it), or (x)(y)(z) (as you write), the x, y, and z are variables, not sets. If one writes $\forall x\in X$ x is the variable and X is the set. You can say "for all choices of x from X" or "for all choices from X", but JPD doesn't want you to say "for all choices for x" because X, not x, is the set.
CRGreathouse (t | c) 12:44, 31 August 2007 (UTC)
At the risk of beating a dead horse, I'm going to throw a few statistics into this discussion. The statistics are just g-hits, from Google Scholar.
Google Scholar lets one choose from "Engineering, Computer Science, and Mathematics" (where most mathematical logic articles are found), or from "Social Sciences, Arts, and Humanities" (encompassing philosophy, plus disciplines like economics and behavioral psychology, etc.). After running a couple of searches, I noticed that the phrase "non transitive" or "non-transitive" is more common than "nontransitive" – I have lumped all three spellings together in the statistics below.
Searching on the terms "nontransitive" and "intransitive" I obtained the following results: Math – 1,941 instances of "non", 3,820 instances of "in"; Humanities – 976 instances of "non", 14,800 instances of "in". So "intransitive" occurs much more frequently than "nontransitive" in both subject areas. Notice, however, that most references to "intransitive" in the Humanities appear to be usages such as "intransitive verb", which really have nothing to do with this discussion.
Searching on the terms "nontransitive relation" and "intransitive relation" I obtained the following results: Math – 67 instances of "non", 40 instances of "in"; Humanities – 69 instances of "non", 63 instances of "in".
So on the preponderance of the evidence presented here it appears that the phrase "nontransitive relation" (or "non transitive relation", or "non-transitive relation") is slightly more common than the phrase "intransitive relation". And the perception most of us have (me, too!) – that "intransitive relation" is commonly used in mathematics, and "nontransitive relation" is not so common – is actually incorrect, and is probably related to the fact that the word "intransitive" is widely used, but is not often found in the phrase "intransitive relation". DavidCBryant 16:17, 31 August 2007 (UTC)
This is a tangent, but I'm not sure that the distinction between mathematics and social sciences is meaningful here. E.g., I tried searching the publications of Doignon (a Belgian mathematician who works in this area) and found slightly more under social sciences than math, because he's published in journals like J. Mathematical Psych., British J. Mathematical and Statistical Psych., etc. On the other hand, Int. J. Man–Machine Studies is listed under mathematics despite the similarity in content with those other journals. It's one of those borderline areas that simplistic classification doesn't work well for, I think. —David Eppstein 17:16, 31 August 2007 (UTC)

## Paradoxes of set theory, redux

I know this was discussed in a previous invocation of this page, but I have to say that after multiple attempts to fix the article by myself (under ip address 71.198.111.245) and others such as User:Mathemaduenn and User:CRGreathouse, the article stands virtually unchanged since April 2007, with the exception that the completely bogus WM invention of "the binary tree" appears to have, finally, been deleted. I have no objection to an article describing the counter-intuitive aspects of infinite cardinality; but this article does more to encourage misunderstanding than it does to bring anything positive to the subject. Sets that have more "reality" than other sets? A cardinality for a "set of gaps", without a definition of "gaps"? "The most important theorem of set theory proves that there are uncountable sets"? The familiar WM usenet argument that omega is a member of the union of all finite sets of naturals? This really is pseudo-math, and shouldn't be on Wikipedia. On the other hand, after putting time into this page without any remnant remaining, I hesitate to enter the fray again. Suggestions on how to proceed are welcome! Chas zzz brown 02:08, 31 August 2007 (UTC)

I'll work on it some; I would appreciate it if some other editors would at least watch the article to give feedback, if not help with the editing. — Carl (CBM · talk) 13:17, 31 August 2007 (UTC)

## the parable of the nontransitive relation

Everybody gather 'round as I tell the parable of the nontransitive relation. I may need some help telling it, so sit close...

I live on a planet with a very similar language to English, and you have come to visit...

Most of the words are the same, but some are a little different. For instance, you visit with a group of delegates in a conference room, and it comes up in conversation about how "Xtall" a delegate is. You inquire into the meaning, and the lead delegate explains to you (without indicating anything about height) that delegate A is "Xtaller" than delegate B, and delegate B is "Xtaller" than delegate C. He does this several times, and the meaning becomes clear to you that it just means the same thing as "tall." However, a new person walks into the room, and the the lead delegate introduces the president of the planet as the "Xtallest of us all." At this point you are confused because the person is obviously not the "tallest" person in the room. On this planet, you conclude, the relation "Xtaller than" is a nontransitive relation and that it may or may not have any connection at all to "tallness" as you know it.

Now it happens to be a strange planet and all that. However, it would have been equally strange if the meaning of "Xtall" had meant that the lead delegate said the same of any person other than the tallest person in the room. That means that there are number of ways in which the nontransitive relation could have occured. All of those ways have the nontransitive relation in common. These are the same relation as far as we are concerned in logic.

If, on the other hand you later find that the vice-president walks into the room and is also introduced as one of the "Xtallest" people on the planet, and is about as tall as the president, who herself is obviously not "tall." You still conclude that "Xtall" is nontransitive, because although all that is required for a relation to be nontransitive, is ONE counterexample, it still is called nontransitive if there in fact exist TWO. All of those ways have the nontransitive relation in common. They are still the same relation as far as we are concerned in logic.

Much later, (after several intergalactic plenary sessions, etc) you have learned a little more about this culture and "Xtallness." It turns out that the planet has a caste system, and every person of caste1 is always "Xtaller" than every person of caste2 and etc. Furthermore, you remember that your original meeting was with a room entirely filled with the diplomatic core. All of those people are members of the same caste AND at least one caste number higher (sociologically lower, that is, you suppose) than the president and the vice president. You also read in a political analysis report that the president only appoints people such as her veep to her most highest caste if they are shorter than she is. This explains a lot.

Now remember the language is close to english, but there are a few new words that are similar. Due to terrain, certain cultural factors, and city planning developments, etc; on this planet there is a word "quintasubproxihoodamate" for "lives five neighborhoods south of" (At least that is how your abridged translation dictionary defines it.) However, you learn from your cultural experiences that there is a lot more to being "quintasubproxihoodamate" ...

It turns out that in the political culture of this planet some neighborhoods are more quintasubproxihoodamate than others --if you know what I mean! You say you don't? How naive brother! I mean that even though everybody knows that two neighborhoods are on the same parallel, the one whose neighborhood association president is a close friend of the director of Geological Surveys will always be considered more southerly. This, it turns out is favorable in applying for government grants on this planet. The planet is just corrupt enough to allow an administration to say what is and is not "south of" but not corrupt enough to influence the grant application process once a neighborhood is labeled as one of those undeserving northerly neighborhoods!

Ordinarily, the quintasubproxihoodamate relation is an intransitive relation. If A has a quintasubproxihoodamate relation B and B has a quintasubproxihoodamate relation to C, then according to the abridged dictionary definition of quintasubproxihoodamate, A will NEVER have a quintasubproxihoodamate relation to C. But it isn't that simple here.

So can anyone tell me what happens when the Director of Geologic Surveys designates the neighborhood at the north pole of the planet as quintasubproxihoodamate to some other existing neighborhood on the planet?

What kind of relation would you call quintasubproxihoodamate then if not merely nontransitive? It sure isn't intransitive anymore. Intransitive is when the relation of the first to the third NEVER holds. In this case it sometimes does. This is still the nontransitive relation because all of the formulae which contain the quantifier $\exists$ are satisfied by the existence of one, two or even all of the particular members of the set as designated by the formula. The nontransitive relation includes the intransitive, not necessarily the other way around.

Anyway, quintasubproxihoodamate isn't what it used to be anymore. Not under this administration.

Gregbard 07:33, 31 August 2007 (UTC)

Sorry, I got completely lost from the fourth paragraph on. Natural language has its limitations. Could you rephrase this parable using logical connectives and quantifiers?  --Lambiam 08:00, 31 August 2007 (UTC)

### parable redux

Such is Transitive: (x)(y)(z)((Rxy & Ryz)→Rxz)

One counter example screws up transitivity and makes the relation a nontransitive relation: Nontransitive: ($\exists$x)($\exists$y)($\exists$z)((Rxy & Ryz)&¬Rxz)

Such is Intransitive: (x)(y)(z)((Rxy & Ryz)→¬Rxz)

One counter example screws up intransitivity and makes the relation a what? It's only transitive for one set of triplets. All the rest are intransitive

i.e. ($\exists$x)($\exists$y)($\exists$z)((Rxy & Ryz)&Rxz) however (u)(v)(w)((Ruv & Rvw)→¬Ruw) holds for all the other values of those sets.

I say this is still called nontransitive because of the meaning of $\exists$. Gregbard 10:41, 31 August 2007 (UTC)

Greg, you are still using the word "relation" to sometimes mean "property of a relation". You said: "That means that there are number of ways in which the nontransitive relation could have occured. All of those ways have the nontransitive relation in common. These are the same relation as far as we are concerned in logic." I would say "There are a number of ways in which the relation could have been nontransitive. All of these would still mean the relation is nontransitive. They all have the same property - nontransitivity" I don't understand the claim that this is the only property we would care about. (Of course, in your parable, the appearance of the Xtallest person in itself doesn't tell us that Xtall is nontransitive, as it is not a counterexample to transitivity - it simply tells us that Xtall is not the same as tall.)
Then, you abuse the terminology further (that is not always a bad thing, but let us look at it in this case). You seem to apply a universal property (transitivity) to individual triplets. By "It's only transitive for one set of triplets." do you mean "There is only one triplet for which the condition for intransitivity fails."? Yes, in that case, it is nontransitive but not intransitive (using the stricter definition of intransitive). This tells us, not that "the nontransitive relation includes the intransitive", but that the set of nontransitive relations includes the set of intransitive relations.
Your very last line also seems confused. What do you mean by "other values of those sets", when using universal quantifiers. I think what you should have said is ($\exists$x)($\exists$y)($\exists$z)((Rxy & Ryz)&Rxz) however ((Ruv & Rvw)→¬Ruw) holds for all the other values. JPD (talk) 11:16, 31 August 2007 (UTC)
Thank you for your correction of my language. I appreciate the fine points you bring up. You are correct on all of them as nearly as I can tell.
I had to use u,v and w at that point because I was talking about a different set. It's the set x is in, the set y is in, and the set z is in minus the one counterexample that makes the intransitive property leave the scene.
I found your observation that the existence of the president is "not a counterexample to transitivity" quite a brilliant one that I missed. I'm not sure how to rephrase such a parable however. In fact the whole caste system I described is merely a very complex relation that still has the transitive property. One can't tell who is Xtaller just by looking, but once it is figured out we find it all quite transitive! My goodness.
Okay so I need a better example. However, I still think there is a better fate for some of these articles than redirects to related material. No one seems too excited to see them at all. I'm quite surprised. Be well, Gregbard 12:14, 31 August 2007 (UTC)
Transitive: $\forall xyz(Rxy \wedge Ryz\rightarrow Rxz)$
Nontransitive: $\exists xyz(Rxy \wedge Ryz \wedge \neg Rxz)$
Intransitive: $\forall xyz(Rxy \wedge Ryz\rightarrow \neg Rxz)$
Your "almost-intransitive" example (Q) is not transitive, nontransitive, and not intransitive. Relations are (1) transitive, but not the others; (2) nontransitive, but not the others; (3) nontransitive and intransitive, but not transitive; or (4) empty, and thus transitive and intransitive but not nontransitive. This covers all relations.
I'm not sure what the story illustrates, though. "Most" relations (viewed as random binary square matrices of arbitrary large size) are of my category (2) like the one in your example. Being transitive or intransitive is 'hard'.
CRGreathouse (t | c) 12:16, 31 August 2007 (UTC)

May I suggest that you continue your talk at a more specific talk page, e.g. Talk:Relation (mathematics)? Jakob.scholbach 12:21, 31 August 2007 (UTC)

## "such that"

Sigh.

Well, there's at least some truth in this article. It needs to be brought into conformance with the usual Wikipedia conventions. But if there's a reason to keep it, it needs a lot more than that. Michael Hardy 22:44, 24 August 2007 (UTC)

Banish it to wikitionary. Arcfrk 03:42, 25 August 2007 (UTC)
Along with "therefore" and "if ... then ..." ? — Carl (CBM · talk) 04:26, 25 August 2007 (UTC)
I am not positive, but I do imagine that wiktionary would want an article on this (as it's a 'set phrase', or whatever they call it). However, it might be appropriate to include it in mathematical jargon and table of mathematical symbols. Actually, I think that mathematical terminology and notation might make a good wikibook, but that is perhaps a bit outside the scope of WPM. --Sopoforic 07:33, 25 August 2007 (UTC)
"Such that" is hardly mathematical jargon, since it is used in precisely the same way in both mathematics and in common language. Mathematicians do apply it to certain properties that tend not to arise in everyday settings, of course. It may indeed belong in the table of symbols, though, given what's currently in such that. Ryan Reich 20:45, 25 August 2007 (UTC)
The article has a unique interpretation of the set-builder notation in which the central symbol is an independent notation. I don't think there is support for that interpretation in any printed reference. — Carl (CBM · talk) 21:08, 25 August 2007 (UTC)
Well, not jargon in the sense of slang, but certainly it is used mostly as a technical term. I don't ordinarily hear it used in casual speech: "J. Random Celebrity has recently purchased several cars such that each car has pink spots on its roof" doesn't quite sound right. However, looking at mathematical jargon, I agree that that isn't really the place for it. It already has a description in table of mathematical symbols and in Set-builder notation, so that's probably sufficient. I support redirecting it to Set-builder notation. --Sopoforic 21:41, 25 August 2007 (UTC)
A redirect sounds like a good solution to me. "Such that" is a term of art deserving some sort of explanation, but not really a whole article, and the proper context for the explanation is set-builder notation. —David Eppstein 07:39, 26 August 2007 (UTC)
I would point out in passing that set-builder notation is not the only context in which the term "such that" arises. However I don't have any strong objection to the redirect; the alternative seems to be deletion and as a practical matter it may not be worth the headache. --Trovatore 08:13, 26 August 2007 (UTC)
It does arise in other situations, of course, but I don't know where else to redirect it to. The article such that is at present totally about the colon or vertical bar used in set-builder notation to represent 'such that'. If you think it should redirect somewhere else, please recommend somewhere. --Sopoforic 19:23, 26 August 2007 (UTC)
To be honest, I think it should be deleted. I'm just not sure the difference between the redirect and getting rid of it entirely, is worth going through AfD. But I'll prod it and see what happens. --Trovatore 19:27, 26 August 2007 (UTC)
Oh, I guess it's been tried. OK, AfD it is, grumble grumble. --Trovatore 19:34, 26 August 2007 (UTC)

"Set-builder notation" (I've always thought that was a childish-sounding phrase) is not the only place where this phrase is used essentially as mathematical jargon. Just look at the usual epsilon-delta stuff. And many many similar cases. Michael Hardy 13:49, 26 August 2007 (UTC)

(AFAIAC, it is a childish phrase: the only place it's ever been uttered to me was in ninth grade.) I still argue that its status as jargon is low, and that it is, at worst, a piece of mathematical language, a manner of speaking like the manner of writing for a particular literary school. That language is de rigeur rigorous, so it tends to be a little more formal, and of course it includes many jargonish phrases, but this one is just a rather stiff alternative to the usual "who/which/that". For example:
"The numbers which are greater than zero..." versus
"The set of all x such that x > 0..."
mean the same thing in math and in English and the only reason we as mathematicians prefer the latter is that it is formulaic and, therefore, precise. This works for "the usual epsilon-delta stuff" too, though you won't believe me because no one names their variables in English. But here are two analogous sentences:
"For every opportunity missed, there's another right around the corner which is bigger and better." (A plausible maxim)
"For every ε > 0, there is an N such that for x > N, 0 < f(x) < ε." (Functions asympotic to zero; I was trying to keep the actual math short)
I assert that the only jargon in the second sentence is the mathematical content itself. I wouldn't advocate rewriting the casually upbeat motto in the same style, but swap out the appropriate blocks and tell me it doesn't sound but too formal. Ryan Reich 16:44, 26 August 2007 (UTC)
Well, no....the reason for preferring the latter is that sometimes you want to talk about sets; e.g. you want to say the cardinality of the set of all real numbers is the same as that of the powerset of the set of all integers, etc. etc. Michael Hardy 17:51, 27 August 2007 (UTC)
The use of "such that" in mathematical writing is jargon in the sense that it is shorthand for "which is such that", a meaning confined to mathematical texts. In non-mathematical use (and occasionally in mathematical texts), the usual meaning is "in such a way that", "so that".  --Lambiam 17:56, 26 August 2007 (UTC)

Some people use a backwards epsilon (with the epsilon stylized for set membership) to represent the phrase "such that" when introducing a variable (though this isn't mentioned in Quantification#Notation_for_quantifiers). I had a professor once that was vehemently against this practice, and called the symbol "meaningless" and "non-mathematical." nadav (talk) 19:54, 26 August 2007 (UTC)

The AfD entry is here. --Sopoforic 23:19, 26 August 2007 (UTC)

Result was delete. --KSmrqT 10:52, 1 September 2007 (UTC)