Wikipedia talk:WikiProject Mathematics/Archive/2006/Nov

Archiving automatically (well almost)
As some of you already know, Wikipedia talk:WikiProject Physics recently started using User:Werdnabot to automatically archive its talk sections when ten days have passed since the last new comment. Perhaps we should start to think about whether we want to follow their example. JRSpriggs 11:51, 22 October 2006 (UTC)


 * Seems a good idea to me. --Salix alba (talk) 19:11, 22 October 2006 (UTC)


 * Rather than base it on elapsed time alone, I suggest that archiving of old material should only be done when a certain page size is reached. There's no point in archiving a question which hasn't been answered after 10 days, if it's the only thing there. StuRat 04:16, 24 October 2006 (UTC)


 * Please read the instructions at User:Werdnabot/Archiver/Howto. You will see that the options are very limited. We can change the time interval between the last signed message in a section and the time of archiving, but we cannot control the size of what is taken or what is left. Our choice is reduced, but we avoid having to do all the archiving manually. JRSpriggs 09:05, 24 October 2006 (UTC)

OK. I tried to turn Werdnabot on for this page. It should run every six hours and archive sections 12 days old or older (last edit). I have never done this before, so I am not sure whether or how well it will work. JRSpriggs 09:28, 27 October 2006 (UTC)
 * By the way, there is one way in which it is not automatic. When we get to November 12, someone will have to create the new archive file for November 2006 and edit the code for Werdnabot invokation to reflect the new file name. The same every month thereafter. JRSpriggs 09:32, 27 October 2006 (UTC)


 * Werdnabot seems to be broken again. It has not done any archiving (for anyone) since 24 October 2006. (Just as I was trying to get it to work for us, too.) And Werdna himself seems to have dropped out of wikipedia (at least temporarily). JRSpriggs 07:04, 28 October 2006 (UTC)
 * It ran on the 28th, so at this point I cannot keep up with whether it is on or off. However, Werdna has apparently been working on some security issues -- vandals had figured out how to use Werdnabot to trash pages by directing its output inappropriately. JRSpriggs 11:54, 29 October 2006 (UTC)
 * To User talk:AzaToth: Since you pushed the list of archive files down into subpage "/archivelist" (which fact is far from obvious), I (after searching to find it) put a link to it at the top of this talk file right after the template. We need a way to get to that list so that we can add new links as we create new archive files (currently once per month). JRSpriggs 08:04, 30 October 2006 (UTC)
 * Neither you nor I will be around here forever. Future archivers must be able to figure out how to use the system without excessive effort. JRSpriggs 08:08, 30 October 2006 (UTC)

The archives template have an edit link at top right. → Aza Toth 11:21, 30 October 2006 (UTC)
 * Sorry, I do not know how I overlooked that edit link. I just tested it by adding a file for November prematurely. JRSpriggs 08:13, 31 October 2006 (UTC)
 * No problem, perhaps I should had marked it better? → Aza Toth 11:23, 31 October 2006 (UTC)

More User:WAREL clones, and blocking
Current (possibly incomplete) list:


 * User:218.133.184.53
 * User:64.213.188.94
 * User:DEWEY
 * User:DYLAN LENNON
 * User:JLISP
 * User:KLIP
 * User:KOJIN
 * User:MACHIDA
 * User:MORI
 * User:POP JAM
 * User:SADTW
 * User:Suslin
 * User:TANAKA
 * User:TELL ME that
 * User:WATARU


 * Should we block more of these? So far, I've only been blocking them if the edits are incorrect, but a number of them are still live.  Was there any ArbCom action taken against him?  I've lost track.  &mdash; Arthur Rubin |  (talk) 21:34, 25 October 2006 (UTC)


 * There has never been an ArbCom action, and none is necessary in my opinion. I think the clones can be blocked on sight. -- Jitse Niesen (talk) 01:24, 26 October 2006 (UTC)


 * Yes I think Jitse is correct. The only question I would have is how do we know they are clones? Paul August &#9742; 03:22, 26 October 2006 (UTC)


 * I blocked User:TELL ME that indefinitely after another edit to perfect number. -- Jitse Niesen (talk) 06:13, 26 October 2006 (UTC)

Add User:Lucky Eight; Big Omega in perfect number. Septentrionalis 15:28, 31 October 2006 (UTC)

Texvc changes
Some new stuff in texvc...


 * Environment array:


 * Under/Overbrace:now they work as intended:

\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq \dashv \asymp \doteq \parallel \longleftrightarrow (awaiting scape at the moment)
 * Some new symbols:

→ Aza Toth 19:31, 29 October 2006 (UTC)


 * Making under/overbrace work properly is great. Many thanks if you are responsible for this. Do you know whether there are any plans to regenerate the PNGs of formulas containing these braces? -- Jitse Niesen (talk) 01:26, 31 October 2006 (UTC)
 * They will probably regenerate over time, but there will be no mass-purrge, as there is over one million images. → Aza Toth 01:28, 31 October 2006 (UTC)
 * Why do you think they'll regenerate? I realize you must know a bit about texvc, because you managed to write a patch, but I still have my doubts. Do you know of any way to make them regenerate, except for deleting all PNGs (which is not an option, as you say)?
 * They won't regenerate, they are static, talked with Tim about the problem, perhaps a solution will emerge. → Aza Toth 12:44, 31 October 2006 (UTC)
 * Incidentally, what does "scape" mean? -- Jitse Niesen (talk) 12:29, 31 October 2006 (UTC)
 * see scap → Aza Toth 12:44, 31 October 2006 (UTC)

Scape done
Ok, the symbols have been scaped now, here they are:

also, one symbol was mission from the help page, that is \rightleftharpoons: $$\rightleftharpoons$$ → Aza Toth 12:05, 31 October 2006 (UTC)
 * So, is all this stuff incorporated into Help:Displaying a formula now? JRSpriggs 12:13, 31 October 2006 (UTC)
 * I'm at the moment updating the page at meta, I'll transviki when I'm done. → Aza Toth 12:44, 31 October 2006 (UTC)

Poor man’s eqnarray
Support for the array environment may be good news for equation series, so we no longer must mix TeX and tables. Compare the following use of array to the current version of this derivation.
 * $$\begin{array}{rcl}

0 & < & \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx \\ & = & \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\ & = & \int_0^1 \left(x^6-4x^5+5x^4-4x^2+4-\frac{4}{1+x^2}\right) \,dx \\ & = & \left.\frac{x^7}{7}-\frac{2x^6}{3}+ x^5- \frac{4x^3}{3}+4x-4\arctan{x}\,\right|_0^1 \\ & = & \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\ \\ & = & \frac{22}{7}-\pi. \end{array}$$ Unfortunately, this example reveals two problems. (1) TeX is not using display style for the equations. (2) TeX cannot handle the elaborate labels with their wiki links. --KSmrqT 15:53, 31 October 2006 (UTC)
 * 1: dont fully understand, 2: problem is that it's saved as an image, and at parse time we don't fully know the image size, if we did, we could parse wikilinks somewhat and create an imagemap.. → Aza Toth 17:38, 31 October 2006 (UTC)


 * To see the need for display style, compare the appearance of the right-hand side of the first line when inside an array,
 * $$\begin{array}{c}\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx\end{array}$$
 * with its appearance otherwise:
 * $$\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx .$$
 * Fortunately, texvc now seems to support the \displaystyle command, so we can work a little harder and produce this.
 * $$\begin{array}{rcl}

0 & < & \displaystyle \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx \\ & = & \displaystyle \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\ & = & \displaystyle \int_0^1 \left(x^6-4x^5+5x^4-4x^2+4-\frac{4}{1+x^2}\right) \,dx \\ & = & \displaystyle \left.\frac{x^7}{7}-\frac{2x^6}{3}+ x^5- \frac{4x^3}{3}+4x-4\arctan{x}\,\right|_0^1 \\ & = & \displaystyle \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\ \\ & = & \displaystyle \frac{22}{7}-\pi. \end{array}$$
 * Unfortunately, although the individual lines are acceptable, the spacing between lines is cramped. Compare the example above to the version at the link. The eqnarray environment would automatically handle both displaystyle and line spacing — if we had it. --KSmrqT 21:40, 31 October 2006 (UTC)
 * A little experimentation suggests a tolerable solution to line spacing. Here is an example.
 * $$\begin{array}{rcl}

0 & < & \displaystyle \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx \\[1em] & = & \displaystyle \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\[1em] & = & \displaystyle \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\ \\[1em] & = & \displaystyle \frac{22}{7}-\pi. \end{array}$$
 * For easy reference, the environment is \begin{array}{rcl}, and the second line has the markup
 * &amp; = &amp; \displaystyle \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx \\[1em]
 * We're still missing a little of what we need for commutative diagrams, but this is progress. Enjoy! --KSmrqT 20:12, 1 November 2006 (UTC)
 * This is how

$$\begin{align} 0 & < \int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx                                                    &&                                                                                                   \\ & = \int_0^1\frac{x^4-4x^5+6x^6-4x^7+x^8}{1+x^2}\,dx                                        && \text{(expanded terms in numerator)}                                                              \\ & = \int_0^1 \left(x^6-4x^5+5x^4-4x^2+4-\frac{4}{1+x^2}\right) \,dx                         && \text{(performed polynomial long division, an important aspect of formulating algebraic geometry)}\\ & = \left.\frac{x^7}{7}-\frac{2x^6}{3}+ x^5- \frac{4x^3}{3}+4x-4\arctan{x}\,\right|_0^1     && \text{(definite integration)}                                                                     \\ & = \frac{1}{7}-\frac{2}{3}+1-\frac{4}{3}+4-\pi\                                            && \text{(substitute one for x, then zero for x, and subtract them—arctan(1) = π/4)}                 \\ & = \frac{22}{7}-\pi                                                                        && \text{(addition)} \end{align}$$ will look after bug 7774 is applied: → Aza Toth 21:18, 1 November 2006 (UTC)

Things in the queue
bug 7774 is in the queue now, adding some more goofy stuff. → Aza Toth 21:54, 31 October 2006 (UTC)

Zeroes or zeros?
Just a quick question: do we have any guidelines over which we prefer - 'zeros' or 'zeroes'? This has probably been discussed before, but I can't see where ... Madmath789 18:33, 30 October 2006 (UTC)
 * My personal preference is for "zeroes". "Zeros" really should be pronounced "zee-ross". But I think there is no great need for project-wide consistency in spelling. --Trovatore 18:40, 30 October 2006 (UTC)
 * Zeros wins by about four to one on Google. —David Eppstein 18:42, 30 October 2006 (UTC)


 * Dictionary.com and Merriam-Webster both give either as acceptable alternatives. I prefer "zeroes", on the infamous model of "potatoes" and "tomatoes", "credos" notwithstanding. Still, since both are correct, we shouldn't change either. Ryan Reich 19:00, 30 October 2006 (UTC)


 * Isn't this just another U.S. spelling vs. U.K. spelling thing? There are already guidelines on that.--C S (Talk) 21:11, 30 October 2006 (UTC)


 * So which one do you think is US and which one do you think is UK? —David Eppstein 21:19, 30 October 2006 (UTC)


 * I had thought "zeros" was US and "zeroes" was UK, but I'm not so sure anymore. OED only gives "zeroes" as plural with no mention of "zeros".  --C S (Talk) 08:12, 1 November 2006 (UTC)


 * According to The American Heritage® Book of English Usage. A Practical and Authoritative Guide to Contemporary English. 1996.:
 * Most nouns ending in o preceded by a consonant also usually add -s to form the plural: alto, altos; casino, casinos; ego, egos; Latino, Latinos; memo, memos; neutrino, neutrinos; poncho, ponchos; silo, silos. However, some nouns ending in o preceded by a consonant add -es: echo, echoes; hero, heroes; jingo, jingoes; no, noes; potato, potatoes; tomato, tomatoes. Some nouns ending in o preceded by a consonant have two plural forms (the preferred form is given first): buffaloes or buffalos; cargoes or cargos; desperadoes or desperados; halos or haloes; mosquitoes or mosquitos; zeros or zeroes..
 * Although both are correct, it seems that zeroes is mainly used in UK. A good place to ask could be --pom 23:21, 30 October 2006 (UTC)


 * Restricting the Google search to .uk addresses didn't seem to make much difference to the much greater number of zeros than zeroes in my Google searches. —David Eppstein 23:28, 30 October 2006 (UTC)


 * My 1979 copy of the (UK) Oxford school dictionary has zeros as the only plural. So us birt don't have a strong claim to zeroes.--Salix alba (talk) 23:39, 30 October 2006 (UTC)
 * It seems to be quite mysterious. I found two american books with zeroes as the only plural (Essentials of English Grammar- a practical guide to the mastery of English by L. Sue Baugh, McGraw-Hill Professional 1993 and Prentice-Hall Handbook for Writer by William Charvat, Glenn H. Leggett, 1982). To the opposite I found two "old" books with zeros as the only plural (Practical Lessons in English- made brief by the omission of non-essentials. 1880 and An English Grammar for Higher Grades in Grammar Schools. 1894). pom 23:58, 30 October 2006 (UTC)

ZEROES. Dmharvey 00:11, 31 October 2006 (UTC)


 * I'm Brit, and I think I've always used "zeros"... that said, given either is acceptable, then it doesn't matter which gets used. Tompw 12:15, 31 October 2006 (UTC)

I looked it up in the OED and found that they had listed 'the' plural as "zeroes". However, I saw that the form "zeroes" was not present in any of the quotations, which all had "zeros", so I sent an e-mail about it and recieved a response the conclusion of which was that "This is a complex matter, and the current recommended form for ZERO, both here and in our dictionaries of current English, is ZEROS". —Centrx→talk &bull; 15:29, 2 November 2006 (UTC)

Tensors
Tensor needs a lot of work. Discusssions a long time ago left the treatment fragmented over pages. Talk:Intermediate treatment of tensors has a recent long comment. I think a merge of Intermediate treatment of tensors into tensor might start some much-needed consolidation and imnprovement. Charles Matthews 10:51, 2 November 2006 (UTC)


 * On a related note: I've long thought that tensor product needs a complete rewrite. I started a draft at User:Fropuff/Draft 8 some time ago but I haven't had time to finish it. If someone wants to take the material and run with it they are more than welcome. -- Fropuff 05:16, 3 November 2006 (UTC)

Research Wikipedias
I am a member of the small community people who actively research tetration. For the last few years I have operated tetration.org, one of the main resources for tetration on the Internet. I became invoked with Wikipedia when I noted that Wikipedia’s entry on tetration was rapidly climbing to the top of search engine queries on tetration. Being very impressed with the goals and achievements of Wikipedia, I contacted other people researching tetration and suggested that we collectively become involved in editing Wikipedia’s tetration entry.

I guess the other folks weren’t as infatuated with Wikipedia as I was, so I ended up making what I thought were some reasonable edits to the tetration and Ackermann function. Tetration is an area of mathematics that attracts much attention from the public and amateur mathematicians while only now is it just becoming a legitimate are of mathematics research. The problem is that people keep adding their non-peer reviewed research to the tetration page on extending tetration beyond the natural numbers Tetration - Extension to real numbers. I didn’t want to try and play cop on the tetration page, but neither did I feel comfortable remaining affiliated with an entry that I felt continually misrepresented what was known about tetration. The solution to the problem is to publish articles in peer reviewed journals that clarify what is and isn’t known about tetration.

My personal problem is that I have a large backlog of research on tetration and related subjects that I need to organize and publish. Just because Wikipedia is not appropriate for documenting research doesn’t mean that the underlying MediaWiki software isn’t magnificence in documenting research; hey, just ask the CIA. I have a new website at tetration.net using MediaWiki; having Asperger’s and over a dozen years as a software developer MediaWiki helps me to do a brain dump of my work. I like the idea of pulling my research together using MediaWiki, publishing it in a peer-reviewed journals and then releasing the entries constituting the peer-reviewed material under GFDL.

The reason I posted this here is I need help in understanding the etiquette and GFDL issues in using stuff like snippets of TeX from the Wikipedia. Can I just cite a Wikipedia entry for a snippet of TeX or must I release the entry under GFDL. Almost all of the TeX snippets I have used are at least slightly edited, how does that impact things. Daniel Geisler 21:23, 2 November 2006 (UTC)


 * I think that an isolated brief formula from Wikipedia would fall under the "fair use" exception to the copyright law. So you would not need to do more than acknowledge the source. JRSpriggs 08:37, 3 November 2006 (UTC)

Leon Henkin
Can anyone confirm that Leon Henkin has died? Charles Matthews 13:10, 3 November 2006 (UTC)


 * Yes, he died on Wednesday, 2006-11-01. Contact Barb at the department via their website if more information is needed. --KSmrqT 20:04, 3 November 2006 (UTC)

Texvc updated again
This was a rather large update, that's wwhy it took such a long time. First of all, bug 1182 is fixed, so non greek greek symbols ($$\Alpha \Beta\,\!$$) are not displayed as italics. Whats new is as following (\binom is more of a bugfix):


 * Some new symbols that where forgotten:

→ Aza Toth 14:36, 4 November 2006 (UTC)
 * Awesome! Thank god for the align stuff, I've needed that many times before. — Mets501 (talk) 14:49, 4 November 2006 (UTC)

Factorization
I have a question about Factorization. Should it stay? Or is it too textbook-like? Thanks for your opinions. — Mets501 (talk) 15:01, 4 November 2006 (UTC)

L'Hôpital's rule
L'Hôpital's rule has had a couple of new proofs added to it, these were mentioned on Village pump(proposals). Could someone have a look over the changes. --Salix alba (talk) 18:58, 30 October 2006 (UTC)


 * I've no time right now, but at first glance both the old and the new proofs look wrong and in any case unconvincing and not well presented. If we need to include a proof at all, let's not do the 0.999... thing but give one solid proof well presented. --Lambiam Talk  05:59, 31 October 2006 (UTC)


 * I'll second that opinion. CMummert 11:39, 31 October 2006 (UTC)


 * Well, I already removed the "proof by definition", which was egregiously wrong. The other two are "right" in the sense that they can be made to work, but I have not really looked at them. Ryan Reich 14:31, 31 October 2006 (UTC)
 * The "proof by local linearity" assumes that we can substitute the tangents to f and g instead of both numerator and denominator without changing the limit. This may be a way of explaining the theorem, but it's not a proof. So I removed it. Septentrionalis 15:33, 31 October 2006 (UTC)
 * You could make that argument work if you went to the trouble of doing epsilons, though. This is not a math book, however, so I agree with your choice.  The "canonical" Cauchy proof is good enough. Ryan Reich 15:52, 31 October 2006 (UTC)

This is kind of off-topic, but anyone have any idea on why the titles of the articles on the person and rule uses L'Hôpital instead of L'Hospital? Is the reason that this is more common (if it is)? Certainly for the article on the person, shouldn't we stick with the spelling used by the person (L'Hospital) in question? I believe that is the usual guideline people have followed in other cases (as with umlauts), even when people often mangle the name in error. --C S (Talk) 00:12, 5 November 2006 (UTC)


 * The French Wikipedia, in its article Guillaume François Antoine, marquis de L'Hôpital, has this to say about it (in my quick and sloppy translation):
 * His name is also written L'Hospital. Contrary to what one might think, the circumflex accent is not an anachronism: while his book does not include an author's name, his friend Varignon, in the supplements to the book he published (1725), always writes his name with a circumflex accent, and in the encyclopedia of d'Alembert-Diderot one finds “L'Hopital”, without accent nor s.
 * --Lambiam Talk 07:40, 5 November 2006 (UTC)

Problem
Can anyone figure out why this is producing an error?

$$ \begin{alignat}{2} (a+b)^{m+1} & = a(a+b)^m + b(a+b)^m &\quad& \text{by the inductive hypothesis} \\ & = a \sum_{k=0}^m { m \choose k } a^{m-k} b^k + b \sum_{j=0}^m { m \choose j } a^{m-j} b^j && \text{by the inductive hypothesis} \\ & = \sum_{k=0}^m { m \choose k } a^{m-k+1} b^k + \sum_{j=0}^m { m \choose j } a^{m-j} b^{j+1} && \text{by multiplying through by } a \text{ and } b \\ & = a^{m+1} + \sum_{k=1}^m { m \choose k } a^{m-k+1} b^k + \sum_{j=0}^m { m \choose j } a^{m-j} b^{j+1} && \text{by pulling out the } k=0 \text{ term} \\ & = a^{m+1} + \sum_{k=1}^m { m \choose k } a^{m-k+1} b^k + \sum_{k=1}^{m+1} { m \choose k-1 }a^{m-k+1}b^{k} && \text{by letting } j = k-1 \\ & = a^{m+1} + \sum_{k=1}^m { m \choose k } a^{m-k+1}b^k + \sum_{k=1}^{m} { m \choose k-1 }a^{m+1-k}b^{k} + b^{m+1} && \text{by pulling out the } k=m+1 \text{ term from the right hand side} \\ & = a^{m+1} + b^{m+1} + \sum_{k=1}^m \left[ { m \choose k } + { m \choose k-1 } \right] a^{m+1-k}b^k && \text{by combining the sums} \\ & = a^{m+1} + b^{m+1} + \sum_{k=1}^m { m+1 \choose k } a^{m+1-k} b^k && \text{from Pascals rule} \\ & = \sum_{k=0}^{m+1} { m+1 \choose k } a^{m+1-k}b^k && \text{by adding in the } m+1 \text{ terms.} \end{alignat} $$


 * It didn't like the ' in Pascal's, I can see if I can fix that→ Aza Toth 15:43, 4 November 2006 (UTC)
 * The  would be in normal LaTeX as , but that's not allowed at the moment. Perhaps fill a bug request about that. → Aza Toth 15:48, 4 November 2006 (UTC)
 * Thanks! I don't know if that will work in the article though, it's quite a bit too wide. — Mets501 (talk) 16:05, 4 November 2006 (UTC)


 * I added in some spaces to this example so the text doesn't get jammed up against the formulae. —David Eppstein 17:43, 4 November 2006 (UTC)

Probability-based strategy
I'm planning on nominating Probability-based strategy for deletion (rationale on article talk page), and I suppose the Catalin Barboianu BLP as well. I thought I'd check see if the readership of this page thinks I'm mistaken before I do so. Pete.Hurd 22:10, 6 November 2006 (UTC)
 * No objection from me, although it's not exactly my field. &mdash; Arthur Rubin | (talk) 00:30, 7 November 2006 (UTC)
 * There is (or was) some material on randomized strategies in some Wp article I worked on over two years ago. This article seems like a confused form of that. --CSTAR 02:01, 7 November 2006 (UTC)

Problem editting a section of this talk page
When Werdnabot ran yesterday, it added the section "General Comment about Math articles from a non-mathematician" from this talk page to the archive, but it did not remove it from this page. I tried to remove it from this page manually, but I could not. There is a part of that section which does not appear in my edit window, and thus I cannot delete that part. Can someone else fix it, please? JRSpriggs 09:10, 7 November 2006 (UTC)
 * The part which cannot be editted begins with "Suggested structure of a mathematics article" bracketted by " " and "< / h 2 >" (with out the blanks, which I added to prevent the problem from happening again here). JRSpriggs 09:15, 7 November 2006 (UTC)
 * Manually removed. --Lambiam Talk  11:10, 7 November 2006 (UTC)
 * To Lambiam: Thank you very much for your help. After I logged out yesterday, it occurred to me that perhaps I should have tried to edit using the "edit this page" tab at the top of the article instead of the "edit" button associated with the section. Is that how you did it? Were you using Mozilla's Firefox as I am or did you use Internet Explorer or what? JRSpriggs 06:10, 8 November 2006 (UTC)
 * That's how I did it using Firefox. Alternatively, I could have edited the various subsections out separately one by one, but that seemed like more work. Did the bot get confused by the html-style header? I did not carefully examine things, but had the impression that some other, not archived sections were decidedly older than this one. --Lambiam Talk  10:38, 8 November 2006 (UTC)

I do not know why Werdnabot failed to remove that section. I can only guess that it might have to do with the embedded " "(minus blanks). I suspect that that code generates the same kind of section separation indication which stopped my editting from reaching the remainder of the section (as a normal section header beginning with ==== would do). As far as the timing of the archiving goes, Werdnabot seems to base its decision on time-stamps with the format produced by ~. If a different format is used, as with, then it does not count. If you examine the section in question in the archive, you will see that the last entry is on November 1, but it uses the "unsigned" format. JRSpriggs 07:54, 9 November 2006 (UTC)

Portal suggestions needed
The lists of suggestions for selected article / selected picture / "Did you know?" for the mathematics portal is begining to get rather small. Could people try and add some items to the lists? This is especially true of the images, as good/interesting maths images can be hard to track down. Tompw 20:17, 8 November 2006 (UTC)
 * I guess all the articles in Category:A-Class mathematics articles, Category:GA-Class mathematics articles and possibly Category:Bplus-Class mathematics articles would be candidates for selected articles. I'm slowly building Category:Mathematics images which might be a good source for pictures. --Salix alba (talk) 11:33, 9 November 2006 (UTC)

Pseudo data up for deletion.
Pseudo data is up for deletion. Current version is non-mathematical although the term seems to be used quite widely in statistics. --Salix alba (talk) 12:47, 9 November 2006 (UTC)

Navboxes for awards?
Please comment: Mikio Sato. My comment: silliness. --Pjacobi 09:57, 10 November 2006 (UTC)
 * Navboxes for awards are a bad idea. I dislike them intensely as they add clutter.  Click on the category if you want to see the winners. 165.189.91.148 19:16, 10 November 2006 (UTC)

Probably WAREL
Anyone have any opinions on this edit? I'm almost certain that this "Imadada" is the newest WAREL clone, but that doesn't necessarily mean he's wrong. I can't get Babelfish to translate the Japanese page for me; it coughs up some kind of error and asks me to send an e-mail. --Trovatore 20:42, 12 November 2006 (UTC)
 * This translation worked for me. darkliight[&pi;alk] 21:38, 12 November 2006 (UTC)
 * That link just brings up the ja.wiki article, untranslated. --Trovatore 21:42, 12 November 2006 (UTC)


 * It is clearly about fields:
 * The body (you want in algebra, field, körper and corps), it is of gathering which has the algebra structure which can make arithmetical operation free. [...] As for K being monoid in regard to the multiplication, the origin other than 0 forms the group: [...]
 * The Japanese article links to our Field (mathematics), which in turn also links to 体 (数学). --Lambiam Talk  21:54, 12 November 2006 (UTC)
 * Postscriptum. I forgot to include: "Whatever kind of origin a of K, concerning b, ab = ba is filled up." The Japanese text (according to the Babelfish translation) the goes into a discussion of the non-commutative case and possible terminological confusion, and does mention, in small print, the term "division ring". Altogether, the link appears reasonable. --Lambiam Talk  22:11, 12 November 2006 (UTC)
 * Postscriptum 2. The inserted link is actually to 斜体, which is a redirect to 体 (数学), which is the Babelfish-translated article. The term "斜体" occurs in the article and is translated by Babelfish as "non-commutative field", and in the article itself as "skew field". --Lambiam Talk  22:23, 12 November 2006 (UTC)
 * I agree with Lambiam, the link is fine. I'm not convinced Imadada is WAREL, because WAREL maintained that division rings are called 体 in the Japanese Wikipedia. -- Jitse Niesen (talk) 01:27, 13 November 2006 (UTC)

Wiki project mathematics userbox
User:NerdyNSK kindly created a userbox for the project, which briefy existed on /Participants. How do people feel about this?
 * Personally I thinks its on the whole a good idea, as it would help publicise the project. Of couse whether to display the box is entirly up to the user in question. --Salix alba (talk) 18:52, 6 November 2006 (UTC)


 * What's wrong with ?
 * —David Eppstein 19:01, 6 November 2006 (UTC)
 * —David Eppstein 19:01, 6 November 2006 (UTC)


 * Bad typesetting. Fredrik Johansson 19:07, 6 November 2006 (UTC)
 * More to the point should we include then on WikiProject Mathematics/Participants? --Salix alba (talk) 19:09, 6 November 2006 (UTC)


 * The 'new' box NerdyNSK made is quite OK. However, the 'old' box Template:User WP Math is about a year old, and employed by (say) three scores of users; the new box User:NerdyNSK/Userboxes/WikiProject Mathematics was made less than two weeks ago and is employed by two users, NerdyNSK and Salix alba.  I don't see an essential typesetting difference; and while I have to admit that the icon on the old box is a bit negative :-), I don't think most of those math project people who already have acquired the old box would feel sufficient interest or reason to change box.  (Besides, I think it looks rather neat.)  Thus, for uniformity, I rather recommend including the old box (and recommend NerdyNSK and Salix alba to switch). --JoergenB 18:32, 10 November 2006 (UTC)
 * Moreover, the old box is consistent with tag. pom 19:02, 10 November 2006 (UTC)

The old one should be modified to put the whole name of this project on the second line as in the new one. Both boxes should be shorter horizontally to reduce the empty space on the right. Then I would prefer the old one. If you want to avoid negativity, try using $$e^{2 \pi i}\!$$ instead of $$e^{i \pi}\!$$. JRSpriggs 08:24, 11 November 2006 (UTC)
 * I had a play with changing text size in my browser, and found that the text in both boxes is a single line which wraps differently. With a bigger font size they both have wiki project mathematics on the second line, with a smaller size they both wrap this text. It could be possible to add a  tag here, however that might be a bad plan as it it might render badly on some browsers, or where the users font size is different. --Salix alba (talk) 22:01, 12 November 2006 (UTC)


 * The existing box with the existing sizes of the icon and text areas lines up nicely with other WikiProject membership boxes (such as the CS one, which I also use in my user page). A replacement box with different dimensions wouldn't line up so well. So I urge keeping the dimensions and the text font the same as they are now. I don't so much care what happens within the icon, though I think a nicely typeset Euler formula is better than a faux-typewritten generic function. —David Eppstein 00:05, 14 November 2006 (UTC)
 * Good point, David. I withdraw my suggestion that the boxes be made narrower. JRSpriggs 04:50, 14 November 2006 (UTC)

Game theory and importance rankings
Hello folks - I noticed an inconsistency with your importance rankings, and I thought maybe somebody might want to take a look. Nash equilibrium is rated "high" importance while Game theory is ranked "mid". It seems to me that a concept in a field ought not be more important than the field itself. I don't really care which way it goes, or even if it gets fixed, but I thought I'd let you all know. --best, kevin [kzollman][talk] 20:15, 10 November 2006 (UTC)


 * Agreed, I've changed the ranking of Game theory since no-one else has commented so far. I think the ranking scheme is pretty informal, so unless anyone else says otherwise, feel free to change the rankings of articles in cases where you feel the change is warranted. Cedars 00:52, 14 November 2006 (UTC)

List of all ten types of Steiner surface?
From Steiner surface: "There are ten different types, including the Roman surface and cross-cap." - List of all ten? -- 201.51.252.63 23:55, 12 November 2006 (UTC)


 * The article consists of three sentences and a reference. Yes, a reference! In fact, a relevant reference, and online so it's easy to access. Furthermore, that page has many, many further references. Or are you asking us to expand the article with the contents cited? --KSmrqT 23:53, 13 November 2006 (UTC)

FYI - Definable number tagged as Original Research
Just an FYI, since it falls under this WikiProject, I tagged the article Definable number with the Original Research tag. It's an interesting article, but it does not appear to be based on external published information. Rather, it is an exploration by the article's authors into the concept of definability. In fact, in the introductory paragraph, the article even concedes that the phrase "definable number" isn't a standard mathematical term, which begs the question if "Definable number" is even the proper title for the article!

Anyway, I'd recommend that interested people here check out the article. If you are familiar with references regarding "definable numbers", feel free to add them to verify that the article isn't just original research. Or, if the article does appear to be entirely original research, then it should be deleted from Wikipedia and/or moved to a site that allows for original mathematical research articles. I didn't immediately tag the article for deletion, though, since I thought it would be more prudent to let you guys and the article's authors try and address the concern first. It is, after all, a good read, so I'd rather see it be fixed than deleted. Dugwiki 18:53, 13 November 2006 (UTC)


 * The concept of a "definable number", under that name and as distinct from computable numbers, certainly appears in the literature, notably in Turing's "On computable numbers with an application to the Entscheidungsproblem" . I think the problem with the article is not OR so much as that it doesn't cite sources and should. —David Eppstein 19:04, 13 November 2006 (UTC)


 * It appears to me that Turing does not attempt to define "definable number" in that paper, or develop any theory of what a "definable number" in general is. He talks about the existence of a definable number that's not computable, but it's more like "here, you can see that this number is definable", not "this is what a definable number is in general". So I would take that to be more of a nonce term, not something we can write an article about. I would be strongly against writing an article based mainly on Turing's notion of definable taken from that paper, because of the fact that (based really just on a text search; I haven't read the paper yet in detail), he never does really define it. --Trovatore 19:20, 13 November 2006 (UTC)


 * Moved to definable real number. There is a fair amount that comes up when you Google that term. Charles Matthews 19:23, 13 November 2006 (UTC)


 * This discussion should move (has moved) to the talk page. CMummert 19:37, 13 November 2006 (UTC)

Commutative diagram
hi, folks. hope someone could help me. how does one make one of those and put it in an article? thanks. Mct mht 05:17, 14 November 2006 (UTC)


 * We do not have full TeX support, and producing diagrams directly in SVG is awkward, so the usual practice is to use an offline method to create a PNG image. A good example is Image:Snake lemma nat.png, which looks like this (in miniature):
 * [[Image:Snake lemma nat.png|thumb|240px|none|Commutative diagram]]
 * The image page documents the means of its production. --KSmrqT 07:57, 14 November 2006 (UTC)

Math articles lacking external references
(Originally posted on the wrong talk page. Moved here.) Just wanted to give you guys a heads up that in the course of perusing various mathematics articles recently I noticed a surprising number of them had no cited references. The information was accurate in these articles, far as I could tell, but they had little or no external citation. It might be a good idea for someone in this project with access to appropriate texts to try and add references that direct readers to verification.

In particular, it would be very nice if articles that state a theorem provide a reader with a citation that leads to an actual proof of that theorem. I've had a few times now where I read something, said "Hmm, that sounds true", but then wasn't quite sure how to go about proving it. Providing a reference or link to actual proofs would be a nice educational aid. Just a thought. Dugwiki 17:13, 6 November 2006 (UTC)


 * There are guidelines for citation in math articles that encourage the sort of citation you are looking for. When you read articles, you can use the unreferenced and fact tags to point out where you would like to see citations.  If an article has no sources at all,  put  at the top. Or put  directly after a particular fact that you would like to see cited (but if there are many such facts, just use  ). Pages marked with these tags are listed here for others to see.


 * Note that some math articles list good reference books at the bottom but don't give explicit inline citations. If you see that there are references at the bottom, it may be more polite to ask for a cite on the talk page first, before putting templates on the article itself.  CMummert 17:49, 6 November 2006 (UTC)


 * I think we should bear in mind that mathematics articles are essentially composed of 'facts', and that for each such fact there will be someone who will find it unfamiliar. We could end up with yards of citations of 'trivia'; they are not trivia, but what has been called 'sorites', the sort of thing a really complete treatment puts in a reference section. This could certainly be detrimental. If someone wants a citation of the fact that the composition of group homomorphisms is a group homomorphism, it is (a) not the sort of thing encyclopedias trouble about, (b) is a timewasting thing to look up, and removing it as unsupported by citation would essentially be vandalism, and (c) it is the sort of thing that anyone is that bothered can and should verify in their own time. Charles Matthews 19:20, 6 November 2006 (UTC)


 * I think everyone here agrees that those are the sorts of facts that are best sourced by having general references at the end of the article. The new guidelines recommend putting a few inline citations to the best general references at the beginning, and otherwise not putting inline citations for easily verifiable facts; this is a sort of compromise between having no inline citations and having one for every trivial fact.  CMummert 19:41, 6 November 2006 (UTC)

If one mathematician 200 years ago proved a theorem, the fact stands for all time. However, the original proof may never have been translated into English, may use methods unfamiliar to modern readers, or may be long and difficult. Even when the proof is modern, it may be unhelpful to most readers who would use the theorem. Notable examples include the four color theorem and Fermat's Last Theorem, where both theorems are easy to state and use, but where both proofs are horrendous. It is quite common for a rigorous textbook full of proofs to omit certain proofs that are especially technical and that provide little insight.
 * Thanks for your interest in improving our mathematics articles. Some comments:
 * Most advanced mathematics readers and editors depend on expert knowledge for verification, not blind trust in numerous citations or ignorant consensus. One reference to a reputable source at the end of an article is often sufficient. Mathematics is based on proofs, not observations or opinions, so is not as vulnerable to quality control problems as other topics.
 * That said, I personally enjoy knowing the history and personalities, seeing original sources, and exploring the rich connections modern mathematics has found among diverse topics. Such peripheral content is welcome, so long as it does not detract from the central content. Unfortunately, this “Further reading” material can be time-consuming to provide, and may be of less interest to the casual reader. Frankly, we count ourselves lucky to have so much as a stub article on many of our more advanced topics, providing information found nowhere else on the web.
 * If you are curious about a proof, please take advantage of our Reference desk/Mathematics. And, of course, if an article (not already marked stub) has no references, a note on its talk page or an unreferenced tag would help bring it to our attention. --KSmrqT 19:27, 6 November 2006 (UTC)


 * Just to reply to some of the above comments, since it appears some of you might think I am an inexperienced user looking for advice on how to tag articles, let me clarify. I'm already tagging articles as unreferenced as I see them when they have no references at all.  My post here, however, was to point out to your project that I have come across a disappointing (to me) number of such unreferenced math articles.  So this post is to make the project aware of a possible trend that is causing too many math articles to go unreferenced.


 * Second, for those thinking I'm looking for explicitly detailed citations for every statement, I was not suggesting a line by line citation is necessary. In many cases, a general citation to a text that discusses the topic at hand is probably sufficient, and a single citation to a text discussing or proving an important  theorem in an article is likewise probably sufficient reference.  The problem is that the articles that spurred my post did not even meet that minimal level of citation.


 * So what I am recommending is a broad, general citation review and clean-up of the math articles. It is a task that I would gladly do myself, had I the math resources available to provide accurate references.  Unfortunately, I don't, so I'm bringing it up here for project editors who do have access to appropriate resources so they can hopefully go through the math articles in a systematic manner checking for and adding references as needed. Hope that clears up what I was getting at.  Good luck! Dugwiki 17:57, 9 November 2006 (UTC)


 * I don't think there is such a trend. I would say the trend that exists is in the opposite direction.  Newer articles are usually better referenced, and the ones completely without references (unless just some random stub) are from more than two years ago.  This kind of thing has been discussed a bunch recently...that's the reason for some of the responses you've been getting.  Rest assured, people have long pondered this matter, discussed it frequently, and well, if things aren't getting done, it's because people are busy.  If you want this kind of big effort, it's better to get involved yourself.  I expect most people don't see a pressing need to dig up references for the most elementary stuff that a lot of people know; they're too busy with verifying the tricky stuff that sounds plausible but could be utter crap.  --C S (Talk) 13:00, 10 November 2006 (UTC)


 * There are a lot of ongoing disagreements about citation, but I think that every opinion expressed by members of this project has been in favor of an appropriately thorough level of citation. There is a large number of "legacy" articles with no references at all, and this is unfortunate, but these are slowly being fixed (or tagged) as they are discovered.
 * I wonder if Jitse's bot could make a list of math articles that have no ==References== section. I could do it from a database dump, but when I tried to download a dump a week ago I noticed they haven't been successful for a long time.  The goal is:  make a list of articles with no references section that are vaguely associated to mathematics. Until this is done, we have to rely on individual pages being tagged.  CMummert 01:29, 10 November 2006 (UTC)


 * Unfortunately, my bot does not download the actual articles, so it can't do that. But the last database dump seems to be okay. Otherwise, go bother User:Mathbot who does download the complete articles, I think. -- Jitse Niesen (talk) 09:13, 10 November 2006 (UTC)


 * OK, I'll do it. Does you bot have the ability to generate a list of the articles that it considers to be "math" articles? Even as a plain text file, this would be very helpful for me. CMummert 13:26, 10 November 2006 (UTC)


 * The list of all math articles is available at list of mathematics articles. My bot (mathbot) has a copy of all math articles on Wikipedia but is rather old (several months). I can have it download them again (which would take a couple of days, 14,000 articles is a lot to download one by one :) and I could run a search through them. But if you want to do it with the database dump, that will work too. Oleg Alexandrov (talk) 16:18, 10 November 2006 (UTC)


 * One place to start if you want to try using a bot might be to search for math articles that do not contain a specific header for either References or External Links. I've also noticed a template for PlanetMath used in some articles; assuming that's an acceptable reference you could also probably filter those out as well.  Also, for my part, I've started trying to systematically go through all the math articles and mark ones with no references using the unreferenced tag.  My rough guess is maybe 1/5 or so are ending up so tagged, with most of the unreferenced articles being shorter articles talking about specific definitions or theorems as opposed to broader topics (eg Supremum is unreferenced, but Interval (mathematics) has references).  So I'm thinking that a main culprit is sub-topics and side articles of larger articles that are split off from the main discussion for space reasons, that sort of thing.  Dugwiki 16:39, 10 November 2006 (UTC)


 * I agree that short articles are the major contributors. I'm waiting while I download a database dump; the script is written and I'll post the results this evening. CMummert 16:53, 10 November 2006 (UTC)

In the process of going through these articles, I took a closer look at PlanetMath and I wasn't sure if it can be used as a sole reference. It appears that PlanetMath is a Wiki style site for math articles, which is great, but like Wiki is doesn't seem to have a formalized fact checking scheme. I couldn't find any formal policy on PlanetMath for verification, fact checking, and so on. Therefore I'm not sure it can technically be used as the only reference for an article. It makes for a good external link, and a good source for creating new Wiki stub articles, but ultimately the Wiki articles would need a source such as a textbook from a major publisher or a math journal with a formal peer review system to use as a formal reference. Unless, that is, I'm missing something about how PlanetMath works. Dugwiki 17:24, 10 November 2006 (UTC)


 * My feeling is that, at least for elementary mathematics, a lot of material can be self-verifying: the correctness of an article may often be seen from the article itself, while the sources are more important for justifying notability, guarding against WP:OR, and documenting assertions about the history of the mathematics in question. But if the only source you can find is a PlanetMath article, I'd think the notability of that subject would be questionable... —David Eppstein 17:31, 10 November 2006 (UTC)


 * To expand on that thought, I agree about simple material being self-verifying. However, what wouldn't be self-verifying are, for example, the names of terms and specific definitions. I'll use the Supremum article as an example.  The material in the article is correct, and the reader can verify for themselves using material in the article that certain properties of a supremum must hold.  But what isn't verified is that the term "supremum" is a preferred formal term, or from where the word "supremum" originates.  To verify that the word "supremum" is used in mathematics circles, you'd need to provide a reference that uses the word (otherwise how would you know that you're using the term properly, or that mathematicians prefer to use an alternate term such as "least upper bound").


 * Another example of information that's not self-verifiable is when a math article mentions a quotation or biographical information about a famous mathematician. For example, the article Complex multiplication mentions in the introduction that "David Hilbert is said to have remarked the theory constitutes the 'most beautiful part of mathematics'."  Obviously that statement can't be self-verified; you'd have to provide a source showing that David Hilbert said that.


 * So while individual, logically self-evident lines of an article wouldn't usually require a seperate reference, you do need general references to verify that the article is using the proper terminology, that otherwise unprovided proofs are available for stated theorems, and that background historical and biographical information is accurate. Dugwiki 17:47, 10 November 2006 (UTC)


 * My general rule of thumb is that short, uncontroversial articles are fine if they have at least one printed reference listed at the bottom of the page. No page numbers are necessary; the purpose is only to give the reader a place to enter the published literature. There has been a lot of discussion about this, which is closely related to Scientific citation guidelines. CMummert 18:10, 10 November 2006 (UTC)


 * The term "self-verifying" is maybe not such a wise choice; try "self-consistent".
 * I agree that "David Hibert remarked…" begs for a source. I wouldn't remove such a statement from an article for lack of a source unless it seemed a dubious claim; but I probably wouldn't block its removal if someone else objected.
 * The comments about the supremum article need exploration. If we do a good job for our readers, they can expect:
 * The contents of the article are correct, unbiased, and adequate.
 * The article contains at least one reference to a reliable source that discusses the topic.
 * The article references one or more sources for additional reading.
 * I claim that it is harmful, unrealistic, and a broken policy to expect references to carry the full weight of verification. Anyone who has done much peer reviewing for journals would be delighted if reviewing could be replaced by reference counting. It can't; and transplanted to Wikipedia, the idea is equally useless.
 * This is relevant to "supremum" as follows. Terminology conventions vary over time, over subfield, over school, and over author. If I have never heard a term myself, that may simply mean I have not been exposed to those who use it. On the flip side, a single instance of use does not tell us whether the term is rare or idiosyncratic. We are unlikely to find a scholarly survey of usage. Also, the concept is old and minor, so not likely to be found as the topic of a journal article. Even in a text it may receive only passing discussion. Therefore, verification must rely on a discussion among editors with expert knowledge. This is especially true when we move past mere correctness to questions of bias and omission.
 * References are a Good Thing, but they cannot substitute for the equivalent of peer review. --KSmrqT 10:08, 11 November 2006 (UTC)
 * There is a problem, though, KSmrq. Namely that Wikipedia has no formal peer review system to verify facts.  Because it has no peer review system, it therefore requires that articles list verifiable references instead to publications that do have a fact checking system in place.  Hence the need to include basic references in all articles, including for example Supremum. References are the only formal way an article can be considered verified for inclusion in Wikipedia. Dugwiki 18:58, 13 November 2006 (UTC)
 * To equate references with verification is like the Indiana legislature trying to equate &pi; with 3.2. The fix to the broken policy is not "stay the course", more of the same, infuse each article with citations until servers groan and eyes bleed. And the down-and-dirty truth is, references are not really how we verify articles; people are. Wikipedia is just afraid to admit it and face the implications. --KSmrqT 07:05, 14 November 2006 (UTC)

To risk stating the obvious, I found google books to be a good way to dig for references. Yes, there searches bring up only a few pages, but it is often enough to tell whether a given book describes well the concept in question or not. Oleg Alexandrov (talk) 18:12, 10 November 2006 (UTC)

Results of a script looking for references
Using the most recent database dump and Mathbot's List of mathematics categories, I made a list of 7287 articles related to mathematics. I tried to eliminate as many stubs as I could, but some slipped through. Of the 7287 articles, Thoughts? CMummert 00:11, 11 November 2006 (UTC)
 * 4328 did not have at least one of Reference(s), Notes, or Further reading as a section header.   These are listed at User:CMummert/Unreferenced
 * 2919 of those didn't have any of those sections or an External links section either. These are listed at User:CMummert/Unreferenced_without_external_links.
 * Cool. That means theres 10,000 articles which do have references. We're doing well! --Salix alba (talk) 00:24, 11 November 2006 (UTC)
 * Salix alba should check his subtraction. 7287 minus 4328 is 2959 which is a lot less than 10,000. JRSpriggs 08:36, 11 November 2006 (UTC)
 * You should probably not count all the List of ... (there are more than one hundered). pom 10:16, 11 November 2006 (UTC)
 * Yes, I know the data isn't perfect; this was just a one-hour hack of a script. One reason that I only have 7287 articles instead of 11000 (Jitse's bot) or 14000 (Mathbot) is that I didn't include most of the biography categories. But even with that margin of error, it appears that over half the articles included in my list of 7287 give no printed references, and over one third have not printed references or external links.  My next plan is make a list of these articles by category. CMummert 12:14, 11 November 2006 (UTC)

One more piece of information. I sorted the unreferenced articles by category and put the results at User:CMummert/Unreferenced articles by category. There are some stubs included, but the general trend seems to be that short articles stating theorems and definitions are the primary contributors. The top seven categories for unreferenced articles are: #1 Mathematical theorems (222). #2 Linear algebra (99). #3 Group theory (97). #4 Abstract algebra (91). #5 Topology (85). #6 Polytopes (82). #7 Mathematical logic (81). #8 Geometry (76). #9 Probability theory (74). #10 Curves (63). CMummert 18:32, 11 November 2006 (UTC)

Paragraph in Fermat's Last Theorem
The page on Fermat's Last Theorem includes the following statement:
 * The main problem that Wiles had to overcome was to establish a correspondence between semistable elliptic curves over the rational field, and the modular semistable elliptic curves over the rationals, which he did by explicitly showing that there were equal numbers of each. Before Wiles' work on the problem, there had been many attempts to count elliptic curves, but no one had found a way to do it.

I think this is misleading, if not plainly incorrect. It is trivial to count elliptic curves over the rationals: there are denumerably many of them, since they are determined by polynomials in two variables which are quadratic in y and cubic in x, and there are plainly an infinity of them. As I understand it, the issue was not simply to show that there were equal numbers of each; again, this is trivial: there are denumerably many modular semistable elliptic curves. The issue, as I understand it, was starting from a semistable elliptic curve, to find a modular form which defined/determined the given elliptic curve. Perhaps someone who is more familiar with this could take a look and fix that paragraph? Magidin 16:31, 14 November 2006 (UTC)


 * Cut those. The talk about flavours of set theory also seems completely out of place. And could be original research Charles Matthews 22:32, 14 November 2006 (UTC)


 * I took care of the set theory part. CMummert 16:06, 15 November 2006 (UTC)

Hypercube nomenclature
There seems to be a discussion going on in Hypercube, Measure polytope, Tesseract, and N-cube about which name should be primary for which page. Tesseract is the 4d polytope, Measure polytope is currently the primary name for the general n-dimensional concept, N-cube has some odd marginally-related number-theoretic content, and Hypercube is currently a small disambiguation page. Contributors including myself disagree on whether Hypercube should redirect to one or the other polytope page, or what the proper name of each page should be. If you're interested, see the talk pages for these articles. —David Eppstein 18:30, 15 November 2006 (UTC)

Monty Hell problem - needs some references
Found another article that needs some references, and thought someone here might be able to track it down. Monty Hell problem (not to be confused with the Monty Hall problem is currently apparently based largely on an internet forum discussion. Unfortunately, forum groups are not acceptable references since anybody can post anything they want on a forum.  In particular, what needs to be verified is that the "Monty Hell problem" appeared in a publication of some sort somewhere at some point in time, and was called by that exact name.  The specific description of the problem also needs to be verified.

I do believe I've seen this problem before, though, so my guess is it was taken from a publication somewhere and posted to the internet. The trick is finding a book of puzzles or logic or probability problems with this paradox. Dugwiki 23:17, 14 November 2006 (UTC)


 * I doubt there's going to be more sourcing of this. It appears to be just one of the results of yet another online discussion.  AFD is my suggestion.  --C S (Talk) 20:30, 18 November 2006 (UTC)

General intelligent design
Is anyone willing to vouch for General intelligent design? It looks crankish to me. CMummert 20:11, 15 November 2006 (UTC)


 * Crank. JoshuaZ 20:19, 15 November 2006 (UTC)


 * Might as well review all other edits of R. Herrmann, also see . (Igny 20:53, 15 November 2006 (UTC))


 * There are two other articles. Consequence operator is standard mathematics, although the article could be improved.  Logic-system may be original research (WP:OR), but it seems better than General intelligent design. Each article should be considered on its own merits. CMummert 21:00, 15 November 2006 (UTC)


 * Proposal:
 * Delete General intelligent design (as db-nonsense)
 * Merge Logic-system into Proof theory
 * Merge Consequence operator into closure operator.
 * As these are related, the discussion should be centralized here. &mdash; Arthur Rubin | (talk) 19:47, 16 November 2006 (UTC)
 * Never mind. Discussion on individual (target) talk pages, User:Raherrmann will be informed, in the interest of fairness.  &mdash; Arthur Rubin |  (talk) 20:06, 16 November 2006 (UTC)


 * Some material from the two remaining pages has appeared (or will soon, according to Herrmann) in respectable journals, like Journal of Symbolic Logic or Theoretical Computer Science and does not qualify as original research. Unfortunately Herrmann does not post preprints of accepted papers on his website. The main problem I see with the articles is that they are written in an uninformative way that is sometimes too vague about what is going on. CMummert 20:22, 16 November 2006 (UTC)


 * Even so, does anyone other than Mr. Herrmann use the name "logic system" or "consequence operator" for these concepts? The name can be a neologism even if in a published article, as the reviewers would check (at most) whether the name is commonly used in that field for something else. &mdash; Arthur Rubin |  (talk) 20:45, 16 November 2006 (UTC)


 * I'd say "logic system" is a neologism. The same concept, or very similar ones, is part of the bread-and-butter of theoretical computer science; I was taught them as an undergraduate. I've seen them called "inference systems" or formal systems; the latter already has an article, which is a bit stubbish and could use improvement. However the text in logic system is not that improvement; I doubt it would be enlightening to someone who does not already know the subject. I suggest redirecting to formal system. Henning Makholm 21:33, 16 November 2006 (UTC)

messy, messy, messy
Proofs of trigonometric identities is a really messy article in two ways (at least):


 * Formatting, typesetting, etc. See my most recent edit.
 * Logical structure. One may prove the identity A = E by writing A = B = C = D = E.  That's what I did in my most recent edit.  One may also prove A = E by saying A = E if blah, and blah is true if blahblah, and blahblahblah is true if etc.etc., and etc.etc. is a known truth (but one must be sure not to write "If A = E then ...."; the "if...then..." has to go in the right direction.
 * It also reads like a copyvio from some elementary trig text. Septentrionalis 04:28, 17 November 2006 (UTC)


 * My inclination is to have this deleted, but I'm unsure about the best rationale. "Messy" will not carry the day. Perhaps OR? Or WP is NOT? --Lambiam Talk  06:50, 17 November 2006 (UTC)


 * I feel this could be a very useful page with a little TLC. I wish I had the time to undertake such a project, but alas I do not.  I urge that we do not delete, despite its current (deplorable) state.  Is there anyone out there who could spend a little time with this one and bring it into shape?  VectorPosse 07:01, 17 November 2006 (UTC)


 * It could perhaps be deleted under the rationale WP:NOT an indiscriminate collection of information, section 4 titled "instruction manuals". Which states that... While Wikipedia has descriptions of people, places, and things, Wikipedia articles should not include instructions or advice (legal, medical, or otherwise), suggestions, or contain "how-to"s. This includes tutorials, walk-throughs, instruction manuals, video game guides, and recipes. Don't really know my position on that article, but I am just pointing out that that could be used as a rationale.--Jersey Devil 07:02, 17 November 2006 (UTC)

Just delete it. Stuff like this is usually deleted because of what Jersey Devil said. We don't need to encourage more tutorial style articles. --C S (Talk) 20:29, 18 November 2006 (UTC)


 * Sorry, but I don't see it. I feel like Jersey Devil's explanation was a stretch (which he or she seems to be acknowledging).  This is not a tutorial, at least not of the type that WP:NOT seems to be condemning.  I also might point out that this is not the only page that has proofs of various mathematical facts.  It would take a hardcore exclusionist to suggest that we should delete  them all.  I mean no offense to Chan-Ho Suh, but I feel that sometimes we have a tendency to get caught up in policies (even ones that don't really apply) and forget that Wikipedia is supposed to be useful.  I have dozens of students in my pre-calculus class right now who would benefit from this page, properly done.  If consensus dictates otherwise, I will back off, but until that point, I'm going to need a lot more convincing rationale for deletion than WP:NOT.  VectorPosse 21:48, 18 November 2006 (UTC)


 * Nobody here is proposing such unilaterial deletion. So bringing that up is just a strawman.  Just because something's useful to somebody isn't a good reason to include it on Wikipedia.  That's why we have clarifying pages like WP:NOT and other Wiki projects.  Your pre-calc students may find these proofs of trig identities useful, but it's better for them to look in a textbook.


 * The page is definitely a kind of tutorial. It explains basic things like tangent is sine divided by cosine in excruciating detail.  It's not really on par with the pages that have been linked in "see also".  For example, the proof of e is irrational really eschews the most trivial details and concentrates on explaining the main conceptual steps.  That fact is also of historical importance, with a number of famous mathematicians expending effort at giving varied proofs, although this is not currently described in the article.  Same reasoning goes for sum of the reciprocals of primes diverging, etc.


 * What really is the point of this page? We have articles on trigonometric function and list of trigonometric identities.  Is it to help out pre-calculus classes work through some manipulation of trig functions?  Sounds like a tutorial to me.  --C S (Talk) 22:52, 18 November 2006 (UTC)

Recurring decimal
I made the following edit on the Recurring decimal article, creating a section where I show that recurring decimals can be expressed in the terms of an infinite series. I just wanted to post it up here for others to check up on my edits (obviously people here are more experienced and I would hate to post up factually incorrect information).--Jersey Devil 07:08, 17 November 2006 (UTC)

Merging suggestion
In the past few days, I've been editing a thing or two in Elementary algebra, and coincidentally another person was too. We started adding things here and there, but it seems that the information is piling up. I'd say it might be too much information for an article that's supposed to be elementary. The section that I've been contributing in is 'System of linear equations'. There is a reference to the supposed main article, which is System of linear equations. However, I can't help but notice that in the main article, there is a clear theoretical definition of the subject, but it has no examples. However, in Elementary algebra, the subject is hardly defined, while examples are abundant. Moreover, System of linear equations does reference to yet another article about systems of equations, Simultaneous equations- not linear equations, but a system of equations in the end. I'm trying to think neutrally here... But why do we have three articles about basically the same thing? And apparently, they could all use some improvement -and I'm more than glad to help there. I thought maybe a basic reference to the subject could be made (with basic examples maybe) in Elementary algebra, while moving the more in-depth examples and info we are creating to the main article, System of linear equations, at the same time merging it with Simultaneous equations. That way, we would be cleaning up three articles and expanding a whole topic. The three articles are about basically the same (Except Elementary algebra, which has other information as well) but the information seems to be spread. The way I see it, that is unnecesary and confusing. Again, I'd be glad to help with my (limited at best) knowledge in this particular topic, but I wanted this out of the way first. I really want to contribute to this subject, but I think it would be better if there was just one main topic about it, having of course, reference to it on Elementary algebra (or other articles for that matter). I am asking for opinions because I think it might be too bold to edit, merge and move all those pages based on my opinion alone. What do you think? Is this a good or bad idea? Why should we do this or why not? (Quadrivium 23:17, 17 November 2006 (UTC))


 * For various reasons I have my doubts about merging System of linear equations (Sole) and Simultaneous equations (Se). (1) If done properly, both articles would be much lengthier. (2) Keeping them separate makes it easier to write a clear article. In particle Sole has a well-defined focus and should have a treatment at various degrees of mathematical sophistication (elementary algebra; other domains than fields). In contrast, after appropriate definitions and generalities, Se is necessarily an incomplete collection of various tricks and heuristics for different cases that may arise. See also my criticism of Se. --Lambiam Talk  02:09, 18 November 2006 (UTC)


 * Thanks for asking first. It is common to “refactor” articles, merging or splitting the material as it evolves; but we do prefer to discuss these changes in advance.
 * The articles in question should remain separate. However, either a copy or move of some examples may be a good idea.
 * Linear equations are common, important, and solvable with specialized methods. Simultaneous equations have three major nested divisions: linear equations, polynomial equations, general equations. And elementary algebra is a broader topic than solving equations.
 * We prefer to limit the size of articles, and to keep a clear focus for each. One way to handle a subtopic is to have a brief paragraph discussing it in the broader context, accompanied by a link to the specialized article. For example, the simultaneous equations article should refer readers to the system of linear equations article for the bulk of the details special to linear equations.
 * The real problem in this instance is that all these articles are in rough shape, especially considering their importance. Paradoxically, it is usually easier to handle an advanced topic well than to write a clear, complete, and compelling article on a basic topic. Wikipedia may not be the best place to learn such material, but readers usually have good alternatives. --KSmrqT 08:46, 18 November 2006 (UTC)


 * Thanks for the feedback- I see what you mean. However, I am still wondering a couple of things.
 * I think I pretty much understood the purpose of Simultaneous equations. But exactly how much should be included or kept in Elementary algebra about this particular subject? And when you say move or copy examples, what do you mean? Because I'm not too sure if there should be less or more info about systems in Elementary algebra-- and I don't really know what part of that info should be moved or copied somewhere else (and where). I think I see why Simultaneous equations and System of linear equations are separate articles, but what is the purpose of System of linear equations? I think the information is great and it should definitely be kept, but what is the article aiming at? What approach is it taking? Should that article have examples as well? Oh, and should Simultaneous equations have definitions as well, or is it just an examples/ways of solving systems article?
 * Anyway, I think I'll be trying to solve some of the points adressed in Criticism of Se in the following days, although I am no expert.
 * Oh, and excuse me if I'm being too annoying with all these questions :) --Quadrivium 17:09, 18 November 2006 (UTC)

Monadic logic
The article (one liner microstub) is on AfD. Could someone take a look what it is worth? TIA Pavel Vozenilek 01:30, 19 November 2006 (UTC)

Calculus: GA collaboration of the week
Yesterday, Calculus was chosen as the collaboration of the week for people that want to push good articles to featured article status. I encourage people from the mathematics project to get involved as this is clearly one of the most important articles on mathematics and likely to be among the most visited. At first glance I would say that there is still a considerable amount of work to be done. Pascal.Tesson 18:32, 20 November 2006 (UTC)

Problem and options
In WP:MSM I didn't see anything about which infix to use for definitions. Some use $$\equiv$$, but I find this very misleading, since it already has two other meanings: equivalence (hence its Latex code) and identity. I would therefore advocate := or the equal sign with "def" underneath. (Sorry, I don't know the Latex code for that.) &mdash; Sebastian (talk) 04:58, 19 October 2006 (UTC)


 * We also have a (carefully hidden) page of conventions, but this convention is not among them. I agree that the “triple equal” is not a good choice. The “colon equal” is my preference; I also like to use it for algorithms (where I save bare “equal” for equality tests). I have not found a decent way to stack something over or under an equality or arrow within the tragically limited abilities of texvc, Wikipedia’s TeX engine. Unicode provides a single character for “Assign” (“≔”, U+2254, &amp;#x2254;), a single character for “triangleq” (“≜”, U+225C, &amp;#x225C;), and one for “equal to by definition” (“≝”, U+225D, &amp;#x225D;). I cannot recommend any of these characters at present, because they will not display well (if at all) for many of our readers. Displayed in a larger font size for clarity, here are the choices mentioned:
 * {| style="font-size:400%" cellspacing="15"


 * }
 * Although in LaTeX itself we could use \overset{\mathrm{def}}{=}</tt>, and blahtex supports this, texvc does not. Thus the two character sequence “colon equal” (“:=”) is left as the only viable choice. However, as always, no matter what convention you adopt, please do not leave readers guessing; tell them explicitly if there is any reasonable chance of misunderstanding. --KSmrqT 06:58, 19 October 2006 (UTC)
 * Although in LaTeX itself we could use <tt>\overset{\mathrm{def}}{=}</tt>, and blahtex supports this, texvc does not. Thus the two character sequence “colon equal” (“:=”) is left as the only viable choice. However, as always, no matter what convention you adopt, please do not leave readers guessing; tell them explicitly if there is any reasonable chance of misunderstanding. --KSmrqT 06:58, 19 October 2006 (UTC)


 * How about $$=_{\operatorname{def}}$$? JRSpriggs 08:55, 19 October 2006 (UTC)
 * Do it like this: $$x \stackrel{\mathrm{def}}{=} x$$ → Aza Toth 19:45, 29 October 2006 (UTC)
 * That's a good idea! Let's do that. &mdash; Sebastian (talk) 06:50, 23 November 2006 (UTC)
 * Actually, it usually is necessary to include a bit more space, so I'm using "\ \stackrel{\mathrm{def}}{=}\ ". &mdash; Sebastian (talk) 07:09, 23 November 2006 (UTC)


 * i am trying to understand why you guys are changing $$ \equiv \ $$ to $$ = \ $$ for definitions in the first place. why is /equiv wrong for that use?  to use it in the definition tells the reader who is glossing over the words that it is a definition and not a derived result of any sort.  i don't get it. r b-j 16:51, 31 October 2006 (UTC)


 * A better question would be: Why do you think that "the reader" would immediately understand \equiv as mening "by definition"? It is not a notation I remember ever seeing before this discussion, even though I've managed to earn a B.S. in mathematics and a Ph.D. in a mathematically heavy area of computer science. In short, it is not as universal as you appear to assume. The only thing meaning any of the symbols can reliably convey is the identity between the defined symbol and its expansion (for which the understandability of = is unrivalled), whereas the fact that something is being defined needs to be spelled out in words if not otherwise clear -- any nonverbal symbolism for that is bound not to be understood by many readers. Henning Makholm 20:49, 1 November 2006 (UTC)


 * I think that it may be a newer notation, because my AP Physics textbook, published a year or two ago, uses \equiv to indicate definitions. Karl Dickman talk 02:48, 6 December 2006 (UTC)

Discussion: "=" vs ":=" vs words
I feel strongly that we should not need the := type symbol here. If something is a definition we should say so in words. The proper use for := is for assignment in computer science. As far as I'm concerned, := is up there with iff as technical language we should always avoid. since it makes articles impenetrable. Charles Matthews 09:00, 19 October 2006 (UTC)


 * I agree that words are preferable, for the reasons given by Charles Matthews. JPD (talk) 10:23, 19 October 2006 (UTC)


 * I would agree. Despite having seen := used in some decent books in recent years, I feel quite strongly that in maths, as opposed to computing, the use of := is a bit of a neologism, and the words should be perfectly clear. Similarly, I assume we agree that we should not use inverted A and E for "for all" and "there exists"? Madmath789 11:10, 19 October 2006 (UTC)


 * Ditto, but := is not so heinous a notation as is being insinuated here ;) Dysprosia 11:18, 19 October 2006 (UTC)


 * To clarify my position, in most cases I also would use something like “Let x be the reciprocal of y” rather than “x := 1&#8260;y.” I believe, so far, I’ve not needed the latter for Wikipedia. However, situations can arise where it is helpful to adopt a distinct notation. Rather than take a fixed position banning it, perhaps we might strongly discourage it, but offer a notation should the need arise. Frankly, given the fact that current technical limitations preclude any really satisfactory symbol, I think most editors will choose to write around the problem, as we prefer. Our style guide already says the following:
 * Careful thought should be given to each formula included, and words should be used instead if possible.
 * Beyond that, if Wikipedia intends to let anyone edit, then we might also want to begin to teach writing skills. A typical mathematical education teaches neither English composition nor technical writing for a broad audience. --KSmrqT 13:00, 19 October 2006 (UTC)

So it seems we have a consensus that we don't want $$\equiv$$ for definitions. This Google search shows that we have less than 60 occurrences, so it is practically feasible to weed out the wrong ones.

Many of these cases may indeed be better expressed with words. But I would not completely rule out ":=". Trying to express every definition in words can get clumsy. E.g. I can't think of a way to rephrase "... where $$c \; $$ is the speed of light and $$\gamma \ := 1/\sqrt{...}$$ is called the Lorentz factor" withouth distracting at least some readers. Moreover, readers who are unfamiliar with ":=" can enter it in the search field (although unfortunately they can't enter a single colon). &mdash; Sebastian (talk) 18:02, 19 October 2006 (UTC)
 * Users can enter it in the search box, but this will lead them to = (which redirects to Equals sign), since an initial colon is discarded; see Naming conventions (technical restrictions). --Lambiam Talk  10:05, 20 October 2006 (UTC)


 * If its just a list of constants then a simple $$\gamma \ = 1/\sqrt{...}$$ seems fine. For more complicated definitions then words are more approprate. --Salix alba (talk) 18:52, 19 October 2006 (UTC)


 * Re the issue with gamma and the Lorentz factor - you can say "... where $$c \; $$ is the speed of light and $$\gamma$$ is the Lorentz factor (defined as $$1/\sqrt{...}$$)." This avoids any equivalency symbology. It actually puts the information in its proper place, as it makes the full Lorentz factor a parenthetical item for those who do not know the Lorentz factor, whereas those who do can just glaze over it. --Carl (talk 02:29, 28 October 2006 (UTC)


 * Good idea - if you like you can add it to the table below, or I'll do so later. &mdash; Sebastian (talk) 02:46, 28 October 2006 (UTC)

In writing about mathematics and physics, I've never found a problem using an equals sign and then stating, in words, whether what you're writing is a definition. I think anything else is just a gimmick. –Joke 18:54, 19 October 2006 (UTC)


 * I don't think your Google search finds pages in which ≡ is typed as a unicode character. In fact I haven't been able to figure out how to get Google to search for that character. And the WP search box only gives me ≡ which is uninformative. So finding all instances of ≡ in WP pages may be problematic. —David Eppstein 21:33, 19 October 2006 (UTC)

David, thanks for thinking of this. I still hope that there are not too many Unicode ≡ instances since it doesn't seem possible to use this in a formula. $$a ≡ b$$ at least yields: $$a ≡ b$$.

Salix and Joke: I think you're missing my point. Of course it is possible to write just an equal sign, but you're losing information: The colon tells the reader unobtrusively: "Don't worry about what this $$\gamma$$ is all about and whether you've seen it before - it is just a definition." And I agree, it is not a problem for anybody who writes English reasonably well to state in words whether it's a definition. But how do you actually do this in a case like the above without overemphasizing a side issue and breaking the flow of thought? &mdash; Sebastian (talk) 22:52, 19 October 2006 (UTC)


 * It only tells the reader something if it is an established convention, the conversation here indicates its not. Picking a random maths book its full of statements like If A=..., let A=...., We define A=.... and where A=.... The preceding words are enough to unambiguiously tell the readers whats happening. Any other notation will break the flow of the text, making the reason pause to think, 'whats this new notation i've not seen before'. Personally I think we should follow KISS principle and minimise inroducing unnecessary notation.--Salix alba (talk) 23:26, 19 October 2006 (UTC)


 * Scroll up. Math tags are for LaTeX code, not Unicode characters. $$a \equiv b$$ uses \equiv, not ≡. Dysprosia 06:48, 20 October 2006 (UTC)


 * I'd like to make the point that it is particularly important for WP to highlight definitions on pages. Not to sneak them into notation. There is indeed a kind of format issue with the typical 'where' construction after a formula. That, I think, is a separate and useful discussion. Mathematicians can take it to be the syntax "let x be an A, y a B, ...", preceding a statement. In science it certainly is frequently done with a trailing "where c is the speed of light ...". These context-establishing things matter quite a lot. But I really don't see that the := assignment is a good thing in there. For one thing it comes from the wrong programming paradigm (functional programming rules ...). Charles Matthews 08:59, 20 October 2006 (UTC)
 * I would expect to see mutable variables with assignment in an imperative programming language, whereas a functional programming language would limit its bindings to “<tt>let</tt>” constructs and function calls. Did you misspeak, or did I misunderstand? --KSmrqT 11:54, 20 October 2006 (UTC)


 * An unambiguous indication that something is a definition has its merits, but I agree that we should avoid conventions that are insufficiently established and may be unnecessarily puzzling to our readers. I've seen maths books using ":=" for definitions, but then somewhere in the introductory parts there will be a section on notation explaining the use. I don't think I ever saw this use in a physics textbook. We should go with a simple "=" sign, making sure the context establishes the definitional nature. Would that some unclarity there was the worst problem in the understandability of our maths articles... --Lambiam Talk  10:19, 20 October 2006 (UTC)

For a whole week, none of the seven people who found it particularly important to highlight definitions made any contribution to actually achieve this. Since it seems that simply replacing "\equiv" with ":=" wherever applicable would be the most sensitive thing to do for now. (Replacing it with just "=" is not good since it would delete information, and other alternatives were even less favored.) I am volunteering to do that. After that, I will be done, and the proponents of prose can edit these occurrences at their leisure. Let me know what you think. &mdash; Sebastian (talk) 21:00, 27 October 2006 (UTC)
 * my main concern is eliminating the ambiguous use of "\equiv";
 * we have over 300 articles with several occurrences each and
 * editing the text to highlight definitions takes a lot of time for each occurrence (at least for me)


 * Well, as I wrote earlier (see below): "We can also simply fix such things as we encounter them. In terms of best use of time to increase the quality of maths articles, it is (in my opinion) more effective to work on some stub articles or other pages that have been flagged as needing attention." And I do not only work on maths articles. I'd say this edit qualifies, though. Further, as I explained before, I'm opposed to using := for definitions. The large majority of readers will not be familiar with this meaning. --Lambiam Talk  23:50, 27 October 2006 (UTC)


 * I'm sorry! I didn't mean to include you. I am really grateful for your active contribution to the table, too.
 * You may be right that many readers of Wikipedia may not be familiar with ":=" - but this is irrelevant in this context. What is relevant is the difference
 * $$Difference = C_{equiv} + K_{equiv} - K_{colon}$$
 * where
 * $$C_{equiv}$$ is the number of people who are confused by the ambiguous use of "≡"
 * $$K_{equiv}$$ is the number of people who don't know "≡" but notice it to the extend that it hurts their understanding of a formula;
 * $$K_{colon}$$ is the number of people who don't know ":=" and notice it to the extend that it hurts their understanding of a formula;
 * I may be wrong, but I believe this difference is positive. I believe that $$K_{equiv} \approx K_{colon}$$ (the added bar is no less conspicuous than the added two dots, and the discussion here showed that "≡" isn't that popular either). And $$C_{equiv} > 0$$, because it includes at least me. ;-)  &mdash; Sebastian (talk) 00:40, 28 October 2006 (UTC)


 * Speaking for the others, when they commented they may well have had the impression that you were requesting input on how to deal with this in WP:MSM, rather than attempting to press-gang them into a task force. As to your exercise in linear programming, aren't you overlooking the quantity $$C_{colon}$$? $$Difference = C_{equiv} + K_{equiv} - C_{colon} - K_{colon}$$. You may say it isn't ambiguous, but there is also the meaning of assignment in Pascal and other programming languages. And I've seen it used for denoting substitutions. How many places are there where ≡ is actually ambiguous? In any case, I suggest that you do not ignore the judgement of several editors that := is not appropriate. --Lambiam Talk  01:25, 28 October 2006 (UTC)


 * I don't know how you come up with the accusation that I'm press-ganging anyone. In the contrary, I have been volunteering my time to fix something that bothers me. I would like to do this in a simple way, as described above. It is others who demand it to be done in a much more work intensive way, which practically makes it impossible for me to do it alone.
 * Re $$C_{colon}$$: I assumed it to be 0, but it actually is less than 0. The connection with assignment is not confusing but helpful.
 * Re How many places are there where ≡ is actually ambiguous?: In every place, by definition. There are three contradicting definitions for "≡" (including "is identical"), and it takes always some extra bit of information to distinguish between them.
 * Re ":= is not appropriate": This is your same absolute statement again, where we need a relative comparison. We have to choose one option. If I understand you correctly, your preferred option seems to be to leave everything as is until we run out of "stub articles and other pages that have been flagged as needing attention" - which will be when pigs fly. I don't think that is any more "appropriate". &mdash; Sebastian (talk) 02:02, 28 October 2006 (UTC)


 * We've got someone who wants to make a productive contribution to Wikipedia mathematics articles. Can we not find a way to put that to good use? If substitution of ":=" for "\equiv" or "≡" is undesirable, which appears to be the consensus, then what task would be helpful? The claim that "we have over 300 articles with several occurrences each", if accurate, could be converted into a list of those articles. That list could be linked here. Interested parties could work through it, eliminating items as they are fixed. What I have found in working through a similar list, the blahtex problem article list, is that often an article that exhibits one dubious construction accompanies it with other problems. This is the wisdom behind the suggestion to fix things as we encounter them.
 * And please, help my frayed nerves and stop abusing TeX. It is wrong to write
 * $$K_{equiv} \approx K_{colon} . \,\!$$
 * A correct form is
 * $$K_{\mathrm{equiv}} \approx K_{\mathrm{colon}} . \,\!$$
 * This is not just a matter of italics; without proper markup TeX thinks you mean to multiply the single-letter variables c, o, l, o, n, and uses the wrong font and the wrong spacing. Compare
 * $$fifty \,\!$$
 * versus
 * $$\mathit{fifty} \,\!$$
 * for appearance. --KSmrqT 03:15, 28 October 2006 (UTC)


 * Thank you, KSmrq! This list exists already: /equivlist (described in next section). After David Eppstein was busy again, today, we might just have touched 300. And I'll take your point about \mathrm. I found that it is already in Help:Math, but hidden in the Rendering section. I thought it was just used to define types. Maybe this could be written a bit more explicitly?  &mdash; Sebastian (talk) 03:26, 28 October 2006 (UTC)

I also strongly agree that ":=" is awfully ugly, and that it should be always avoided in math. Oleg Alexandrov (talk) 03:27, 28 October 2006 (UTC)
 * To KSmrq: I have not used "\mathrm{...}" because I do not know what it means. What does it mean? I have used "\operatorname{...}" in some similar situations. JRSpriggs 06:04, 28 October 2006 (UTC)


 * operatorname and mathrm are different, IIRC because the former adjusts the spacing for operators (compare entering $|$ and $\mid$ into TeX), the other does not. Dysprosia 06:46, 28 October 2006 (UTC)
 * What? Could someone translate that into English, please. What does "IIRC" mean? What are "$|$" and "$\mid$"? JRSpriggs 07:13, 28 October 2006 (UTC)
 * IIRC means: "If I Recall/Remember Correctly". In TeX "$...$" means the same as " $$...$$ " does here. In math mode, "|" and "\mid" produce the same symbol, but presumably with subtly different spacings. --Lambiam Talk  09:59, 28 October 2006 (UTC)


 * I very much appreciate the willingness to spend effort on improving a weak point in our maths articles, and I do not suggest (nor have I suggested) that one should wait till there are no more stubs, but, rather, that, following the "ant algorithm" embodying Wikipedia, they may be fixed as one runs into them. As to the concrete way of fixing them, here is an ordering of some ways of presenting a definition, ordered – according to my personal preferences – from most to least desirable:
 * The frobnitz ψ, defined by ψ = ∂u/∂v, forms a core.
 * The frobnitz ψ, defined as ∂u/∂v, forms a core.
 * The frobnitz ψ, defined by ψ ≡ ∂u/∂v, forms a core.
 * The frobnitz ψ, defined by ψ := ∂u/∂v, forms a core.
 * The frobnitz ψ = ∂u/∂v forms a core.
 * The frobnitz ψ ≡ ∂u/∂v forms a core.
 * The frobnitz ψ := ∂u/∂v forms a core.
 * Perhaps it explains why I am not entirely enthusiastic about addressing the issue by replacing \equivs by colon-equalses. --Lambiam Talk  10:40, 28 October 2006 (UTC)


 * Ah, that helps indeed! My list looks like this:
 * The frobnitz ψ, defined by ψ = ∂u/∂v, forms a core. (=d)
 * The frobnitz ψ, defined as ∂u/∂v, forms a core. (0d)
 * The frobnitz ψ, defined by ψ := ∂u/∂v, forms a core. (:d)
 * The frobnitz ψ := ∂u/∂v forms a core. (:0)
 * The frobnitz ψ = ∂u/∂v forms a core. (=0)
 * The frobnitz ψ, defined by ψ ≡ ∂u/∂v, forms a core. (≡d)
 * The frobnitz ψ ≡ ∂u/∂v forms a core. (≡0)
 * (For easier reference, I added a mnemonic after each. First character refers to the infix, second to the word "definition")
 * In short: Anything is better than using "≡" in the wrong place. This means: At least we agree that replacing every wrong "≡" with "=" would be an improvement. (This is what David Eppstein has been diligently doing in many instances. Accomplished mathematician that he is, I am not concerned about his edits. But if someone did it with search and replace then there will be cases where we lose information, which is why I prefer (:0).)
 * So may I ask why you prefer "≡" over ":=" despite its ambiguity? I thought I made it pretty clear above why this is really bad, and so far my reasoning has not been refuted. &mdash; Sebastian (talk) 18:13, 28 October 2006 (UTC)


 * Just a note here: I would characterize the bulk of my work in this direction, not as any kind of replacement, but as identifying the articles that use &equiv; for modular congruences, Boolean equivalence, and other uses that have nothing to do with definition, and removing them from your list of targets for editing. But at this point it seems that a lot of what's left is physics or areas of math that I'm less familiar with, so I've stopped doing as much on this. —David Eppstein 18:19, 28 October 2006 (UTC)


 * Since the $$\equiv$$ symbol has reasonable uses for math articles, merely replacing them all with := won't work. If someone wants to replace only the equivs that are part of a definition with :=, that would be fine with me, because I think that both symbols are equally bad for definitions.  At least := stands out more, making it more likely to be spotted by editors in the future. But it might require a lot of editing by hand to do the replacing.  CMummert 14:04, 28 October 2006 (UTC)
 * Exactly! Disambiguating the uses by getting rid of the wrong use of "≡" for definitions is the whole point of what I'm trying to achieve! &mdash; Sebastian (talk) 18:13, 28 October 2006 (UTC)


 * Unless you are familiar with the article, it will in general take some time in each instance to understand the context in which the symbol is used and whether this is truly a definition. If it is immediately obvious that this is a definition, then it should be safe to replace \equiv by =, since that then introduces no possible misunderstanding. I consider all cases of the form "F(ψ), where ψ = ∂u/∂v", obviously definitions. Also, if the meaning of "frobnitz" is something that could not possibly be an equation (e.g., when it is a scalar, vector, or metric), then "the frobnitz ψ = ∂u/∂v ..." is quite unambiguous. If it takes some time to understand the situation so that you can be sure this use is a definition, it means that the article urgently needs some text like "defining the frobnitz ψ by". While it takes a few extra seconds to add that text, it is then a minor part of the undertaking.
 * I'm not the only one not in favour of ":=". The reason I prefer "≡" over ":=" is simply that I expect it will lead to less confusion or puzzlement among our readers who need this least. Does any physics textbook, or any commonly used mathematics textbook, use the notation ":="? --Lambiam Talk  21:15, 28 October 2006 (UTC)


 * For what it's worth, Wolfgang Rindler's excellent Relativity: Special, General and Cosmological uses the ":=" notation, without (as far as I can see) explicitly introducing it. It sometimes also turns the symbol around and says something like "... and thus we see the importance of ∂u/∂v =: ψ = the frobnitz" to define ψ and the word frobnitz in one go. No, I don't find that particularly readable, and prefer prose where disambiguation is needed. In contrast (and still for what it's worth) I can't remember ever seeing "≡" for definitions in a respectable source. Henning Makholm 21:33, 28 October 2006 (UTC)

Conclusion and /equivlist
Thanks Charles, Salix and Lambian – you make enough good points to elevate your preferred solution (of banning ":=") within my margin of error close to my preferred solution (of allowing it where it helps). The reason I'm not entirely swayed is that I absolutely disagree with Lambian’s last remark: It is precisely because our math articles are often hard to understand that readers need help. Even small things can provide a straw for struggling readers to cling to. But I acknowledge that there is a tradeoff, and which solution actually provides more help is a moot judgment call. &mdash; Sebastian (talk) 20:57, 21 October 2006 (UTC)


 * I'm slightly puzzled by your absolute disagreement with my last remark. I only meant to express dissatisfaction with the complete lack of understandability of several of our maths articles. While small things might make the difference of the proverbial straw for some articles, too many articles are like a heavy block of concrete dropped on the camel. So all this lamentation – which you should also see in light of my expressed opinion that ":=" is more problematic – is saying is this: I wish possible ambiguity of "=" was the worst problem we have. I don't think you want to claim that it is actually the worst, or that you wish for worse problems.  --Lambiam Talk  03:09, 22 October 2006 (UTC)
 * No worries! If that statement wasn't meant as an argument against any small improvements then I agree with it, of course. &mdash; Sebastian (talk) 17:06, 22 October 2006 (UTC)

OK, now that we agree that we don't want to use \equiv for definitions, we need to do two things:
 * 1) Add the policy to WP:MSM. I'm fine with the policy proposed by Charles, Salix and Lambian, but I wouldn't want to be the one who adds it to MSM.
 * 2) Change "\equiv" to "=" where it means definition. Here's a list of all articles that contain "\equiv": /equivlist. Let's work with this together: Whoever cleared an article, just deletes its line from the list. I'll begin with articles that I understand. &mdash; Sebastian (talk) 17:06, 22 October 2006 (UTC)

Dang! I just realized that my original query yields far too few results. Unfortunately, searching for "math" does not, as I thought, yield all pages that contain the tag, but only those that contain the word "math" in plain text - which are mostly entries like "J. Math. Pures Appl.". Replacing "math" in the query with "function" already yields 408 results. Does anyone have an idea how to filter all mathematical articles in a Google (or other) search? &mdash; Sebastian (talk) 18:05, 22 October 2006 (UTC)

I replaced the list with the result of this query, which gives us a few too many articles, but at least we won't miss any. &mdash; Sebastian (talk) 19:25, 22 October 2006 (UTC)


 * We can also simply fix such things as we encounter them. In terms of best use of time to increase the quality of maths articles, it is (in my opinion) more effective to work on some stub articles or other pages that have been flagged as needing attention. --Lambiam Talk  20:57, 22 October 2006 (UTC)

I just found out about this discussion, and I really need to register my strong objection to changing \equiv, :=, and = to $$\stackrel{\mathrm{def}}{=}$$, for a number of reasons: Again, most of objection relates to the concept that we shouldn't make up our own conventions. This is really starting to bug me. Also, I don't think you've taken a broad enough poll to be establishing this as convention, and the discussion above doesn't look like consensus to me. Please stop, at least until it is clear that a consensus among editors (not just people in this discussion) has been reached. --MOBle 19:46, 25 November 2006 (UTC)
 * 1) I have never (in my very broad reading of math and physics) even seen this before.  We shouldn't make up new conventions.
 * 2) The appearance of this word above the = sign is distracting to me, even when I know the equation perfectly well.
 * 3) \equiv does mean that two things are identical, which they are when they are defined as such.
 * 4) I see no problem with using a simple = sign when words to the effect of "defined as" appear nearby.
 * := and \equiv are variously standard in various publications. Why can't we use them, if they're good enough for Cambridge University Press, Springer, etc?  If a reader looks for related ideas in a book, these are what he/she will see.  Consistency is good.
 * This is a stale discussion, with decisions made and actions taken, so I'll keep my response brief. You raise legitimate concerns, but reach unsupported conclusions. We agree that we should stick to established conventions. How? Mathematicians and physicists and engineers can differ in their conventions, and among themselves. If I have seen a convention frequently, and you have never seen it at all, is it a convention? The equal sign with the letters "def" above it has a Unicode code point, U+225D, so the standards body thinks it important. Yet it is not enough to know that a symbol is used, we must also examine how it is used, and by whom. Most important is that our readers understand. The colon-equal is familiar in computer science, but with the meaning of assignment, not definition. The \equiv is familiar in mathematics, but often with the meaning of a congruence in modular arithmetic, not a definition. The equal-by-definition symbol has no such ambiguity, but is less widely used, and many readers will not have a font including it. The wisest course, and our consensus, is to prefer a plain equal sign accompanied by words and context to make clear that a definition is intended. --KSmrqT 20:31, 25 November 2006 (UTC)


 * I agree with most of what you wrote, but I disagree about what the consensus was. In the discussion, we talked that there were over 300 articles with "\equiv", and no one was willing to go through all of them and write the appropriate, wise prose. So that course, while desirable, was just not viable. By contrast, there was consensus that =^def was better than \equiv, which is the replacement I did. &mdash; Sebastian (talk) 22:16, 25 November 2006 (UTC)


 * It is true that things are identical when they are defined to be, but the reverse implication does not hold: Things can be identical for other reasons than a definition. Therefore $$\equiv$$ is not a reliable way of indicating definitions. Neither $$\equiv$$ nor := are universally recognized as definition signs; therefore we should not assume that a reader knows them, and the only reliable way to point out that an equation is a definition is to say so in prose. Finally, discussions such as this one is the only way we have to gauge consensus. What do you suggest that we do otherwise - autopost messages on the talk pages of everybody who has ever edited a math article? Henning Makholm 20:07, 25 November 2006 (UTC)


 * I suggest we stop changing \equiv to something that is completely unrecognized, i.e. $$\stackrel{\mathrm{def}}{=}$$. Either leave it alone, or write the prose. PAR 20:13, 25 November 2006 (UTC)
 * Also - Does anyone have a problem with \equiv as long as it is accompanied by prose? PAR 20:19, 25 November 2006 (UTC)


 * As you may guess, I fully agree with PAR. I don't think it would be reasonable to autopost messages.  How about posting on some relevant main talk pages (e.g., General relativity)?  Moreover, I don't think that the people who have commented agree with the =^def decision.
 * I have seen alternate usages for basically every form of equality symbol there is. It's unfortunate that there is no universal agreement on \equiv, or :=, or =^Delta... even ~, or \approx, etc.  However, that's the way it is.  Real authors and editors have to deal with this issue, and generally use =, :=, and \equiv anyways.  My point is that we shouldn't go making up our own conventions.  I have never seen =^def or =_def anywhere, and I have seen =, \equiv, and :=, so I really feel that we should stick to convention.
 * I ask that the changes be stopped at least until some sort of formal poll is taken and a reasonable number of editors have chimed in. There must be some standard thing, like "Request for Comment", or something? --MOBle 20:35, 25 November 2006 (UTC)


 * Sorry, I hadn't seen KSmrq's comment. I've still never seen =^def in any text, which is what should matter.  Also, KSmrq seems to say that we should just use =, with accompanying prose.  So why is everything being changed? --MOBle 20:38, 25 November 2006 (UTC)


 * What is the "everything" of which you speak, that is being changed? As far as I can read, the conclusion of this discussion was to use plain '=' and qualify in prose if it is not clear that a definition is taking place. You seem to be complaining against the fact that somebody once in an old discussion advocated using =^def instead. Can't you just let it be? Henning Makholm 20:52, 25 November 2006 (UTC)


 * Thank you, Henning, but I think there may be a minsunderstanding. The complaint was about my replacement of \equiv with =^def in all articles on /equivlist where it was used for a definition. &mdash; Sebastian (talk) 20:58, 25 November 2006 (UTC)


 * (edit conflict) OK, I'm stopping it till we reach an agreement. I'm sorry, I thought it was clear that nobody liked the ambiguity of $$\equiv$$ being used for several different purposes. (See discussion in the rest of this section.) Unfortunately, this is not a good place to stop since I'm three quarters through the list, so I'm hoping we can reach agreement soon.
 * Regarding MOBle's points:
 * This is not something any of us made up, but I agree that we should use symbols that are as widely understood as possible. This was actually part of my motivation for doing this: I think that $$\stackrel{\mathrm{def}}{=}$$ is easier understood than $$\equiv$$.
 * I agree - I feel the same way.
 * I disagree, in addition to Henning Makholm's point: How are 2 and 7 (mod 5) any more identical than 2 and 2?
 * I agree. Please feel free to replace these cases when you see them.
 * I would love to use :=, but many people here felt it was not common enough.
 * In reply to PAR: I do have a problem if \equiv is used in places where it is not commonly agreed standard. I think we should avoid ambiguous symbols whenever reasonably possible. &mdash; Sebastian (talk) 20:57, 25 November 2006 (UTC)


 * Okay. I'm glad to learn that this was a misunderstanding.
 * As for Sebastian and number 3, I realized that \equiv has different uses, but this ambiguity is just something most authors live with. I wouldn't mind seeing :=, either, but I can see the point that it might not be common enough.  I've honestly never understood why = and context are not enough, so I guess my vote is for a simple = with accompanying text saying that it is a definition. --MOBle 21:04, 25 November 2006 (UTC)


 * I've used and seen \equiv as a definition in the literature, but I have never researched the subject. The use of = with explanation is ok, I still think \equiv with explanation is better, but if, outside my experience, it is used ambiguously, then perhaps = with text is best. PAR 23:48, 25 November 2006 (UTC)


 * "=" and context can be enough, and of course, good explanations are best. This means, we need to take loving care for the context, which takes more time than a simple replacement. With 81 remaining articles on /equivlist and about 3-4 occurrences per article, we got around 300 contexts or explanations to care for. So, do we have any volunteers to do this? &mdash; Sebastian (talk) 00:08, 26 November 2006 (UTC)


 * I'll do some, but is there a list we can check off? PAR 02:58, 26 November 2006 (UTC)
 * Cool, thanks! The list is /equivlist - just delete the bullet points for articles you completed. &mdash; Sebastian (talk) 06:32, 26 November 2006 (UTC)

Adding my opinion based on lots of math experience... First a fact of math writing:  The symbol \equiv has several common meanings in mathematics. Sometimes it means a definition, sometimes it means arithmetic congruence, sometimes it means equivalence under an equivalence relation. Probably it has other meanings. In a math paper or book, one has to see from context, or from an explicit explanation by the author (in words), what it means in each case. IMHO, that eliminates it as a standard Wikipedia conventional symbol for a definition. I don't have a strong opinion on := vs. other options, but I do think that when you define something, it always helps if you say that you're defining it, and then the = sign should be clear, and also := or =^def. (I have seen the latter used in print, though not often.) It comes down to the opinion expressed earlier, that if you want to be clear, you have to say what you mean in plain language, even if it's longer. End HO. Zaslav 06:11, 1 December 2006 (UTC)


 * For what it's worth, my late mother frequently used =_Df in her textbooks (especially in a mathematical logic book in which $$ A \equiv B =_{\mathrm{Df}} \ldots$$ might make sense. I wouldn't recommend using it here even if it were standard in some fields of mathematics, because the what the... factor is higher. &mdash; Arthur Rubin |  (talk) 17:42, 3 December 2006 (UTC)


 * The problem is not pure mathematics. The problem is physics, physical chemistry, engineering, etc. For a century, thermodyamicists have said things like "The Helmholtz free energy is defined to be $$A\equiv U-TS$$" and you folks are now charging through ruining perfectly good articles with this jihad against a notation that has been in use as long as the field has existed. Stop. Just stop. End this hideous equals-with-a-def-over-it abomination. All fields of study are not the same, and I assure you that those who study statistical mechanics and other fields do not want you tramping in and changing the notation on the basis of a discussion among a small self-selected group of people. This discussion is not widely known. This so-called "consensus" is not the consensus of the bulk of the people editing and maintaining pages in twenty different subjects in physics, chemistry, engineering, etc. where \equiv is in wide use. This change to a notation used nowhere but Wikipedia is not something that is widely acceptable. I don't know how many ways to say "there is not a consensus". If you feel that the \equiv notation is not understandable to people outside the field, then the right thing to do is to explain it. Put in a brief notation that "the symbol $$\equiv$$ in this context means "is defined as"" or some such. If you change the notation, what will someone do when they go from the encyclopedia article to a textbook on thermodynamics and find the \equiv symbol and wonder about it -- have you done them any service, or have you just confused them more in your attempt to invent a notation used nowhere else in the field? Again, stop this silliness, reverse these ridiculous edits, and simply explain what \equiv means when it is appropriately used. --Pmetzger 18:51, 3 December 2006 (UTC)


 * But your article doesn't say "The Helmholtz free energy is defined to be $$A\equiv U-TS$$". It just says "$$A\equiv U-TS$$". That makes it difficult to read for people who are not already so familiar with that discipline that they recognize &equiv; as a definition, instead of a logical equivalence, or an equivalence relation, or modular congruence, or... —David Eppstein 19:25, 3 December 2006 (UTC)
 * Then why not compromise and change the wording rather than the formula?


 * Introducing a notation unfamiliar in thermodynamics is at least as bad as keeping a notation that would mean something else in group theory; I don't expect Helmholtz free energy to suddenly begin talking about congruences, so I'm not sure that confusion is a real risk. Septentrionalis 20:52, 3 December 2006 (UTC)


 * I've repeatedly suggested what you are calling a "compromise". The rational thing to do is just explain what \equiv means in articles where it might cause confusion. The rational rule is "use the notation that is most commonly understood in a given field, explaining it if necessary", not "mindlessly adopt a consistent notation at the expense of clarity in fields that have traditionally used a different notation". The latter is a procrustean solution, acceptable only to those who do not understand the consequences. The proposed "compromise" is exactly what I've suggested, but it is claimed that we have "consensus" to do otherwise -- an incorrect claim, since clearly a lot of people are not agreeing. Meanwhile, people are altering articles that they have no business altering in the name of implementing said procrustean non-consensus, as though it was already a foregone conclusion. --Pmetzger 22:50, 3 December 2006 (UTC)


 * No, no, no! The rational thing is not to try to use any particular symbol with the meaning "defined" as, because no such symbol will be generally understood by all readers. Nobody is going to misunderstand "The Helmholtz free energy $$A$$ is defined as $$U-TS$$", and that is the true compromise between adherents of different symbols. Henning Makholm 23:38, 3 December 2006 (UTC)

A similar usage in probability theory
The notation


 * $$ X \ \stackrel{\mathcal{L}}{=}\ Y. $$

conventionally means that the two random variables X and Y both have the same probability distribution. The letter "L" stands for "law"; probability distributions are sometimes called "laws". Michael Hardy 04:11, 25 November 2006 (UTC)

Policy for WP:MSM
So, what exactly should we add to WP:MSM? How about the following: We could also recommend "$$=_{def} \, $$", as used in Implementation of mathematics in set theory. &mdash; Sebastian (talk) 23:18, 24 October 2006 (UTC)
 * For definitions, do not use "\equiv". If something is a definition try to say so in words. If that isn't possible, use ":=".


 * That article specifically discusses how to "define" (actually "implement") things in terms of other things, and then you want these "definitions" to stand out. Because they aren't truly definitions in the usual sense, we should not take them as examples.


 * It is different when definitions are introduced in the course of a discursive account. There are many ways of doing this:


 * We denote g_1(x) + g_2(x) + ... + g_n(x) by f_n(x). Then the sum f(x) is the limit lim f_n(x).
 * Letting f_n(x) stand for g_1(x) + g_2(x) + ... + g_n(x), we now define the sum f(x) to be the limit lim f_n(x).
 * Define f_n(x) = g_1(x) + g_2(x) + ... + g_n(x). Then the sum f(x) is simply the limit lim f_n(x).
 * Let a sequence of functions f_n be defined by f_n(x) = g_1(x) + g_2(x) + ... + g_n(x). Then the sum f(x) is the limit lim f_n(x).
 * We can then define the sum f(x) by f(x) = lim f_n(x), the limit of a sequence of approximations, where f_n(x) = g_1(x) + g_2(x) + ... + g_n(x).


 * In most cases the problem is not so much the ambiguity of a form like X = Y by itself, but the lack of appropriate text connecting the formulas. I don't want to outlaw the use of =def, but it shouldn't be encouraged by our style manual.


 * Perhaps we can collect some bad examples and show how to fix them. One candidate I'm nominating is in Geometric mean, where it is not obvious (I think) to the mathematically unwashed that in the first maths display the l.h.s. is not a definiend. Here no new symbol is being introduced. Contrast this with Polylogarithm. Here the opposite confusion might be possible: a reader stumbling upon the article might think that the two expressions connected by an equality sign are just two different, already understood, ways of saying the same thing. An easy fix is to amend the first line to read: "... is the special function Li_s that is defined by:". Or one could write: "The polylogarithm (also known as Jonquiere's function) Li_s is a special function that is defined by:". --Lambiam Talk  02:40, 25 October 2006 (UTC)


 * Good idea! Here's the seed for such a table, taken from my recent edits. I never claimed I was good at writing math prose, so I'm sure you'll have some ideas for improvements. Please don't hesitate to edit them directly in the table. I added a column "Found in" so we can easily take the improvement to the article. &mdash; Sebastian (talk) 20:24, 25 October 2006 (UTC)

Old version of table deleted - see new version below.


 * Hamilton's characteristic function &lt;math&gt;W&lt;/math&gt; is often defined as ... seems to mean that Hamilton's characteristic function has different definitions and that the often used one is ... This is not the same meaning as the initial sentence, which is that Hamilton's characteristic function, which is defined as ..., is also often used. Isnt't it right? pom 20:56, 25 October 2006 (UTC)
 * Good point! The word "often" is a bit overused in that article (and maybe Wikipedia in general) anyway. For the reader, much more relevant than how often something is used is what it's used for, and if it helps him/her solve his/her problem. I'll take a closer look at that article and see what I can do. &mdash; Sebastian (talk) 21:41, 25 October 2006 (UTC)
 * I suggest: "another action function, Hamilton's characteristic function $$W$$, is often introduced. It is defined as ...". I find LaTeX notation hard to read and have produced a typeset version below, in which I've tentatively applied this suggestion (but not in the actual article). By the way, all the examples use(d) \equiv, but many articles using = for definitions would also improve by similar changes. --Lambiam Talk  22:24, 25 October 2006 (UTC)
 * Yes, I like your proposed wording. But since I just rewrote the whole section it would doesn't fit exactly anymore. Please feel free to change as you see fit. I also prefer the typeset, so we don't need to keep my old table. I agree with your point that these changes have a wider applicability - all the more reason to put something like this table in the style guide. &mdash; Sebastian (talk) 22:45, 25 October 2006 (UTC)

Related problems encountered in listed articles
Optimal stopping uses &equiv; to state the distribution of a random variable. That is, they write X &equiv; D where X is a variable and D is a distribution. Is that one of the uses of &equiv; we should be avoiding, or is it ok? Maybe it should be a membership symbol rather than either = or &equiv;? —David Eppstein 21:31, 22 October 2006 (UTC)


 * I believe X &equiv; D is very much a non-standard use and should therefore be avoided. What is wrong with saying in words that X is a random variable with distribution D? Independence has to be stated in words anyway; we have no notation for that. --Lambiam Talk  01:14, 25 October 2006 (UTC)


 * Thanks for the suggestion — I agree that saying it words works better than notation here, and have made that change. The rest of the article could still use some work, but that's beyond the scope of what I want to do with it tonight. —David Eppstein 02:51, 25 October 2006 (UTC)

Bugzilla
Added bug 7753. → Aza Toth 21:45, 29 October 2006 (UTC)

Strong objection to ditching \equiv
I was just informed on the talk page for an article that I help maintain that some people here appear to believe that Wikipedia gets to revise a century of usage by ditching $$\equiv$$, and that, indeed, said decision has "already been made".

Pardon my saying so, but no, that's not really Wikipedia's decision to make. $$\equiv$$ is in wide use in all sorts of places. Those who claim to have math degrees and to have never seen it before, well, I don't know what math classes you were taking, but there is a strong reason that Knuth put the character in TeX's math font, and it wasn't perversity.

I see that some believe this issue is "decided", but that's absurd. \equiv is not going from articles I edit, because it is there in all the references I use and all the papers I read. If you don't like it, the place to take it up is with organizations like the American Mathematical Society, and not in a Wikipedia project talk page. Abolishing it is the moral equivalent of Wikipedia deciding, as a matter of style, to rename Hydrogen "Element One" because that is "more logical". No, sorry, that's not what we get to do around here. Wikipedia is a reference, not a place to try to change the world's notational conventions. This is an encyclopedia, not a reform movement. If you don't like the way professionals in certain fields write their equations, take it up with them directly.

Repeating, in the specific case of particular pages I edit regularly, I've checked the standard notation in reference works, and it is \equiv (i.e. $$\equiv$$), and so that is how it should remain on those pages until such time as the textbooks and papers in the field change. Let me know when you have gotten all the textbooks revised. --Pmetzger 21:12, 2 December 2006 (UTC)


 * Sorry, but you do not own those pages. Regardless of what you believe, many readers will not understand without additional explanation that "$$A\mbox{ }\equiv\mbox{ }U-TS = \mu n - PV$$" is supposed to mean: "$$A$$ is defined by the equation $$A = U-TS$$, which, by the way, happens to be equal to $$\mu n - PV$$." Why wouldn't it mean: "the proposition $$A$$ is true if and only if the equality $$U-TS = \mu n - PV$$ holds"? Have you read the discussion on this page at all? --Lambiam Talk  21:57, 2 December 2006 (UTC)


 * First, I never claimed to "own" any pages. I'm just an editor like everyone else. Second, I've consulted several texts that discuss thermodynamics in the last few hours. Of them, only Fermi's treatment from the 1930s used $$=$$ rather than $$\equiv$$ -- the rest use \equiv. If people don't know what $$\equiv$$ means, then I have no objection to explaining what it means. By all means, lets add annotations explaining what the symbol is for -- explaining things is, after all, the purpose of an encyclopedia. I do, however, object to our deviating from common notation. --Pmetzger 01:30, 3 December 2006 (UTC)


 * I agree with Lambiam. It seems odd that Pmetzger would come and post so vehemently right below a very long and, I believe, fruitful discussion addressing this issue.  But to be fair, what are these textbooks that use \equiv to mean definition?  Maybe this is a "field of study" issue.  In pure mathematics, I have never seen it used, but that's not to say that other fields don't use it.    If it can be demonstrated that there is a large number of textbooks in a well-established field of study that considers this usage a proper convention, then we may have no choice.  It may be like the serial comma: something people have strong feelings about, but that ought not to be changed upon sight. VectorPosse 00:53, 3 December 2006 (UTC)


 * Even though there may be textbooks that use $$\equiv$$ for definitions, we certainly do have a choice as to whether to use this notation in our encyclopedia. At least, this discussion has demonstrated that some people would not understand it on sight, and it is not as if people who do understand it would not also understand a definition set out in prose. Henning Makholm 01:08, 3 December 2006 (UTC)


 * If people don't understand it on sight, then explain it. One would have to put prose in to explain that an equals sign was intended as a definition anyway, so there is no rational reason you can't instead explain what an \equiv symbol means. As for the vehemence of of my remarks, it is because there are a variety of areas of study and they have a variety of common notations and it is not our job to change them. If you want just one example of a book that uses $$\equiv$$, have a look at Levine's "Physical Chemistry". I could find a dozen more examples, and if people insist I will keep enumerating them until the point is made. As for the discussion, I think the fact that most people who edit pages do not keep up with every discussion is likely why you haven't heard more objection. --Pmetzger 01:30, 3 December 2006 (UTC)


 * I agree with Pmetzger. The notion that ":=" would be better understood is also nonsense, and the "def" on top of an equal sign is even worse, something that is going to be totally strange to almost everybody.  Gene Nygaard 01:37, 3 December 2006 (UTC)

For what it is worth, I should point out to readers here that using &equiv; for definitions is very common in physics (much more common than := or alternatives). In fact, the first five textbooks I pulled off my shelf all use it. They are I agree that good prose is the best solution, but I wouldn't go so far as to banish &equiv; from physics articles. It is, after all, a very standard notation in that field. -- Fropuff 01:38, 3 December 2006 (UTC)
 * Jose and Saletan, Classical Dynamics
 * Hassani, Mathematical Physics
 * Sakurai, Quantum Mechanics
 * Griffiths, Introduction to Electrodynamics
 * Callen, Thermodynamics and an Introduction to Thermostatistics


 * That was my thought too; very common, and more likely to be understood than the alternatives. And the really incomprehensible thing about some of the discussion above is the notion that \equiv ($$\equiv$$) is somehow different from &amp;equiv; (&equiv;) or &amp;#x2261; &#x2261; or &amp;#8801; &#8801; or just entering the ≡ character (by copy and paste or whatever).  Gene Nygaard 01:53, 3 December 2006 (UTC)


 * So you think that alternative B below is more likely to be understood than A?
 * A. The second Chebyshev function $$\psi(x)\,$$ is defined by
 * $$\psi(x) = \sum_{n \leq x} \Lambda(n).\,$$
 * B. The second Chebyshev function
 * $$\psi(x) \equiv \sum_{n \leq x} \Lambda(n).\,$$
 * Somehow I find that unlikely. The use of "equiv" as meaning "is defined as" is definitely not usual in mathematical texts, and I doubt it will ever become so, because the symbol already has several meanings (equivalence, congruence), and overloading it thus is likely to create confusion. Just consider defining negation by "¬p ≡ p ≡ false", or the divisibility relation by "m|n ≡ n ≡ 0 (mod m)". Physics texts don't have this problem because they don't deal with logic or number theory. I'm fairly sure that most of our readers have never opened a physics textbook beyond the elementary level. In the texts on physics topics at wikiversity (e.g. ) I don't see the use of "equiv" for definitions. I also don't see it in any text I can easily get my hands on, which, I must confess, are all many decades old. In any case, as far as I can see from the above discussion the main issue most participants in the discussion have is not the use of "equals" versus "equiv" per se, but the use of these symbols for a definition without making it clear in the context that the symbol indicates a definition. --Lambiam Talk  08:10, 3 December 2006 (UTC)

It seems the obvious answer here is that physics represents a field where &equiv; is both commonly used and unambiguous (while in mathematics it is not - to me in means congruence modulo something) and in that case it seems only reasonable to follow the publications in the field and use &equiv; in the physics articles on subjects that traditionally use it. On the other hand I tend to agree with with the eventual consensus view here, at least for pure mathematics articles, that &equiv; isn't the best option due to rarity and ambiguity of meaning, and that clear prose is the answer. Leland McInnes 09:38, 3 December 2006 (UTC)


 * Re the example given: why does it have to be the first versus the second? This is silly. Clearly the right thing is to say:
 * The second Chebyshev function $$\psi(x)\,$$ is defined by
 * $$\psi(x) \equiv \sum_{n \leq x} \Lambda(n).\,$$
 * and then the intent is quite clear. Say what the \equiv means, leave the equiv, all is well. However, I don't even see why this is necessary in the sense that the problem is not replacing all definitions with the use of \equiv but removing all uses of \equiv from contexts like thermodynamics, statistical mechanics, etc., where the use is traditional. If people want to leave pure math articles alone, fine -- different fields have different notations. However, people are now going through and replacing \equiv with the abomination equals-sign-with-def-over-it that was invented here only a few days ago for articles in areas where \equiv has been used forever. If people are confused about what \equiv means, just add an explanation (as above) to the prose and leave the \equiv -- which has been in use in these fields for decades if not a century -- alone! --Pmetzger 18:40, 3 December 2006 (UTC)


 * I hate to break it to you but equals with def over it is the common format in many fields of mathematics and has been in common use for quite some time (there's a reason there's a unicode character for it). I've also seen both &#x2254; and &#x225C; used reasonably frequently. The aim of the discussion here was to try and come to some agreement on a common notation for Wikipedia for the sake of consistency. If your field has a consistent common notation already then fine, use that in the articles on that field. The discussion and conclusions here are still valuable, and it seems to me that the only issue is that some people are pushing things a little too hard and a little too far outside the logical domain (let's be honest you are discussing physics articles and this is WikiProject Mathematics). -- Leland McInnes 20:28, 3 December 2006 (UTC)


 * I don't ask anyone to stop using what they are already using, but the same deference isn't being shown in both directions. You may say "lets be honest you are discussing physics articles and this is WikiProject Mathematics" but people are editing physics articles to remove the use of \equiv, and they're pointing us here for the reason why. I've said, repeatedly, articles should reflect usage common in the field, but then people have said "no, we have to be consistent and use one thing across the whole encyclopedia", and they've gone off to implement this madness. The only reasonable rule is "follow the notation commonly used in a field, and explain it if necessary". --Pmetzger 22:43, 3 December 2006 (UTC)


 * I agree with Pmetzger that people shouldn't go to physics pages (or even applied maths) and replace $$\equiv$$ with $$\stackrel{\text{def}}{=}$$. I doubt the latter is clearer for people reading physics articles. However, I agree with others here that "The second Chebyshev function $$\psi(x)$$ is defined by $$\psi(x) = \ldots$$" is preferable to "The second Chebyshev function $$\psi(x)$$ is defined by $$\psi(x) \equiv \ldots$$", even in physics pages, since I think former is clearer to everybody and in wider use (even better in my opinion would be "The second Chebyshev function $$\psi$$ is defined by &hellip;", but that's a different matter). -- Jitse Niesen (talk) 00:54, 4 December 2006 (UTC)

Re #1: This is not a "jihad against symbols". It is an endeavor to disambiguate the different uses of \equiv (demonstrated so nicely by Lambiam above). Re #2: It is the best, but it takes a lot of time. We're still at about 300 occurrences - if you really feel strongly about this, please help by editing the articles on /equivlist.

If this is not immediately obvous to you, please read the older parts of this section. I'm tired of hearing these misconceptions over and over again. &mdash; Sebastian (talk) 02:31, 4 December 2006 (UTC), amended 03:47, 4 December 2006 (UTC)


 * Maybe it is time you paid some attention to the objections. You might claim here that "this is not about ditching \equiv" but that quite clearly was the result of the previous discussions, with editors going on a rampage to delete it.  You might claim now that "nobody here denies that \equiv has legitimate uses" but the fact of the matter is, until Pmetzger spoke up, most editors would reasonably have assumed that denial.
 * Why are all the people so worried about theoretical ambiguities not on a rampage against the "=" symbol? Gene Nygaard 11:45, 4 December 2006 (UTC)

Here is American Institute of Physics, AIP Style Manual,, 4th ed. 1990, Appendix F:Special symbols available for typesetting, p. 44:


 * R3  ≜   corresponds to
 * R4  ≡   identically equal to; equivalent to; triple bond
 * R5  ≢   not identically equal to; not equivalent to; not always equal to

Note that ≝ is nowhere to be found. Nor is :=, but that of course can be composed of two characters without a special typesetting symbol. Gene Nygaard 14:08, 4 December 2006 (UTC)


 * A general usage in physics books and articles certainly should be respected. However, the 'worry about theoretical ambiguities' has rather concrete grounds.  Two points:
 * Pmetzger and Gene Nygaard, are you familiar with notation like $$ 17 \equiv 33 \pmod 8\,$$, do you recognise what this means in 'ordinary mathematemathics', and do you understand that this is the by far most common usage of the &equiv; symbol at least our math students meet in their courses? ('Our math students' here means 'The students at the Department of Mathematics of the University of Stockholm, except possibly at our section of mathemathical statistics', but I strongly suspect that the same is true for most places where physics and pure mathematics are taught at different departments.  They might meet &equiv; in the sense of implication, if they take a course in mathematical logic.)  If you are not, you may reread Lambian's explanation supra.
 * Our students will in all probability not meet similarly widely different usages of the equality sign = ; except, possibly, in connection with a usage of the Ordo symbols. (However, some text books avoid this ambiguity by consistingly using words instead of the equality symbol in order contexts; ' f(x) is O(x2)' instead of ' f(x) = O(x2)').
 * I am 'old enough' to recognise the usage of &equiv; in the meaning 'identically equivalent to' in calculus. (I have once or twice tried to convince some of our 'youngsters' (ph. d. students et cetera) that this usage is not an outright error of students, and that they actually may have met this alternative usage of the symbol at school.)  However, while this usage is closer to the usage of &equiv; in definitions, it does not quite coincide with it.  Being indentically equivalent is a symmetric relation; you may as well write $$ g(x)^2 \equiv f(x)\,$$ as $$f(x) \equiv g(x)^2\,$$, since both formulations simply mean that are defined for the same values of x, and that $$f(a)\,$$ and $$g(a)^2\,$$ coincide for each such value a.  A definition is assymetric, on the other hand.
 * In other words: There are real reasons for concern, and it should be recognised in articles which are not 'clearly mathematical' or 'clearly physical' but aiming at being understood from both sides. IMO, the Chebychev polynomials belong to this intersection of areas.


 * With this said, I agree with Pmetzger and Gene Nygaard, that mathematicians shouldn't try to force a certain usage onto 'pure physics' articles in the name of an encyclopaedian uniformity. I don't think you'll find such a far-reaching uniformity (going further than the main-stream scientists have achieved themselves) in other major encyclopaedia.  What we could do, on the other hand, is to try to be more aware of the differences, and try to find some way to help students of both subjects translate notation and concepts from one area to the other.  I've noticed other examples of such 'Babel language confusion'; e. g., when theoretical physicists suddenly chock pure mathematicians by employing the Einstein summation convention.  Probably we are causing similar troubles for physicists, now and then.  I think we should try together to identify such differences, and make some easily accessed pages explaining the differences.  IMO, this could yield a tangible contribution to the wikipedia.--JoergenB 17:50, 4 December 2006 (UTC)


 * Perhaps this is a regional difference in addition to a field difference. As far as I know, the above modulo statement should be written with a standard '=' sign.  These differences should be worked out, but I agree with Pmetzger that the "equals sign with def" should be avoided.  Can ≡s be wiki-linked to Table of mathematical symbols, or is that unfeasible? johnpseudo 18:08, 4 December 2006 (UTC)


 * Unfortunately, linking doesn't work in mathematical formulas. &mdash; Sebastian (talk) 18:58, 4 December 2006 (UTC)

If everyone agrees that adding prose is the best option
Sebastian, I believe, claims that the beginning of this discussion shows that everyone agrees that adding prose, presumably such forms as "We define" and so forth, is the best option. This is not at all obvious to me; but if it is so, let's agree to go do it, as part of the slow improvement that is Wikipedia. It will take a long time; but so will lots of other important things. Septentrionalis 18:19, 4 December 2006 (UTC)


 * Yes, that's what I claimed. At least I'm not aware of anyone opposes it. But I do disagree that it will all just work out magically by the Wikipedia ant process. It hasn't done so in the past - in the contrary, we accumulated thousands of formulas where ≡ is used for definitions. This is a misleading deviation from approved standard.


 * As Gene Nygaard writes above, the American Institute of Physics defines "≡" as "identically equal to; equivalent to; triple bond". Using "≡" for "definition" is misleading. I was confused about it myself - which was in fact the reason why I started this whole thread with my initial question, and why I still believe we should eliminate this misleading wrong usage. &mdash; Sebastian (talk) 18:51, 4 December 2006 (UTC)

Here's a table with the options we have so far - please feel free to amend: &mdash; Sebastian (talk) 19:27, 4 December 2006 (UTC)

One question to all who believe that slow improvement (the "ant algorithm") fixes the problem: Why are you confident that it will improve formulas with \equiv signs, but not formulas with =^def signs? &mdash; Sebastian (talk) 19:41, 4 December 2006 (UTC)


 * Spelling out the definition in words will improve the readability of an article no matter which kind of symbolism it previously tried to use for "is defined as". Replacing one symbol with another symbol will not improve anything at all; it will just make the article look strange to a different set of people than it looked strange to previously. Your assertion that =^def is a "lesser evil" or "only a third as bad" as \equiv (as implied by the difference between B-A versus D-A) appears to be essentially unsupported by this discussion. Henning Makholm 21:46, 4 December 2006 (UTC)
 * It is the lesser evil because it is not ambiguous. This has been discussed ad nauseam already, and nobody ever countered this argument. &mdash; Sebastian (talk) 21:53, 4 December 2006 (UTC)
 * Each symbol is unfamiliar to some people. It ought to be clear to any reader of this discussions that there are people who understand \equive more readily than =^def (or at least they claim to, and why whould they lie?) The fact that \equiv has some other legitimate uses should not change the relative merits more than to, say: \equiv: F; =^def: E-; prose: A. Henning Makholm 22:06, 4 December 2006 (UTC)
 * I agree, and I changed the table accordingly. &mdash; Sebastian (talk) 22:16, 4 December 2006 (UTC)


 * I appreciate that this debate has very poor timing- a lot of work has already gone into this, and changing course now would certainly result in a lot of wasted man-hours. However, what does =^def add that ≡ doesn't have?  While ≡ is a standard that people in most fields of science would understand, =^def is brand new, and it is just as confusing to the casual reader if it isn't clarified using prose.  Wikipedia is just an encyclopedia, and for people inclined to get more in-depth understanding on these topics, developing non-standard mark-up will not help. johnpseudo 21:03, 4 December 2006 (UTC)


 * What it adds is DISAMBIGUATION. Sorry for shouting, but it sometimes is necessary to get heard. &mdash; Sebastian (talk) 21:53, 4 December 2006 (UTC)


 * Your assertion that "≡ is a standard that people in most fields of science would understand" is just plain wrong, as evidenced by this very discussion. Henning Makholm 21:48, 4 December 2006 (UTC)


 * I feel like this forum is not an accurate judge of the level of acceptance of ≡. This unfamiliarity with ≡ is a little foreign to me, so I'll see if I can do a little research.  Re Sebastian: I'll listen, whether or not you shout :-) johnpseudo 23:08, 4 December 2006 (UTC)


 * OK, thanks. I know, it's hard to jump into a discussion that already is several pages long and understand what it's all about right away. It was just an excuse for me to draw attention to a point that many who join this discussion are not aware of. So, this is really not about unfamiliarity. I would really appreciate if you could confirm that the information that this is about disambiguation has reached you. &mdash; Sebastian (talk) 23:17, 4 December 2006 (UTC)
 * One of the goals here certainly is to disambiguate between equality and definition, but we must also keep in mind that non-standard symbols reduce the usefulness of an encyclopedia by forcing readers to learn extraneous information. The key here is to determine the proper balance between these two factors. johnpseudo 00:06, 5 December 2006 (UTC)


 * This is a very nice statement, but what does it mean in practice? If you have any idea for a concrete plan of action, please let us know and I'll be happy to list it in the table above. &mdash; Sebastian (talk) 17:50, 5 December 2006 (UTC)


 * Since we all agree that prose is what will distinguish between a clear article and an unclear one, perhaps we treat symbol terminology the same way we do dialects. As long as what the authors of the article have written is clear, they can use whatever symbol they feel is most appropriate.  This may help with the problem of different fields using different terminology.  Trying to reach some kind of consensus between all scientific fields here in this forum wouldn't work.  Making grand, sweeping changes to every article that uses an /equiv should be avoided, but in articles in which the "definition" clarification is important, the symbol should be accompanied by good prose.
 * That doesn't really help us in our current situation though, because there have been grand, sweeping changes made already. I think the changes should be reverted to whatever terminology was used before. johnpseudo 18:20, 5 December 2006 (UTC)
 * Yes, it is very reasonable to change things back (for now at least) to the way they were before this thread. As I have already suggested in this discussion earlier, this is similar to many issues of punctuation and spelling on Wikipedia.  We leave things the way the original editor had them insofar as they are correct for a large group of our readers.  I hope to insist at least a little bit that pure math articles maintain the strong tradition of using = only (plus prose, of course).  But I'm happy for physics articles--even ones that border on pure math--to use \equiv since it is widely accpepted in that community.  And CS articles should use := if that is an established method of "assignment" in that field.  I despise =_def and =^def and all variants thereof, but only  because = is more common, more universally understood, and less obtrusive.  Even at that, I would think twice before changing =^def to = in an article "just because".  VectorPosse 19:30, 5 December 2006 (UTC)


 * You are both digressing. Your statements do not address disambiguation, which is the point of this initiative. &mdash; Sebastian (talk) 21:31, 5 December 2006 (UTC)
 * Disambiguation applies to articles. It is not necessary (or possible) to disambiguate each symbol from all other possible uses in Wikipedia as long as it is clear in context. Septentrionalis 21:39, 5 December 2006 (UTC)


 * No, disambiguation is a general term. It does not only apply to Wikipedia articles. Your second sentence is true, but your premise is not true: This particular symbol is not always clear in context. &mdash; Sebastian (talk) 21:57, 5 December 2006 (UTC)
 * And most editors here agree that the solution is to make the context clear when necessary. Septentrionalis 22:04, 5 December 2006 (UTC)
 * Yes. Actually, everybody agrees that it's the best solution, as the name of this subsection correctly states. But it is not feasible. &mdash; Sebastian (talk) 22:11, 5 December 2006 (UTC)


 * I do not believe it is a digression to request that the "fixes" which turn out not to be fixes and have upset people (especially in physics) be reverted until real consensus is formed. As for disambiguation, it is not our place to rewrite math notation to make it clearer in fields that already have well-established traditions.  This has always been a problem in math.  Clear exposition is the answer.  There has been consensus on that much, but little else has been decided.  (Just to be sure, I went back and read the whole thread one more time.  Nobody agrees on anything else.) VectorPosse 22:15, 5 December 2006 (UTC)
 * To be clear about my point: the equal sign does not need disambiguation. If it did, the math community would have changed it a long time ago. VectorPosse 22:18, 5 December 2006 (UTC)
 * I'm not sure how you plan to revert the changes, since many of them were made by different people at different times. Could you give some examples of non-math articles where these changes were made?  I thought that the discussion here was clearly only intended for math articles. It is certainly appropriate for the math editors to write a Manual of style (mathematics), and the presentation of definitions could be covered there.  CMummert 22:29, 5 December 2006 (UTC)
 * I don't know how to revert the changes. I thought Sebastian was keeping a list since he said earlier that 75% of the work was done.  I figured someone was keeping track.  If not, then I suppose there's not much that can be done.  Also, I assumed that physics articles were affected due to the entrance in this thread of several editors crying foul about physics articles.  I have no first-hand knowledge of which articles have been changed. VectorPosse 22:55, 5 December 2006 (UTC)


 * Thank you for rereading the whole thread. It's really a lot of work to go through all of this largely unstructured text. I'm starting to think that it might be better to start over in a more collaborative way, similar to a Wikipedia article.
 * Maybe the term "digression" was a bit harsh. What happened was that I had just reached an agreement with Johnpseudo that "One of the goals here certainly is to disambiguate", then he proposed a policy which did not disambiguate anything, and you followed up on the same tangent. &mdash; Sebastian (talk) 22:32, 5 December 2006 (UTC)

Way too serious. I mean, way way too serious about a format issue. As on some other points (e.g. spelling) if there is not going to be a settled consensus, just try not to annoy others on this. The wiki way isn't about six-week threads that settle nothing. Charles Matthews 22:35, 5 December 2006 (UTC)


 * Thank you! That's a good point which I hope everyone reads who considers this a mere format issue. I hope we can move to a rational discussion, where people who see this as a problem that impedes understanding, and who do the right thing by following "WP:SOFIXIT", are not held up by rants, many of which posted without care for what has been said in the discussion before. &mdash; Sebastian (talk) 23:52, 5 December 2006 (UTC)


 * I would like to address the issue that ≡ is "a standard that people in most fields of science would understand" while ≝ is "brand new". I think it's clear from discussion here that for a great many people ≡ means something other than definition - for most mathematicians it means congruence or a similar statement of identity or exact equivalence. Equally impotantly it needs to be recognised that ≝ is not "brand new", but is in fact quite common is many fields. That it is not new should be clear from the fact that there is a unicode character for it, U+225D: EQUAL TO BY DEFINITION. Indeed the only other equivalence relation character in Unicode to specify itself as being definitional is U+225C (≜) which is described as equal to by definition in the comment (though is named DELTA EQUAL TO). I have sympathy for the physicists who are having their toes trod on here, and would be more than happy to leave physics articles to use whatever notational convention they agree on. What I object to is the implication that, since people are apparently only familiar with their own field, their particular notation is "a standard that everyone understands" and anything else is just people making stuff up. -- Leland McInnes 22:41, 5 December 2006 (UTC)


 * I disagree with the idea that improving context is "not feasible". It may not be able to be done en-masse, with hundreds of edits in a week or two, but it is certainly feasible in the long term and will achieve the goal of disambiguation.  I agree with Charles Matthews, CMummert, and VectorPosse, and I think that this change to =^def can serve math articles well but should be carefully kept out of other fields. johnpseudo 22:54, 5 December 2006 (UTC)
 * Of course it's feasible. Feasible does not mean "done by next week." We have the list of articles which use \equiv; and those of us who feel this is the most important thing thatWikipedia can do can work on that. The rest of us will remember to edit any definition we come across to say "definition." Septentrionalis 02:55, 6 December 2006 (UTC)
 * Well, maybe I've been impatient. I'd be happy to be proven wrong. I'll take another break from this for a month or two and we'll see how much the situation improves. If there still is no promising progress towards eliminating unnecessary misleading uses of \equiv, then I'll volunteer my easy 2-hour solution again. &mdash; Sebastian (talk) 07:47, 6 December 2006 (UTC)

Implementing proposal
I've created Wikipedia talk:WikiProject Mathematics/equivlistrevert for reverting non-math changes. Sebastian, you should finish the job you've done on /equivlist with math articles. johnpseudo 15:47, 6 December 2006 (UTC)
 * Hold on a second. As I've pointed out, there's no consensus that things should be changed even in math articles.  Many of us have expressed that especially in pure math articles, the = should remain.  Maybe I am misunderstading what you mean by the "job", but if by that you mean changing = to =_def (or something like that), then Sebastian should not finish the job but should still plan to take a month or two off like he suggested he would.  Please correct me if I have misunderstood the thrust of your comment. VectorPosse 16:18, 6 December 2006 (UTC)
 * Never mind. I think you're saying to change \equiv to =^def and not = to =^def.  Well, I still disagree with that, but since both \equiv and =^def are equally bad in my book (for pure math articles at least), I won't say anything either way about it. VectorPosse 16:46, 6 December 2006 (UTC)
 * I thought the agreed on change was "=...as a definition" and that sort of thing, which which no one, so far, has any problem. Septentrionalis 20:16, 6 December 2006 (UTC)

Euler reciprocity?
I did some edits to Euler reciprocity relationship. I agree with whoever put the "context" tag there: its opening sentence is horribly abrupt, not informing the reader that mathematics is what the article is to be about, etc. But I wonder if this article ought to exist. As nearly as I can understand it, it's another statement of what is called Clairaut's theorem. (If you tell me that it's obviously supposed to be Clairaut's theorem, that may be because I edited it to say what I guessed it was intended to say.) Michael Hardy 01:25, 17 November 2006 (UTC)


 * I also tried to find out what Euler reciprocity relationship is supposed to refer to, before you edited the article. As far as I could see, it's indeed the same as Clairout's theorem, but I wasn't certain because I found only a few references and none were very clear. I think a redirect is in order. By the way, symmetry of partial derivatives is also on that subject. -- Jitse Niesen (talk) 04:10, 17 November 2006 (UTC)

Now I've put "merge" tags on these three articles. Michael Hardy 04:13, 25 November 2006 (UTC)


 * This seems like yet another instance of "theorems are named after the first person after Euler or Gauss to re-discover them" -- Euler was indeed the first to discover this. By the way, in Thermodynamics, the relation is used a lot, for example to prove the Maxwell relations, and it is generally known as the Euler Reciprocity Relationship there. I would make sure that both names are featured prominently because people reading things like thermodynamics texts will be hunting for explanation under the name "Euler Reciprocity Relationship" and not "Clairaut's theorem" --Pmetzger 05:15, 3 December 2006 (UTC)


 * John L. Greenberg seems to claim that Clairaut had priority (in the 1730s, versus Euler in the 1740s) in a book review appearing in Annals of Science 41 (1984), 171–177. He refers to his (Greenberg's) prior article, in the same journal, volume 39 (1982), 1–36. Michael Slone (talk) 06:56, 3 December 2006 (UTC)

STIX Fonts
The STIX Fonts project will make the beta version of its fonts available for download in early December. This will be a great boon to all mathematics readers, and of special interest to the Wikipedia mathematics community. The fonts come with a generous license, and now would be a good time for experts here to review it to decide if it will cause any problems for us. For example, does item 2 apply if a Wikipedia page displays an equation as a PNG typeset with these fonts? (What is considered a "derivative work"?) --KSmrqT 10:38, 20 November 2006 (UTC)


 * you could always stick text metadata in a chunk in a PNG. the text from the license is pretty small; it could be abbreviated and then compressed in the PNG, but it still might be a big price to pay for zillions of little PNGs.  (200 bytes?)  someone could write to the STIX project to ask if it's necessary for each image; that is, the Wikipedia as a whole could be the work.  Lunch 19:47, 20 November 2006 (UTC)


 * What I'm hoping is that using the fonts in a document does not constitute a derivative work. Otherwise, anyone who typesets a paper using these fonts has the same problem. I'm hoping they mean something much more narrow, like a new font derived from these. --KSmrqT 22:52, 20 November 2006 (UTC)


 * They seem very hazy on the how the fonts are published, in terms of what formats. They may be true-type fonts or similar which can be easily resized. Ideally we would of course use MathML for the output, in which case font selection would be left to the browser. In any case we'll need to sweet talk some of the MediaWiki developers, and probably file a bug when they are finally released. --Salix alba (talk) 23:59, 20 November 2006 (UTC)


 * Looking at item 3 of the licence: You may (a) convert the Fonts from one format to another (e.g., from TrueType to Postscript), nd (b) embed or include a subset of the Fonts in a document for the purposes of allowing users to read text in the document that utilizes the Fonts. So this seems to give explit permission for our needs. I guess we could probably just add the Stix Fonts to the general Copyrights page, or link to it from that. I'm guessing a document that includes the fonts is not a derivative work, but a program which convert to PNG would be. --Salix alba (talk) 00:12, 21 November 2006 (UTC)


 * with regards to using the fonts to produce a document, copies of fonts included in PostScript and PDF files often have (short) copyright notices included/encoded with them (but not whole licenses). as to what's considered a "derivative work", that may be partly up to the copyright holder and what's set in law and court precedents in a given country; i dunno - ask an IP lawyer or the STIX project.  if someone does approach the STIX project, they might also ask if the fonts could be released under the GFDL.  MicroPress might not want to though.  salix is right in thinking that we could punt on the whole issue if we used MathML and had the browsers worry about rendering... :)  Lunch 20:16, 21 November 2006 (UTC)


 * Some of the legal issues with FOSS and font licenses are addressed in a February, 2006 article by Bruce Byfield. He mentions that the STIX license evolved in response to feedback.EdJohnston 17:32, 24 November 2006 (UTC)

Expert requests
Hey there folks. I've been sorting through the tags over the last few days and there are a couple requets in your pile. Could you take a look at Category:Pages needing expert attention from the Mathematics Portal? Don't be thrown by the word portal; It's pretty much just a category of math articles that requested expert help. Thanks much! --Brad Beattie (talk) 19:03, 20 November 2006 (UTC)


 * Category is defunct; now there is Category:Pages needing expert attention from Mathematics experts. And there is, of course, as always, Pages needing attention/Mathematics/Lists. --Lambiam Talk  10:13, 23 November 2006 (UTC)

Thales' Theorem
Some of the interwiki links provided on this page describe another theorem, also credited to Thales of Miletus, proving that parallel lines intersecting a pair of intersecting lines create similar triangles. (See the featured article on the French wikipedia, fr:Théorème de Thalès for probably the best explanation). What is this theorem called in English, and is there an article here about it? (There should be.) Rigadoun (talk) 16:22, 22 November 2006 (UTC)


 * After exploring a little, I believe that two fundamentally different theorems are tied to Thales' name. The French article picked one; we picked the other. Each has some importance, but each can also be seen as a simple corollary of something more basic. --KSmrqT 05:21, 24 November 2006 (UTC)

Corrections to inverse trigonometric functions
I made a number of corrections to the article Inverse trigonometric function, in particular to the section Definitions as integrals, which was riddled with errors (about as many as it has formulas). It would be a good idea if someone who has access to a textbook with such formulas, or Abramowitz & Stegun, checked this, and if possible perhaps also the other formulas in the article. --Lambiam Talk 17:15, 22 November 2006 (UTC)
 * I have checked and reformatted the series and integral sections. The advent of "align" is a boon.
 * A general note: do not set the "d" in "dx" as roman; it should be italic. Thus, for example,
 * $$ \int_a^b x^2\,dx $$
 * not
 * $$ \int_a^b x^2\,\mathrm{d}x $$
 * should be used. --KSmrqT 03:20, 25 November 2006 (UTC)

I hadn't noticed we now have "align"---thanks for mentioning this. Using \begin{matrix}, etc., for this produced some really ugly results in many cases. Michael Hardy 03:44, 25 November 2006 (UTC)


 * Several people worked on the article, most recently myself, and I think that it is substantially better now. However, I still feel uncomfortable with the section Inverse trigonometric function. Specifically with distinguishing the principal branchs of the complex functions and making sure that the branch cuts are in the right place. JRSpriggs 06:25, 7 December 2006 (UTC)

Long-range dependency and heavy-tailed distribution
These were formerly a single article, which conflated LRD processes with long-tailed distributions as if the presence of a long-tailed distribution only ever arose as a result of LRD, and vice versa, and that they were, in effect, two aspects of a single concept. Terms like "memoryless distribution" were used...

I've tried to separate the two, but I'm no expert, and I'm pretty sure the result is still a mess. Can anyone with some probability/statistics/queueing theory knowledge help tidy these up and proofread them for errors? -- The Anome 00:03, 24 November 2006 (UTC)

Dǎnuţ Marcu
I just made an article on a serial plagiarist Dǎnuţ Marcu. The hope is that "contributions" of this person become better known. Please take a look and contribute to make the article adherent to WP style. Also, keep an eye on it - I am afriad there might be a "speedy deletion" move by the Marcu himself. Mhym 02:29, 24 November 2006 (UTC)


 * You must be very careful. You are stating that actual plagiarism has taken place. That is not the proper, neutral form of statement. You must state all claims and counter-claims. What you have posted is in effect an attack piece. In order to survive speedy deletion by administrators, you must rewrite it in a neutral style. Charles Matthews 17:38, 24 November 2006 (UTC)


 * The article seems quite okay to me, with the possible exception of the second sentence ("best known for a long series of plagiarised papers"). I was not able to find any counterclaim, and the evidence is clear that plagiarism has taken place. In my opinion stating that actual plagiarism has taken place is the proper and neutral form of statement. -- Jitse Niesen (talk) 04:20, 25 November 2006 (UTC)

That second sentence is clearly unsourced and a violation of WP:BLP, and so I removed it. Unfortunately, mhym, whom I'm sure is familiar with the policy, has re-added it. I suggest people watch the article to make sure these violations are not re-added. --C S (Talk) 04:10, 26 November 2006 (UTC)


 * For interested parties, a discussion between me and mhym has started at Talk:Dǎnuţ Marcu. --C S (Talk) 04:28, 26 November 2006 (UTC)