Wikipedia talk:WikiProject Mathematics/Archive/2011/Sep

Deletion nominations for numbers 1387 and 3571

I've nominated 1387 (number) and 3571 (number) as not notable. Comments, anyone? — Arthur Rubin (talk) 08:56, 28 August 2011 (UTC)

Why not just move the content of those pages to 1000 (number) and 3000 (number) respectively, and replace the pages with redirects, the same way that we have 301 (number) redirecting to 300 (number)?

I agree that these numbers do not appear to be notable. Mgnbar (talk) 12:17, 28 August 2011 (UTC)

Every number is notable, by the well-ordering principle. (Otherwise, there would be a smallest number that is not notable: Being the smallest non-notable number would make the number notable.)  Kiefer.Wolfowitz 12:19, 28 August 2011 (UTC)

See Interesting number paradox. -- The Anome (talk) 12:42, 28 August 2011 (UTC)

AfD's closed, articles redirected, as all the interesting information was already there. Thanks for your time. — Arthur Rubin (talk) 14:23, 28 August 2011 (UTC)

At least some of the redirections were reverted. CRGreathouse (t | c) 14:54, 1 September 2011 (UTC)

I reverted the redirect of 1387 (number), which I think might scrape through WP:NUMBER. I have no problem if someone wants to reinstate the AfD to establish consensus. Gandalf61 (talk) 15:02, 1 September 2011 (UTC)

It should by {{mergeto}}, rather than {{AfD}}. In any case, I'll suggest it. — Arthur Rubin (talk) 16:03, 1 September 2011 (UTC)

Discussion at Talk:1387 (number)#Notability. — Arthur Rubin (talk) 16:13, 1 September 2011 (UTC)

What is a limit ordinal?

TricksterWolf (talk · contribs) changed the articles Fixed-point lemma for normal functions, Normal function, and Limit ordinal in a way which does not conform to conventional definition of limit ordinal as a nonzero nonsuccessor ordinal. I changed them back; but now after a delay, he is changing them again. He claims to have certain authors on his side, but it sounds to me like those authors were just being sloppy in the definitions to which he refers (assuming he is reporting correctly what they said). His definition is that a limit ordinal is a nonsuccessor ordinal. That is, he includes zero as a limit ordinal. His definition is bad for the following reasons: (1) it contradicts the definition of limit used in topology and analysis, (2) it makes "limit" a synonym of "nonsuccessor" thereby eliminating a useful concept (nonzero nonsuccessors) which means that we must use more complicated expressions to get our points across, (3) it is inconsistent with the usage in the rest of Wikipedia, and (4) zero is clearly different from limits since the cofinality of zero is zero while the cofinality of limits is infinite (and cofinality of successors is one). JRSpriggs (talk) 06:51, 31 August 2011 (UTC)

I'm not sure I may revert, as my late mother is one of the authors who uses the standard definition. — Arthur Rubin (talk) 07:00, 31 August 2011 (UTC)

Apparently different authors use different definitions. Jech, given as a reference in 'Limit ordinal' does include 0, see [1]. However Rosenstein excludes 0. Since this is an encyclopedia we need to include both versions if they both can be sourced and use verbiage like "Some authors, such as (give a ref.) include 0 while some, such as (another ref.), do not.--RDBury (talk) 07:58, 31 August 2011 (UTC)

But we do not need to mention every variation every place it occurs. There's a standard definition for a limit ordinal; the limit ordinal article should mention alternatives, but other articles shouldn't. Ozob (talk) 11:01, 31 August 2011 (UTC)

When you start trying to decide on "standard" versus "alternative" you open the door for pointless debate and edit warring; the "standard" definitions is usually the one you learned as an undergraduate and that may depend on which textbook your professor happened to like. We could decide on a convention to use in WP and list it in WP:MOSMATH#Terminology conventions, as long as we're not claiming it to be for use outside WP. Whatever convention is chosen, allowance should be made for people who may be more familiar with the other definition to avoid confusion, so I don't think there's any way to avoid at least some clarification of what is meant on each page where the term is used.--RDBury (talk) 13:23, 31 August 2011 (UTC)

To JRSpriggs (talk · contribs): First off, TricksterWolf (talk · contribs) is a "she", despite the fact I enjoy math.  :)

Rather than presuppose, see if you can find a preview of Jech online; you will discover that Jech is anything but sloppy (his treatment of Set Theory is extremely rigorous). As for your particular points: 1) There are multiple uses of the term limit in topology. For one, the empty set is a closed set because it contains all of its limit points (despite the fact it contains no points). The process-oriented use of limit in analysis is substantially different from the use of limit in well-ordering, and I do not expect the two to coincide, particularly since real analysis is performed on an uncountably infinite field so the issue would not come up in the same way. 2) If you have read Jech or other authors who use this definition, you would clearly see that it's a toss-up: many things are easier to define, some things are harder to define, but the vast majority of things do not change one way or the other. An inaccessible cardinal is still any uncountable limit cardinal, even though zero is a limit cardinal under this definition (like ω). 3) What matters in Wikipedia is not edit tradition or edit history, but reliable sources. If reliable sources disagree with Wikipedia, it's not the sources that need to change to accommodate the encyclopedia. 4) The cofinality of zero is naturally zero by some definitions, and can be arbitrarily defined for the convenience in others. It does not typically matter for zero, however, as cf. 0 is rarely interesting to examine. Cofinality may be defined as the least of the cardinalities of the cofinal subsets of a set (so vacuously, cf. ∅ = 0), or alternately as least limit ordinal such that there is an increasing sequence <α_ξ : ξ < β> cofinal in that set (so cf. ∅ = 0 if we allow the empty sequence which is usually the case, otherwise we can define it arbitrarily or just leave it undefined).

Either way, "zero is clearly different from limits" is your opinion, not a mathematical statement. Zero meets all of the criteria for limit definitions which do not specifically exclude zero, and this is probably the motivation for authors who include it. It is the supremum of all ordinals less than it, it has no predecessor, and more importantly, unlike any successor ordinal, it is its own union (the union of 1 is 0, but the union of 0 is 0, just as the union of ω is ω). The only way to define zero to not be a limit ordinal is to specifically exclude it by creating a third classification that is neither successor nor limit, which is neither good nor bad but arbitrary. The fact that it would be the only finite limit ordinal is a curiosity but no more an objection to its definition than the fact that ω is the only countably infinite (or simply countable, by some definitions) limit cardinal.

The point here is both definitions appear in published textbooks by professional mathematicians outstanding in their respective fields, so treatment on Wikipedia should aim for a neutral definition that is correct for both cases, when it is possible to do so without over-complicating the articles. It isn't productive to revert repeatedly without posting on the talk page to request consensus when sources have already been provided (comments in the edit summary notwithstanding), so I appreciate you opening this topic. TricksterWolf (talk) 18:03, 31 August 2011 (UTC)

We can write: "A non-zero ordinal is called a limit ordinal, if ..." (and formulate everything related in such a way as to never ask whether 0 is limit, just as we never ask whether π is prime). Boris Tsirelson (talk) 20:38, 31 August 2011 (UTC)

A more relevant comparison would be whether we can avoid asking whether 1 is prime. As with 0 and limit ordinals, the most natural definitions of "prime number" include 1 unless it is explicitly excluded (there are awkward workarounds like "exactly two factors" but they don't really seem to be aimed at the heart of the matter). But in practice, it turns out that it's almost always more convenient for 1 not to be considered prime.

My view is that it's also almost always more convenient to exclude zero from the limit ordinals, $\aleph _{0}$ from the measurable cardinals, and a bunch of other similar cases. I think that's the usual view. Certainly not all authors do it that way, which is a fact that needs to be mentioned. --Trovatore (talk) 21:34, 31 August 2011 (UTC)

That doesn't really solve the problem for the definition, as a lot of authors would right that to say that limit ordinals must be non-zero. But if we standardise on non-zero limit ordinals, then this language is fine in other places where the notion is used. Hans Adler 21:35, 31 August 2011 (UTC)

The problem is salient not only to the definition of limit ordinal, but also its usage in other articles where ambiguity may result. The use of the term "nonzero limit ordinal" was not palatable to JRSpriggs (talk · contribs) because it suggested something that, according to the definition of limit ordinal familiar to him, was impossible. This is an understandable concern because it could be seen as implying preference for the zero-inclusive definition (which is not my intent). I have no stake in "pushing" one definition over another. I just want the definitions to be consistent with current texts, and as inclusive as is reasonable. The biggest danger here is not "we have to make sure every common definition is represented", but "we have to make sure the definitions we use don't mislead readers who use other common definitions into an incorrect reading". It is important that a reader be able to correctly interpret other definitions which use "limit ordinal" in their definition without ambiguity (particularly for definitions not given in the limit ordinal article, such as the definition of normal function). This is an issue that plagues the math articles in Wikipedia because there are a multitude of definitions for many simple concepts (even things as fundamental as "sequence", "graph", "function", etc).

Curiously, the original statement in one of the articles I modified was already equivalent to the change I made: initially, it said "infinite limit ordinal" and I replaced "infinite" with "nonzero", as I recall. Although this definition seems oddly redundant to users of the zero-exclusive definition for limit ordinal (and, is admittedly less appealing to me as well, since "nonzero" is far easier to define theoretically than "infinite" is), at least it does not directly imply that zero can be a limit ordinal for those unfamiliar with that definition. Perhaps in that circumstance, the redundant "infinite" would be a more neutral choice than "nonzero". I'd be open to that possibility if the word "nonzero" raises too many hackles. But either way, I don't think it's confusing to imply that zero might be a limit ordinal since the user who disagrees or is confused can easily cross-check with limit ordinal to verify the existence of other definitions.

My general feeling is that articles on mathematical structures which have common, rigorous definitions should start with the definition, then immediately add something like: "Some authors define/include blah blah blah." I'd prefer, for example, that limit ordinal begin with:

"A limit ordinal is an ordinal number which is neither zero nor a successor ordinal. Some authors include zero as a limit ordinal. Excluding zero, various equivalent definitions of limit ordinal include:"

The zero-inclusive definition is currently much further down than is useful and stated as a "controversy" which is a bit of an exaggeration. I think it's better to mention all of the common definitions up front, and then you can ignore the secondary definitions except when it becomes important to reference them (i.e., if another concept is defined in the same article where the choice of definition you use could lead to a misunderstanding). I've had similar edit issues with graph theory articles, which led me to completely rewrite the null graph article, so that's a reasonable example of how I try to tackle the issue. Just because most graph theorists exclude the order-zero graph does not mean this object is absent from literature (particularly in other fields, such as category theory). Math terminology is variable enough as it is, so a faithful description of the common scope of each definition is important. Falling back to the most common definition is fine provided the scope is re-referenced in places where it may conflict with additional definitions which are built upon the definition in question.

As for prime numbers, to my knowledge no contemporary text considers the number 1 to be either prime or composite (primes and composites are only defined on integers ≥ 2), so this is not the same situation except when referencing historical information (it's safe to assume that archaic definitions are not the standard in other definitions). We're not part of a super-secret mathematics society deciding which standards to adopt (sheesh, why isn't there one of these...?), so comparisons with unrelated terms aren't productive. We don't get to "decide" which definitions are more or less useful. All that matters are reliable sources, and an unbiased representation of current textbook definitions. Though, like many of you, I certainly have opinions on what would be best if I had the godlike power to declare Pluto "not a planet", etc.  :) For one math example, kurtosis has multiple conflicting definitions in the literature, which proved unbelievably annoying the last time I tried writing a statistical dice-rolling package for personal use. I had to try multiple definitions until I came upon one that worked, and each step of the way there were multiple sub-definitions for things like moment and k-statistic, only one of each which properly fit the formula I was trying out. What a mess! Even though Wolfram MathWorld does not list the definition of 0 as a limit ordinal, I usually trust it as a first source on math information before I trust Wikipedia. They are often biased, but usually less self-contradictory. Yet, I find numerous inconsistencies between documents there as well, and I even find inconsistencies in OEIS. Some of their solutions to disputed terminology are rather humorous: MathWorld "recommends" against using the term "natural number" at all, which is rather laughable to the set theorist or computer scientist (they suggest "nonnegative integer", which is certainly less ambiguous, but silly in a CS or set theoretical context). Every textbook will define its terms as they appear, and different fields use different common standards for the same objects and concepts. We just have to deal with it and try to make our articles clear despite the mishmash of terminology that exists. TricksterWolf (talk) 06:01, 1 September 2011 (UTC)

First comment: Conciseness goes a long way. I'm not going to pretend I read that whole thing.

From what I did see in scanning it, no, you're right, we don't decide which definitions are more useful; that's not our role as encyclopedists. However it is reasonable for editors knowledgeable about the field to weigh the extent to which various ones are used in practice.

In my experience, including zero as a limit ordinal is somewhat idiosyncratic. I think you know it is, and you're arguing about it because you personally like it. But that's not our role.

That said, you're quite right that we need to report that the definition is used, and there is no need for us to make any value judgments in doing so. But we ourselves can/should use the more standard definition. --Trovatore (talk) 06:07, 1 September 2011 (UTC)

I can't confirm this. I'm at an institution dominated by set theorists. For our basic set theory teaching we generally use Kunen's book (not Jech's). It gives the inclusive definition and then says explicitly: "We also consider 0 a limit ordinal [...]." IMO it makes sense because in transfinite induction proofs one often needs to distinguish between limit and successor ordinals, but it's very rarely necessary to treat 0 as a special case separate from infinite limit ordinals. Hans Adler 10:16, 1 September 2011 (UTC)

Well, you generally have a base case, although it's true that lots of times it's not indexed by zero. --Trovatore (talk) 18:32, 1 September 2011 (UTC)

Often you don't need a "base case". If the proof has a clause of the form "P(λ) follows from [P(β) for all β < λ]" or "P(lim(S)) follows from [P(β) for all β ∈ S]" then it follows for P(0) vacuously, without any need for a special case. —Mark Dominus (talk) 19:23, 1 September 2011 (UTC)

This is a bit off-topic, but in actual practice for arguments of any serious complexity, you almost always have a base case. You can always make it look formally as though you don't, but generally by "cheating". --Trovatore (talk) 01:52, 2 September 2011 (UTC)

That's not really the point...Hans's point is still valid. Multiple authors use this definition, not just Jech, and despite Trovatore's amazing psychic ability to read my mind and tell everyone that I am a biased liar (WP:AGF please), I must again repeat that I don't care which definition is used. Both definitions are common enough that articles reliant upon limit ordinal should be made inclusive to prevent ambiguous reads. I would argue the same way if only the zero-inclusive definition was being used and other articles made that assumption in their definitions. TricksterWolf (talk) 19:29, 1 September 2011 (UTC)

I never called you a liar, TW, and I don't think that. If I contradicted a claim that you made that you don't in fact care, then probably I skipped over that because your contribution was too long. --Trovatore (talk) 20:17, 1 September 2011 (UTC)

It seems clear to me (as a largely disinterested observer) that we have solid reliable sources for both points of view, and that our article on limit ordinals should therefore cover both points of view without taking sides. It doesn't have to be a big part of the article, just a sentence saying that some sources[cite] include zero as a limit ordinal while others[cite] explicitly exclude it. In other articles that refer to limit ordinals, in those (possibly rare?) cases where it make a difference, we should specify more precisely whether it makes sense to think of zero as a limit or not, according to what the reliable sources for those other subjects say. —David Eppstein (talk) 20:26, 1 September 2011 (UTC)

Naturally I agree, but it may be a bit tricky as I have discovered there are numerous editors who will see the changes and immediately attempt a revert. Later this weekend I will, pending this conversation dies down, make a claim of consensus, link the talk pages of the three articles in question to this one, and attempt to make changes that will satisfy all parties (with the hope someone will read the talk page and come here prior to reverting).

I'd better get my mathematician-herding shoes (on the whole, they're considerably less cooperative than cats)... TricksterWolf (talk) 21:27, 1 September 2011 (UTC)

Grumble. I just checked through my set theory textbooks, and they are split, although 0 excluded is a firm majority. We might as well restore the non-zero qualifier to those articles which refer to "limit ordinal", but I think the 0 inclusive case is a little too prominent in the present version of limit ordinal. — Arthur Rubin (talk) 15:44, 3 September 2011 (UTC)

Proposed deletion of Metadefinition

The article Metadefinition has been proposed for deletion because of the following concern:

Article consists of WP:OR and WP:SYNTH building on a computer science concept better discussed at Metamodeling.

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. 202.124.73.181 (talk) 02:34, 3 September 2011 (UTC)

Shea Zellweger

The addition of an image of a so-called "logic garnet" to the logic article put me on a path that stumbled on the article about Shea Zellweger. To me the article seems to be written from a promotional point of view. Does anyone know anything about Zellweger's work? --Trovatore (talk) 20:15, 3 September 2011 (UTC)

The article lacks references, although it has some internet links. You might ask User:The_Tetrast or on the C.S. Peirce talk page.  Kiefer.Wolfowitz 22:41, 3 September 2011 (UTC)

Merge help

Mathmaticians, please comment at Talk:Abel's binomial theorem as to whether to merge the page to Binomial theorem. Thank you, D O N D E groovily Talk to me 22:33, 3 September 2011 (UTC)

Bourbaki dangerous bend symbol

Bourbaki dangerous bend symbol claims, without any sourcing, that the "dangerous bend" symbol was introduced by Bourbaki and later adopted by Knuth. I find this rather hard to believe. First, Bourbaki was a French group -- why would they choose a street sign of distinctly American design? Second, Knuth is always meticulous about crediting earlier work, and does not mention Bourbaki in this context in the TeXbook at all. Third, though I've never read Bourbaki myself, everything I've heard about them indicates that the idea of warning the reader about difficult sections is not one they would embrace. In particular Knuth's use of the symbol to justify substantive forward references in the text would be anathema to Bourbaki, wouldn't it? –Henning Makholm (talk) 11:57, 3 September 2011 (UTC)

But any source? -- Taku (talk) 12:16, 3 September 2011 (UTC)

Bourbaki definitely does use this symbol, and they were most active in the 1950s, well before Knuth. However, I think some secondary sources are required if our article is to remain. Sławomir Biały (talk) 12:25, 3 September 2011 (UTC)

"Certains passages sont destinés à prémunir le lecteur contre des erreurs graves, où il risquerait de tomber; ces passages sont signalés en marge par le signe [omitted] («tournant dangereux»)". Bourbaki, Theorie des Ensembles, Chaiptre III, p. 2, 1956.

Their version doesn't look like a street sign. It looks like a backwards child's S. Ozob (talk) 12:30, 3 September 2011 (UTC)

To clarify, there's no silly sign cartoon in the Bourbaki version, just the symbol itself. Sławomir Biały (talk) 13:07, 3 September 2011 (UTC)

I see that the Bourbaki symbol indeed looks like the contents of that sign, rather than like a European warning sign. -- 202.124.75.95 (talk) 03:26, 4 September 2011 (UTC)

Article looks much improved now. Good work, everyone. –Henning Makholm (talk) 17:04, 5 September 2011 (UTC)

"Algebra II"

Algebra II is about as silly an article as I've seen in a while. How to proceed? Michael Hardy (talk) 03:23, 4 September 2011 (UTC)

The content is pretty negligible, but the topic (meaning the existence of the course in the US secondary math curriculum) is surely "notable". In general our coverage of common elements of the mathematics curriculum leaves much to be desired. I'm not sure how best to improve it; there must be sources somewhere though. --Trovatore (talk) 03:29, 4 September 2011 (UTC)

I would suggest a PROD, or redirect to Mathematics education (as for Algebra I). The content of an "Algebra II" course differs radically from one institution to another. -- 202.124.75.95 (talk) 03:41, 4 September 2011 (UTC)

I'm somewhat unsatisfied with that. As far as I saw (I didn't explicitly search), the mathematics education article doesn't even mention Algebra I or II.

Someone really ought to be able to write a decent article on these topics, maybe with a name like standard secondary mathematics curriculum in the United States, and that would the be a reasonable place to redirect these two, along with pre-algebra. --Trovatore (talk) 08:21, 4 September 2011 (UTC)

Too US-centric? I had algebra II in high school (in Japan). We need an article on "algebra education in the world." No idea what should it be titled. -- Taku (talk) 12:51, 4 September 2011 (UTC)

Hmm, if other countries also use the names Algebra I and Algebra II then there needs to be disambiguation rather than a straight redirect. I think the US curriculum should probably be treated in its own article. --Trovatore (talk) 19:41, 4 September 2011 (UTC)

My bad. The actual name was Mathematics II. (It's basically algebra and early calculus, so I thought it's algebra II. Interesting enough, we had Mathematics A, B; they are discrete mathematics like probability.) Anyway, I think the question whether we organize materials by nationality or by subject. Since we can't possibily have an article for each country, I think that the subject-wise scheme makese more sense. -- 23:24, 4 September 2011 (UTC)

There's already an article on UK secondary mathematics, Advanced level mathematics.--JohnBlackburne^words_deeds 00:03, 5 September 2011 (UTC)

I don't know why we "can't have an article for each country". Anyway there's no requirement that every country be represented at the same time; content can be added as there are editors to add it.

The reason to do it by country (or even smaller units) is that there aren't really "subjects" per se. There are curricula of topics that tend to be taught at the same time in a given educational milieu. The organization is not necessarily logical.

I think it's a serious omission that there's no article on the United States curriculum. I really don't care much whether there's one on the curriculum in Belize. --Trovatore (talk) 01:17, 5 September 2011 (UTC)

I'd love to see an article comparing math education across countries. CRGreathouse (t | c) 06:13, 5 September 2011 (UTC)

No objection to that, but that's orthogonal to the problem. --Trovatore (talk) 06:20, 5 September 2011 (UTC)

In the UK, Australia, India, and other English-speaking countries, the name "Algebra II" is used for a range of different high-school and university subjects, covering material from elementary algebra to advanced abstract algebra. Even in the US, Algebra II is also the name of a range of different university subjects (e.g [2]).

Some articles on mathematics education would be good, but the former Algebra II wasn't worth keeping – it was a stub full of ridiculous WP:OR, such as "Algebra II is generally the first mathematics course that deeply involves abstract and non-linear thinking. People who can visualize things extremely well almost always do well in this class." -- 202.124.74.78 (talk) 08:28, 5 September 2011 (UTC)

Classifications of the fields of math?

The Mathematics Subject Classification is an attempt to organize the fields of mathematics. It seems to be international, although maybe just North American and European. Are there any other popular classification schemes? I ask because I'm trying to get figure out what the fields are, in a citable way, for the sake of the Mathematics article. Mgnbar (talk) 23:04, 4 September 2011 (UTC)

Um, Areas of mathematics mentions the Dewey Decimal System, etc. So let me refine my question: What are the relative merits of the various schemes, and should one of the schemes be used to organize the fields of mathematics on Wikipedia? Mgnbar (talk) 23:08, 4 September 2011 (UTC)

I don't think you're going to do any better than the MSC2010. The Dewey Decimal System is pretty old and the Library of Congress system while a bit better is still pretty awkward when it gets down to sub-classes. The MSC is active and up-to-date (at least for now). You can't really hope to keep ahead of the ever proliferating number of sub-topics in math, so handing off the job to the two major mathematics abstracters makes a lot of sense. They are not going out of business and it is their job to make this listing as complete as possible. Wcherowi (talk) 02:00, 5 September 2011 (UTC)

The arXiv uses its own classification system, which is probably an improvement (in the sense of better-adapted to research papers published in 2011) over the MSC. No telling how it will stand up over time, though. CRGreathouse (t | c) 04:46, 5 September 2011 (UTC)

That was not my experience with arXiv (which is why I didn't mention it earlier). I found their classification system to be very crude (at least in Geometry). This is not to say that I think MSC is perfect, it isn't. I often have trouble finding exactly the right classification for a review, but I can usually come pretty close. Wcherowi (talk) 05:28, 5 September 2011 (UTC)

Certainly the arXiv classification is coarser; if you need fine divisions MSC is better. On the other hand, if you want to chunk math into a small number of groups I find arXiv superior to the top-level MSC codes. CRGreathouse (t | c) 06:08, 5 September 2011 (UTC)

A similar, but not identical, question has come up before. See Wikipedia_talk:WikiProject_Mathematics/Archive_59#article_assessments:_issues_with_.22field.22_and_progress_report and the followup, Wikipedia_talk:WikiProject_Mathematics/Archive_59#Article_assessment_proposal. Ozob (talk) 13:03, 5 September 2011 (UTC)

Thanks, all. To put a finer point on it: The Mathematics article lists the fields of pure mathematics as "quantity", "change", "structure", and "space". For each of these it lists some subfields; for example, the subfields of "quantity" are "natural numbers", "integers", "rational numbers", "real numbers", and "complex numbers". Am I the only one who thinks that this is crazy? No mathematician speaks like this; does anyone else, in the 21st century? At Talk:Mathematics I've offered the MSC and data on PhDs awarded, but have gotten no traction. Mgnbar (talk) 13:31, 5 September 2011 (UTC)

I think it's not uncommon to describe the field, as a whole, as considering matters of quantity, change, space, etc. But you are of course right that no mathematician categorizes fields of math that way. CRGreathouse (t | c) 18:58, 5 September 2011 (UTC)

Euclidean trees

I hesitate to ask this, but why are Stern–Brocot tree and Calkin–Wilf tree separate articles? The only difference is whether the tree is directed toward the root or away from the root. I'd ask on the individual articles, but it might lead to a naming war, so I thought I'd ask on "neutral territory". — Arthur Rubin (talk) 14:43, 5 September 2011 (UTC)

Arthur, the standard spelling is "Euclidean". Michael Hardy (talk) 14:52, 5 September 2011 (UTC)

Sorry, fixed. — Arthur Rubin (talk) 15:06, 5 September 2011 (UTC)

Actually, I did find a difference, although it wasn't apparent from the two articles.

In the CW tree, the elements further from the root from a/b are a/(a+b) and (a+b)/b.

In the SB tree, the elements further from the root from a/b are only easily expressible by the sequence of terms at each level; if a/b and c/d are adjacent terms in the sequence at level n, then the new child at level n+1 is (a+b)/(c+d), attached to whichever of the "parent" fractions is strictly at level n.

I found these trees from Euclidean algorithm; it seems to me that the CW tree should be named there, rather than the first-named SB tree. — Arthur Rubin (talk) 15:05, 5 September 2011 (UTC)

Some more differences: in the SB tree the two children of each node have value very close to it; in the CW tree one child is greater than one and the other is between zero and one. In the SB tree the nodes are ordered as a binary search tree; in the CW tree they are not. In the CW tree the sequences of numerators and denominators are the same (just shifted by one position from each other), in the SB tree they are not. I don't know why you think the CW tree should be mentioned in the Euclidean algorithm, but the Euclidean algorithm follows a path in the SB tree not the CW tree. —David Eppstein (talk) 16:51, 5 September 2011 (UTC)

On the contrary, it follows a path in the CW tree, as "a, b" is changed to "a, (b-a)" or "(a-b), b", which is exactly the (reverse-directed) CW tree. — Arthur Rubin (talk) 17:04, 5 September 2011 (UTC)

Oops, you're right. I was thinking of the sequence of approximants one gets from continued fraction expansion, which are the turning points in the path to the given number in the SB tree. —David Eppstein (talk) 19:21, 5 September 2011 (UTC)

Going-up_theorem

In Going-up_theorem it is assumed that A⊆B is an integral extension. Then when the 'going down' property is discussed, it is additionally assumed that A is integrally closed in B, but doesn't this make A=B and everything trivial? If so, can someone point out the correct hypotheses to use for the going down statement? Thanks. Rschwieb (talk) 15:48, 3 September 2011 (UTC)

I think (but don't have any book with me right now) A has to be an integrally closed domain so that there could still be a nontrivial integral extension. You don't need "domain", I think, but the general case simply reduces to this case (by passage to a quotient.) Anyway, someone should just consult sources. -- Taku (talk) 16:18, 3 September 2011 (UTC)

The article currently states the hypothesis that A is integrally closed. This does not mean that A is integrally closed in B, it means that A is integrally closed in its field of fractions. RobHar (talk) 18:19, 3 September 2011 (UTC)

Then you both seem to agree that 'domain' is missing... that does seem to line up with some Googlebooks info I've paged across. I'll add that to the hypotheses. Thanks for the help doublechecking, Rschwieb (talk) 22:26, 3 September 2011 (UTC)

Ah, I see what you're saying. In fact, domain is not needed. Either see Cohen–Seidenberg's original paper (where they say the case of domains was proved by Krull), or Theorem 2.2.7 of the book by Huneke and Swanson in the references to the article Integral element: turns out that B need not be a domain, but simply that none of its zero-divisors lie in A. RobHar (talk) 05:19, 4 September 2011 (UTC)

Feel free to work in a sharpening: my ability to view sources in this field is limited at the moment. Rschwieb (talk) 13:56, 5 September 2011 (UTC)

"Sharpening"! *LOL* Sharp's book is so great that I tempted to quote the evaluation from the first MR as a short annotation.  Kiefer.Wolfowitz 14:54, 5 September 2011 (UTC)

• Cackle* You aren't going to believe me if I tell you that pun was unintended, are you... Rschwieb (talk) 16:09, 6 September 2011 (UTC)

Maybe simple versions could stated before the reader faces morphitication. (Sharp's book has nice statements that might be considered.)  Kiefer.Wolfowitz 14:54, 5 September 2011 (UTC) (belated, due to senility and aftershocks of recent "explosion")

I think I know what you mean. That content was part of the disorganized material I was attempting to rework, and I was reluctant to leave out too much material. I'll leave repairing that up to someone who's familiar with a good exposition. Rschwieb (talk) 14:07, 5 September 2011 (UTC)

Former featured articles list

I made some formatting changes to the Former featured articles list on the main page. Probably not controversial but I'm mentioning it in case someone wants to review.--RDBury (talk) 16:19, 7 September 2011 (UTC)

You have Ordinal listed as a former featured article, but that is just a disambiguation page now. I guessed that the article which was featured is the one now called Ordinal number. But that seems to have only been a good article at one time. Ordinal number (linguistics) (the only other reasonable possibility) does not look like it was ever even good. Please provide a link to the article which was featured when it was featured, so that I can verify that it was featured and determine which article today corresponds to it. JRSpriggs (talk) 19:11, 7 September 2011 (UTC)

See [3], the Featured article list as of the Phase II conversion; edit histories become a bit sketchy before that. This is ancient history and much about FA's were different, for example there was no talk page banner and there was no FA of the day on the main page. In any case, the 'Ordinal' article was there before, the only one I added was Cryptography since it was delisted recently.--RDBury (talk) 00:04, 9 September 2011 (UTC)

PS. You can see the pre-conversion 'Ordinal' article here, so that's more or less what the link on the FA page from 2002 would have pointed to at the time. I'm sure it wouldn't even pass a GA review today but this was a long time ago.--RDBury (talk) 00:37, 9 September 2011 (UTC)

Well, that old article clearly corresponds to the current ordinal number article. So should we not change the link? JRSpriggs (talk) 10:00, 9 September 2011 (UTC)

Done.--RDBury (talk) 10:14, 9 September 2011 (UTC)

Brazilian National Math Olympiad for Public Schools deletion

A thread was started here about the speedy delete of two articles on Brazilian math competitions. I case anyone wants to add their $.02.--RDBury (talk) 15:29, 9 September 2011 (UTC)

Cylinder (algebra)

This link redirects to Cartesian product, which makes no mention of cylinders. If you look at Cylinder (disambiguation), it says a cylinder in algebra is a cartesian product of a set with its superset. The superset article also makes no mention of cylinders. Does anyone know what this is all about? -GTBacchus^(talk) 00:47, 11 September 2011 (UTC)

The only sensible link in is from FKG inequality, an uncited remark though. The history of cylinder (algebra) shows what it used to say. The definition used is not that of cylinder set, and appears to be a marginal usage. Charles Matthews (talk) 07:54, 11 September 2011 (UTC)

Alpha shape

Alpha shape is a new article.

• It could use some illustrations of concrete examples. The "Everything you wanted to know" external link has an applet that draws alpha shapes. That's where it becomes clear what these things actually are. It looks as if the interesting case is when α < 0.
• Only one article links to it. Appropriate other articles should link to it.

Michael Hardy (talk) 10:48, 11 September 2011 (UTC)

I made a few changes. It was unclear (to me, at least) that the alpha shapes are always (possibly non-convex) polygons, or that they necessarily inhabit the plane. Some illustrations would go a long way, I agree. Sławomir Biały (talk) 14:01, 11 September 2011 (UTC)

Changes at Prime number theorem

Several consecutive edits were made to Prime number theorem [4]. Can someone familiar with the history check these? They move credit from Gauss to Dirichlet, add the French revolutionary date in addition to the modern date, and discuss Euler's use of the zeta function.

CRGreathouse (t | c) 16:30, 1 September 2011 (UTC)

what I know (e.g. JSTOR 2319162) supports the older version (with attribution to Gauss). Sasha (talk) 18:07, 13 September 2011 (UTC)

Stone's representation theorem for Boolean algebras

Strangely, we cannot agree on a very simple matter; please visit Talk:Stone's representation theorem for Boolean algebras#Strange phrase. Boris Tsirelson (talk) 05:22, 12 September 2011 (UTC)

I think it's fixed now. — Carl (CBM · talk) 11:53, 12 September 2011 (UTC)

Vital articles

I've made some suggestions for mathematics-related additions to the level 4 Vital Articles list here: Wikipedia talk:Vital_articles/Expanded#Mathematics. Currently the Mathematics section is somewhat on the lean side. Regards, RJH (talk) 20:36, 12 September 2011 (UTC)

My understanding is that each area had a limited number of articles allocated, so the only way to add new articles was to remove others. Also, what criteria are you using to create this list?--RDBury (talk) 10:59, 13 September 2011 (UTC)

There are several lists of "vital" articles. This particular one has 10,000 articles, so there's a lot of room. He says at the linked talk page that his list is somehow based on which pages get the most views.

My conclusion after trying to improve the mathematics articles at m:List of articles every Wikipedia should have was that these kinds of projects are an annoying waste of time. Ozob (talk) 11:32, 13 September 2011 (UTC)

Classical orthogonal polynomials still under construction

Classical orthogonal polynomials has a stale 'Under construction' tag. I know there was a recent split with Orthogonal polynomials and presumably its related to that. The article also seems to have very few links to it.--RDBury (talk) 13:06, 13 September 2011 (UTC)

You can take the tag down if it bothers you. Given the obvious nature of the content as known reference material (e.g. [5]) it is hardly a problematic article in itself. Charles Matthews (talk) 14:18, 13 September 2011 (UTC)

I removed it, just wanted to make sure the article wasn't in a half-finished state with misplaced paragraphs etc.--RDBury (talk) 17:06, 13 September 2011 (UTC)

I agree that the article can not be under construction forever, so it was a good idea to remove the tag. I initially placed it since after the split it contained large pieces which should be moved to the OP article. There are still a few, and the article is not yet quite readable, the main problem, to my opinion, being too much information). Sasha (talk) 17:43, 13 September 2011 (UTC)

arsinh, etc.

I noticed some of our articles use arsinh, arcosh, artanh for inverse hyperbolic functions rather than the, to my mind, more conventional arcsinh, arccosh, arctanh. I don't like bringing up another notational issue, especially since nothing ever seems to be decided with them and there are potentially so many. I'm thinking the best way to avoid unnecessary discussion is to defer to some freely available external authority wherever possible, for example Abramowitz and Stegun or Digital Library of Mathematical Functions. I don't particularly care which standard is used, but when I go from one page to another and see differences in spelling or notation I think there's a typo or spelling error.--RDBury (talk) 17:54, 13 September 2011 (UTC)

Yes, I prefer to use "arc", but some people insist on "ar". It just depends on who edited the article last. JRSpriggs (talk) 20:10, 13 September 2011 (UTC)

I've never heard of "ar"; I've always used "arc". Michael Hardy (talk) 00:41, 14 September 2011 (UTC)

I've occasionally seen "arg", never "ar", usually "arc". — Arthur Rubin (talk) 02:06, 14 September 2011 (UTC)

This is new to me too. But it's well explained in the notes to Inverse hyperbolic function. As with many other things on Wikipedia, I think we need to accept both conventions. Jowa fan (talk) 02:15, 14 September 2011 (UTC)

Actually there was an earlier discussion Talk:Inverse hyperbolic function#ar vs. arc (Notation challenge continued) which I participated in but forgot about. In any case my main point is there should a way of deciding such things without a lot of back and forth about which is more standard or which makes more sense. We have a section in MOSMATH on notational conventions, but it seems to me that deciding these issues case by case is unnecessarily time-consuming.--RDBury (talk) 13:08, 14 September 2011 (UTC)

I don't think we need accept "random" conventions - if working mathematicians have to look twice, then it will be confusing for almost everyone. I would say it is fine to restrict to very common usages. Charles Matthews (talk) 13:20, 14 September 2011 (UTC)

That sort of reasoning easily misses cultural differences that may exist between different fields or geographical regions. Although, I'm not sure that that is the case here. The convention doesn't seem totally random. A quick gscholar search shows that the ratio of arctanh to artanh is about 4:1. I can't immediately see a common field for the artanh usage.TR 15:14, 14 September 2011 (UTC)

The rationale seems to be that "arc" is about arc lengths, but this is about area rather than arc lengths. Michael Hardy (talk) 13:21, 15 September 2011 (UTC)

"arc" can be just a synonym for "angle". Whether the angle is measured by the length of the arc of a circle or twice the area bounded by two rays and the arc of a hyperbola is a side issue. JRSpriggs (talk) 05:02, 16 September 2011 (UTC)

Lindblad superoperator

Hello. I found this new article tagged as {{db-a1}}. I admit, the article is incomprehensible also to me, however, G-scholar gives a lot of links for this term, and I think it should be properly discussed. Is there any valuable information for this project? Btw, the page is completely unreferenced. Thanks for any help. Regards. --Vejvančický (talk | contribs) 11:55, 14 September 2011 (UTC)

I'm not familiar with this myself but it looks to me that the article could easily be merged with Lindblad equation which is pretty stubby as it stands.--RDBury (talk) 13:19, 14 September 2011 (UTC)

Hmm, Lindblad equation is listed under WP:PHYSICS, maybe I should ask there. Thanks anyway. --Vejvančický (talk | contribs) 14:11, 14 September 2011 (UTC)

List of points

I've just started the article. I don't know if someone created a page like this in the past but got it deleted. I don't think it's completely useless; it provides some red links at least. To a long-time contributor such as myself, it is quite amusing that there is no integral point. Really?? -- Taku (talk) 18:20, 14 September 2011 (UTC)

Not really a project for me. I only work on pointless lists. Sławomir Biały (talk) 19:41, 14 September 2011 (UTC) Sorry, couldn't resist.

No, no, no. My point was that it is not pointless because it has a point because it got points. (couldn't resist.) -- Taku (talk) 20:18, 14 September 2011 (UTC)

I'm just waiting for a third party to intervene and complain that we're both violation WP:POINT. Sławomir Biały (talk) 20:56, 14 September 2011 (UTC)

This list is much more ambitious than Point in the math department!Rschwieb (talk) 16:30, 15 September 2011 (UTC)

Undiscussed List -> Outline moves

As I don't have much time right now, see User talk:Gamewizard71#Apparently undiscussed moves List -> Outline and the user's contributions. Hans Adler 07:15, 4 September 2011 (UTC)

I was just about to post the following I noticed Gamewizard71 (talk · contribs) has moved a number of "list" articles. The following are recent and appear relevant to this project:

• List of Boolean algebra topics → Outline of Boolean algebra
• List of Fourier analysis topics → Outline of Fourier analysis
• List of Lie group topics → Outline of Lie groups
• List of abstract algebra topics → Outline of abstract algebra
• List of algebraic geometry topics → Outline of algebraic geometry
• List of algebraic topology topics → Outline of algebraic topology
• List of circle topics → Outline of circles
• List of commutative algebra topics → Outline of commutative algebra
• List of complex analysis topics → Outline of complex analysis
• List of convexity topics → Outline of convexity
• List of curve topics → Outline of curves
• List of differential geometry topics → Outline of differential geometry
• List of functional programming topics → Outline of functional programming
• List of geometric topology topics → Outline of geometric topology
• List of graph theory topics → Outline of graph theory
• List of group theory topics → Outline of group theory
• List of harmonic analysis topics → Outline of harmonic analysis
• List of knot theory topics → Outline of knot theory
• List of lemmas → Index of lemmas
• List of linear algebra topics → Outline of linear algebra
• List of multivariable calculus topics → Outline of multivariable calculus
• List of number theory topics → Outline of number theory
• List of numerical analysis topics → Outline of numerical analysis
• List of order theory topics → Outline of order theory
• List of real analysis topics → Outline of real analysis
• List of representation theory topics → Outline of representation theory
• List of topics related to π → Outline of pi
• List of topology topics → Outline of topology
• List of triangle topics → Outline of triangles

Are these moves helpful? Johnuniq (talk) 07:19, 4 September 2011 (UTC)

Each article has been placed in these categories: Category:Incomplete outlines and Category:Outlines, and Lists of mathematics topics has been edited to use the new links. It's easier to see the moves with this log. Johnuniq (talk) 07:32, 4 September 2011 (UTC)

I don't like these moves. The title "Outline..." suggests some expository prose giving an overview of the subject. If it is simply a list and nothing more, then the title should be "List...". Jowa fan (talk) 09:48, 4 September 2011 (UTC)

I third this. "Outline of triangles" involving such topics as Triangle group is a mockery and almost a patented nonsense. I proceed to rename it back without redirect. Incnis Mrsi (talk) 10:10, 4 September 2011 (UTC)

I fourth this. We didn't like this before, and I don't think we like this now:

• Wikipedia_talk:WikiProject_Mathematics/Archive_38#Rename_of_lists.
• Wikipedia_talk:WikiProject_Mathematics/Archive_45#Topic_outlines
• Wikipedia_talk:WikiProject_Mathematics/Archive_54#List_of_X_topics_vs_Outline_of_X
• Wikipedia_talk:WikiProject_Mathematics/Archive_63#Outline_of_mathematics

Ozob (talk) 10:57, 4 September 2011 (UTC)

Upon further inspection, it seems that Gamewizard71 spent all yesterday making these moves, not just to math articles, but to other articles as well: List of clinical research topics became Outline of clinical research, List of electrical engineering topics became Outline of electrical engineering, List of skiing topics became Outline of skiing, etc. In addition, he moved a lot of "List of years in ..." to "Timeline of ...", as in List of years in home video to Timeline of home video, List of years in country music to Timeline of country music, etc. I have the feeling that someone needs to undo his last 24 hours. Ozob (talk) 11:14, 4 September 2011 (UTC)

Probably not just the last 24 hours: User_talk:Gamewizard71#Some_issues_with_edits --Joel B. Lewis (talk) 12:47, 4 September 2011 (UTC)

So what's the best way to proceed? Do we set about undoing the moves one by one? (The list at Category:Outlines is useful.) Or is there a way to automate the process? Jowa fan (talk) 13:35, 4 September 2011 (UTC)

There's a particularly interesting situation with Outline of mathematical logic (whose lead proclaims it to be a list) and Outline of logic (whose talk page has some heated discussion of the list/outline issue) existing as two independent pages but with a lot of shared content. Both have been called lists in the past. Jowa fan (talk) 13:58, 4 September 2011 (UTC)

See also WP:ANI#Gamewizard71. He apparently hasn't edited since this thread was started, but he's done at least 4 cut/paste moves. It appears that Transhumanist approves of most of these moves, per his comments at User talk:Gamewizard71. — Arthur Rubin (talk) 15:23, 4 September 2011 (UTC)

I made no comment about supporting the moves. I merely commented on the cut/paste nature of moves, and how to do one correctly. The example I provided was one of the math lists he had moved, but the thread didn't mention how many moves he made, and I didn't become fully aware of scale of the move until two or three days ago. The Transhumanist 23:28, 16 September 2011 (UTC)

I, too, think these moves are ridiculous. The WikiProject Outline every now and then goes ahead and makes these changes and people complain and after much needless discussion things are put back until the next time someone from WP outline changes them again. You'll notice that the first phrase in the wikipedia article Outline (summary) is "An outline is a list", so you may have trouble convincing them that a list is not what most people will first think of if they see an encyclopedia article with "outline" in the title. Back before this edit on April 13, 2010, the first sentence was "An outline is a rough draft or summary of the main features of a given topic." and was sourced to the OED. Wikitionary here of course knows that an outline is "A general description of some subject" (definition 4) and doesn't mention the word "list". Is there anyway that we can prevent future occurrences of these unwanted mass pages moves? Can there be a guideline against it? RobHar (talk) 15:24, 4 September 2011 (UTC)

• Undo all. There is clear consensus against these kind of page moves. There was never, as far as I can tell, even any attempt to get consensus through discussion and compromise. There are a variety of ways that we discuss moves like this: on talk pages, through requested moves, and via an RfC. None of these has ever seemed to be used by anyone advocating this nonsense. Sławomir Biały (talk) 17:35, 4 September 2011 (UTC)

• Yes, these moves should be undone. Paul August ☎ 17:50, 4 September 2011 (UTC)

• It seems that there's consensus to undo all these moves. How do we go about doing this? Judging from Wikipedia:Moving a page#Automating multiple page moves it looks like there's some way for admins to mass move pages. And I think someone with rollback can fix all the categories. Anyone know how to move this forward? Ozob (talk) 18:32, 4 September 2011 (UTC)

You dont like them? Oh I'm sorry for trying to creating logical lists that are more organized and useful. If you undo them all I will revert them. The reason why it is a list is because you are too lazy to actually create an outline from the topics. They are just moved to Outline of ... and are not reorganized. Most of these lists arnt even organized properly. They are just an alphabetical list or in a random order. I WILL HAVE TURN THEM INTO OUTLINES BECAUSE YOU APPARENTLY CANT DO ANYTHING BUT TALK ABOUT HOW IT'S NOT AN OUTLINE!Gamewizard71 (talk) 20:41, 4 September 2011 (UTC)

GW71: Woah -- easy, tiger. With all "due" respect, you're new here (since June) and as a new member of a community are advised to take the time to learn the ropes before tugging on everything in sight. All you're going to do is antagonise everyone who's been here for somewhat longer. Over what? Trivial piffling "organising" of lists. What a pointless waste of a weekend, I say. --Matt Westwood 21:40, 4 September 2011 (UTC)

An alphabetical list (of articles that we happen to have on a topic) is not the same thing as an outline. They are different things, and serve different (useful) purposes. Changing the name of a List to an Outline does not make a list into an outline. Sławomir Biały (talk) 21:35, 4 September 2011 (UTC)

Also, I see that Gamewizard71 is continuing to move "List of..." articles to "Outline of..." articles after this discussion is already well underway. I think it would be best to stop, because eventually someone is going to have to undo all of these moves. Sławomir Biały (talk) 21:51, 4 September 2011 (UTC)

• Undo. An outline is not the same thing as a list. Some of these lists are organized into subtopics and some of them ought to be, but that's not the same as the expository material that the word "outline" suggests, and the name should make it clear that they are lists. Another word sometimes used is "index" is in "index of circle topics", etc. Opinions of that word? Michael Hardy (talk) 02:10, 5 September 2011 (UTC)

I'm fine with Index, where that seems appropriate. Sławomir Biały (talk) 16:25, 5 September 2011 (UTC)

• Undo all of the changes. Would someone find the last time this came up and give a reference to the preexisting consensus? CRGreathouse (t | c) 05:39, 5 September 2011 (UTC)
  • Previous discussions: /Archive 38#Rename of lists, /Archive 45#Topic outlines, /Archive 54#List of X topics vs Outline of X. Algebraist 07:32, 5 September 2011 (UTC)

@Gamewizard71: No one is preventing you from creating outlines on all of these topics, we'd just prefer if you created the content first and then named the article, whereas what you've done is rename articles based on future content. That's confusing and unhelpful. You can just go ahead and create a new blank article called "Outline of algebraic geometry" and start adding content to it. RobHar (talk) 21:57, 4 September 2011 (UTC)

It's worth pointing out that the page List of algebraic structures (which oddly hasn't been renamed to "outline...") really does look like an outline. The difference between this and a bare list of links should be very clear. Jowa fan (talk) 04:23, 5 September 2011 (UTC)

• Comment. At some point, someone is going to need to nip this "Outline..." nonsense in the bud. Renaming lists to outlines has resulted in rather bizzarre "outline" trees that really do make more sense as just lists. This mess seems to be largely the work of one or two editors, in the face of a clear consensus against their actions. Their modus operandi seems to have been to throw as much stuff as possible against the wall, hoping that something sticks. Now there are hundreds of "Outline of..." articles. The existence of these articles has been used, rather cynically, as an argument by User:Transhumanist as an argument to keep this project alive at Wikipedia:Miscellany_for_deletion/Portal:Contents/Outlines. This argument even seems to have persuaded other editors who apparently hadn't been paying attention to the history of this endeavor. Well, enough is enough. What can be done about this? Sławomir Biały (talk) 12:49, 5 September 2011 (UTC)

Well, for the moment I would just like to see all of Gamewizard71's changes undone. Is there an admin here willing to do this?

In the longer term, I would like to forcibly disband Wikipedia:WikiProject Outlines. As far as I can tell, all they do is disrupt Wikipedia. Ozob (talk) 13:08, 5 September 2011 (UTC)

I've posted at Wikipedia:Administrators' noticeboard/Incidents#Gamewizard71 requesting admin assistance with undoing the page moves. I'm not sure if that's the best place to ask for help, but it's an unusual situation and I can't think where else to mention it. Jowa fan (talk) 13:40, 5 September 2011 (UTC)

For the short-term solution, ANI is probably ok. For the larger issue of Wikipedia:WikiProject Outlines, maybe WP:AN or the village pump is better since it likely requires wider input from the community. Sławomir Biały (talk) 14:07, 5 September 2011 (UTC)

I have moved the first nine items on the list above back to "list of....". I haven't yet checked "what links here" on any of them. Michael Hardy (talk) 15:36, 5 September 2011 (UTC)

....Now I'm down to "differential geometry". Could others start working on the "what links here" items, correcting any double redirects or otherwise bypassing inappropriate redirects, and report here which ones they've done? Michael Hardy (talk) 15:52, 5 September 2011 (UTC)

I just when through and moved a whole bunch. I think we must have been doing this at the same time, so we may have stepped on each other. Ozob (talk) 15:56, 5 September 2011 (UTC)

I've moved some pages listed at Portal:Contents/Outlines#Mathematics_and_logic, including some that have been called "outlines" for a long time but nevertheless look more like lists. Things that I didn't move: Outline of logic is possibly outside the scope of this WikiProject; Outline of algebra I think would be better deleted; there's some overlap between Outline of geometry and List of geometry topics; Outline of trigonometry and List of trigonometry topics (the latter being an alphabetical index rather than a list); Outline of calculus and List of calculus topics; Outline of statistics and List of statistics topics (alphabetical again). — Preceding unsigned comment added by Jowa fan (talk • contribs) 01:52, 6 September 2011 (UTC)

In the rare cases where something actually is an outline rather than a list, I think we should be ready to acknowledge this. Comments welcome at Talk:List of algebraic structures#Requested_move "List ..." -> "Outline ..." — Preceding unsigned comment added by Jowa fan (talk • contribs) 03:04, 6 September 2011 (UTC)

RfC: Elimination of outline articles

See Wikipedia:Village_pump_(proposals)#RfC:_Elimination_of_outline_articles. Ozob (talk) 00:02, 6 September 2011 (UTC)

Śleszyński–Pringsheim theorem

Śleszyński–Pringsheim theorem is a new and imperfect article. I have some uncertainties about its content, which I hope will be resolved shortly. Do what you can with it. Michael Hardy (talk) 12:52, 12 September 2011 (UTC)

I've created links from the following articles to the new article; others should be created as appropriate:

• Continued fraction
• Alfred Pringsheim
• Ivan Śleszyński
• Śleszyńsky–Pringsheim theorem (redirect page)
• Sleszynsky–Pringsheim theorem (redirect page)
• Sleszynski–Pringsheim theorem (redirect page)
• Śleszyńsky-Pringsheim theorem (redirect page)
• Sleszynsky-Pringsheim theorem (redirect page)
• Sleszynski-Pringsheim theorem (redirect page)
• Śleszyński-Pringsheim theorem (redirect page)

Michael Hardy (talk) 13:07, 12 September 2011 (UTC)

Our article on Absolute convergence does not define the term for continued fractions, only sums. I don't know the definition myself but it would be helpful to add it somewhere.--RDBury (talk) 16:02, 12 September 2011 (UTC)

To do in this article:

• Find out what "absolute convergence" means when applied to continued fractions and put that information in the article. (I suspect that's explained in the book that is cited in the article.)
• Clarify the meaning of one or two other statements in the book's version of the theorem, and edit the article accordingly.
• Cite the original papers of Śleszyński and Pringsheim. That's also in the book but I couldn't see those pages via Google Books, IIRC.
• Cite other relevant literature.
• If you're feeling even more energetic than that, maybe add a proof of the theorem. Or several proofs?

Michael Hardy (talk) 17:19, 13 September 2011 (UTC)

I found a copy of Thron's "Should the Pringsheim criterion be renamed the Śleszyński criterion?". I was hoping to give the original citation -- Śleszyński apparently proved it around 1888. But it's not clear to me (it might be clear to someone else!) which of these papers actually contains the result. This secondary source is all I have; I don't have the original papers, nor could I read them if I did (my Russian is very poor). The papers, as Thron gives them:

• (a) Concerning the continued fraction expansion of analytic functions (in Russian), Novorussian J. Odessa VI (1886), 33-104.
• (b) On the convergence of continued fractions (in Russian), Novorussian J. Odessa VIII (1888),97:-127.
• (c) Proof of the existence of certain limits (in Russian), Novorussian J. Odessa VIII (1888), 129-137.
• (d). On the convergence of continued fractions (in Russian), Mat. Sbornik 14 (1888), 337-343.
• (e) Supplement to a note on the convergence of continued fractions (in Russian), Mat. Sbornik 14 (1888), 436-438.
• (f) On the convergence of continued fractions (in Russian), Novorussian J. Odessa X (1889), 201-256.

The full name of the journal for a-c and f (again according to Thron) is Zapiski matematicheskago otodieleniia Novorrussiiskago obshchestva estesvoispytatelei. My Russian coworker says it should be transliterated Zapiski matematicheskogo otdeleniya Novorosiyskogo obschestva yestestvoispytateley; either way I don't find any hits on Google.

CRGreathouse (t | c) 17:39, 13 September 2011 (UTC)

is Thron's paper available online? I saw it cited too, but did not manage to find it. Sasha (talk) 18:13, 13 September 2011 (UTC)

Not as far as I know. I had to get it via interlibrary loan. CRGreathouse (t | c) 19:02, 13 September 2011 (UTC)

Try Google search for "Записки Математического отделения Новороссийского общества естествоиспытателей", perhaps? —Mark Dominus (talk) 19:45, 13 September 2011 (UTC)

Oh, I have found a link: [6], the theorem appears there. I will have a look. Sasha (talk) 22:25, 13 September 2011 (UTC)

Indeed: the paper

• Слешинскій, И. В. (1889). "Дополненiе къ замѣткѣ о сходимости непрерывныхъ дробей". Матем. сб. 14 (3): 436–438.

contains the Śleszyński–Pringsheim theorem in identical notation. Absolute convergence probably means that the series

$\sum (p_{n}/q_{n}-p_{n-1}/q_{n-1})$

converges absolutely. At least, this is the statement Śleszyński actually proves.

Apparently, some special cases of the theorem were proved in earlier papers of Śleszyński.

Sasha (talk) 00:18, 14 September 2011 (UTC)

I am really curious how Thron got from "Zapiski matematicheskogo otdeleniya Novorosiyskogo obschestva yestestvoispytateley" to "Novorussian J. Odessa". Does anyone understand? —Mark Dominus (talk) 16:03, 14 September 2011 (UTC)

The paper of Sl. above (1889) has the big advantage of being online, so I can say what is written there (the SP criterion appears there, and he mentions a special case which he proved in an earlier paper). I do not want to update the S-P wikipage before understanding what Thron writes (so perhaps one of the happy possessors of Thron's paper can do it better).

Is Sl. (1889) cited in Thron's paper? The English transliteration of the journal is "Matematicheskij sbornik" (it still exists, called Mat. Sb. by MathSciNet). If not (i.e. if Thron cites a later paper), perhaps Thron is also historically inaccurate.

Here is another ref (for someone willing to visit the library): . MR 0532545. {{cite journal}}: Cite journal requires |journal= (help); Missing or empty |title= (help); it is a review of Sl's work on continued fractions. Sasha (talk) 16:29, 14 September 2011 (UTC)

That looks like (e) on Thron's list. I wouldn't worry too much about the date; between differences in calendars and multi-year volumes this isn't surprising for that time (and still happens today!).

Mark: All Thron says about the abbreviation is:

The full title of the journal in which most of his early papers are published is "Zapiski matematicheskago otodieleniia Novorrussiiskago obshchestva estesvoispytatelei." We shall refer to it here simply as "Novorussian J. Odessa."

CRGreathouse (t | c) 19:05, 14 September 2011 (UTC)

I have updated the Śleszyński–Pringsheim theorem; happy possessors of Thron's article: please have a look to check I quoted him adequately. Sasha (talk) 00:22, 17 September 2011 (UTC)

Lead image at pi again

There is, once again, an issue about the lead image at the article pi. It was settled several times in the past that the best lead image for that article is the image File:Pi-unrolled-720.gif. However, User:Anythingyouwant (apparently the only editor staunchly opposed to that image) has once again replaced it with something else and has now reverted me to again include his preferred montage of images. The pi unrolled image is one of the best images I have ever seen in a mathematics article, and I feel strongly that it should be included in the lead. It is utterly naive: it communicates precisely what π is, without any need whatsoever for equations or specialized mathematical notation. By contrast, both of the lead images in the current montage require equations and further explanation in order to be understood by a reader. They are less suitable for an immediate understanding of the topic to as wide a readership as possible. I have started a thread at Talk:Pi#Pi unrolled to solicit broader input on this matter. Sławomir Biały (talk) 00:40, 17 September 2011 (UTC)

Can you provide links to such previous discussion? I found Talk:Pi/Archive_8#Pi_.22Unrolled.22_animation, which establishes that the animation is better than some picture of a mosaic, but I didn't see anyone asserting that the animation is the best possible image, or any comparisons between the animations and the images currently used. Jowa fan (talk) 02:42, 17 September 2011 (UTC)

This was also the image on the pi article when it achieved GA status as well (see also featured image discussions for various versions of this file). I do not understand the reason it was removed. (There was even a long time when the image was not in the article, or was very poorly placed.) This was never properly discussed, as I see it. It seems to have been one editor's particular objection to the image, whereas the consensus seems to be in favor of it. Sławomir Biały (talk) 03:24, 17 September 2011 (UTC)

I don't see anything relevant at File_talk:Pi-unrolled-720.gif. Can you provide a link to the discussions you're referring to? Jowa fan (talk) 05:48, 17 September 2011 (UTC)

There are various other versions of this image. Maybe look at File:Pi-unrolled.gif Sławomir Biały (talk) 17:39, 18 September 2011 (UTC)

Here is (one of the?) featured picture discussion(s). Sławomir Biały (talk) 17:45, 18 September 2011 (UTC)

Other than my general objection to all moving images, it seems like a good image. However, if it must move without being activated by the user, please at least slow it down a tad. JRSpriggs (talk) 05:58, 17 September 2011 (UTC)

There is a slightly slower version at File:Pi-unrolled slow.gif. Hans Adler 09:18, 17 September 2011 (UTC)

Finding the transformations of a matrix

The paragraph http://en.wikipedia.org/wiki/Transformation_matrix#Finding_the_matrix_of_a_transformation explains how to find the matrix belonging to a linear map. But how do I find the transformations that belong to a given matrix, which means finding the angle of rotation, scale factor and so on for the basic transformations? In other words: how to decompose a matrix into the basic transformations mentioned in said paragraph. — Preceding unsigned comment added by 84.157.37.3 (talk) 16:01, 17 September 2011 (UTC)

I'm reposting your question to Wikipedia:Reference desk/Mathematics which is the forum for asking for math help.--RDBury (talk) 19:57, 17 September 2011 (UTC)

Comment request at Talk:Fourier transform

Opinions of this edit are requested at Talk:Fourier transform#Unreferenced additions of special functions to the table. Sławomir Biały (talk) 17:37, 18 September 2011 (UTC)

New images at Function composition, Fixed point (mathematics) and other pages

A new image has just been added to the two pages Function composition and Fixed point (mathematics). I think the picture is interesting but potentially confusing. What do other people think? See also Fraction (mathematics) and Translation (geometry). Jowa fan (talk) 02:24, 19 September 2011 (UTC)

Yes, I think this image by Yves Baelde is confusing. It contains too many elements. It does not make clear where the center is. It gives the (false, I think) impression of being the projection of a three dimensional object. JRSpriggs (talk) 06:35, 19 September 2011 (UTC)

The author is very prolific but my impression is many of the images are overly complex. The Fraction one is especially egregious since the article itself should be accessible to grade schoolers but the diagram has trigonometry and radical signs. The SVG code is rather abstruse itself since white space has been stripped and there are no comments, despite the info page claim that it was created with a text editor. We do have a Wikipedia:Manual of Style/Diagrams and maps but it is currently inactive and so perhaps it should be revived. We should be encouraging people to create more diagrams for articles; I've made a few myself and it's surprisingly difficult and time consuming. I think having a good set of guidelines will help prevent that effort from being wasted.--RDBury (talk) 14:10, 19 September 2011 (UTC)

Right. This is the dilemma: I don't want to revert all of this person's edits, because I'd hate to dampen their enthusiam. But I don't think the articles are better for these pictures. I've removed the image from the Fraction page but left the rest alone for now, hoping for more input from other editors. Jowa fan (talk) 04:06, 21 September 2011 (UTC)

Mixed messages regarding fraction template

Can anyone explain why the use of the {{frac}} template is recommended at Wikipedia:Manual_of_Style_(dates_and_numbers)#Fractions but proscribed at Wikipedia:Manual_of_Style/Mathematics#Fractions? I note that someone has just added frac templates to fraction (mathematics). Jowa fan (talk) 07:22, 20 September 2011 (UTC)

I believe it was because of how the output of {{frac}} looks, but I don't recall the details. I think the discussion was either here or at WT:MOSMATH. Ozob (talk) 11:44, 20 September 2011 (UTC)

I found it: Wikipedia_talk:Manual_of_Style/Mathematics/Archive_1#Fractions. Ozob (talk) 11:48, 20 September 2011 (UTC)

The truth is that there is no good solution, the tfrac idea resembles what you would see in books, but only as long as you aren't using an unusual font size and ignore the fact that the font itself is going to be different than all the other numbers on the page. The example "The value increases from 2 to $2{\tfrac {1}{2}}$," shows how inconsistent it looks. (Exactly how bad it is depends on your browser etc.) The {{frac}} template at least keeps the fonts consistent, "The value increases from 2 to 21⁄2," but it looks amateurish. (No one here is being paid to do this so perhaps it's fair.) A professional web designer could probably kludge something up in HTML with <div> tags or tables but the results might be inconsistent or buggy. So the best solution is use decimals unless it's impossible to avoid it.--RDBury (talk) 13:52, 20 September 2011 (UTC)

There was a discussion either here or at MOSMATH where the mathematicians we overwhelmingly against this. It might be helpful to dig up the discussion. If I recall, this breaks exponents, so shouldn't be used in math pages. Sławomir Biały (talk) 15:31, 20 September 2011 (UTC)

Literature of phase boundaries

Literature of phase boundaries is a new article. The format---including getting the software to number the references, if that is appropriate in this case---could use some work by someone skilled in Wikipedia's conventions for this sort of thing.

Are there particular lists that should link to this?

And which articles should link to this? The links still need to be put there. Michael Hardy (talk) 16:04, 20 September 2011 (UTC)

I'm not convinced this should be an article. GBooks will give you a list of book on a particular subject, so there's no need to copy their results here. Perhaps trim it down to the best half-dozen and add make it a 'Further reading' section in the main article.--RDBury (talk) 17:31, 20 September 2011 (UTC)

It doesn't seem to be intended to be a list of books. Some of the items listed are books. Some of those are books of collected papers. I thought it was supposed to be the most important works in the subject. Michael Hardy (talk) 01:31, 21 September 2011 (UTC)

I think the title is wrong. There looks to be an adequate literature of evolution of phase boundaries that might qualify as mathematical physics. The whole area seems to suffer from neglect: phase boundary, interface (chemistry), interface and colloid science, ... Those might fall into different disciplines. The topic which is essentially about PDE modelling where that works is probably legitimate enough. Charles Matthews (talk) 13:25, 21 September 2011 (UTC)

Table of Fourier transforms

We have no article titled Table of Fourier transforms. Does it exist under another title to which that should redirect? If not, should it be created? Michael Hardy (talk) 16:11, 20 September 2011 (UTC)

I would think a table of Laplace transforms would be at least as useful in the real world. We have a table but it's a section within the main article. I'm also thinking use "List of ..." instead of "Table of ..." for titles.--RDBury (talk) 17:22, 20 September 2011 (UTC)

Perhaps you could redirect it to Fourier transform#Square-integrable functions. And see #Comment request at Talk:Fourier transform above. JRSpriggs (talk) 05:37, 21 September 2011 (UTC)

Note that List of Fourier transforms already exists and is a redirect to Fourier transform#Tables of important Fourier transforms. I concur with the sentiment, that there should exist a separate list article for the table of Fourier transforms. For this we should establish a set of inclusion criteria (a comprehensive list of all Fourier transforms is not practically possible or desirable). Please comment at Talk:List of Fourier transforms.TR 09:23, 21 September 2011 (UTC)

Laguerre polynomials

The article Laguerre polynomials contains vast lists of unreferenced identities, virtually all of which were added by User:A. Pichler, a long-time problem editor of special functions articles (that I have alerted the project about before, but failed to generate sufficient interest at the time). I'm not sure what should be done with it, but it's a complete disaster at the moment. It's almost tempting to roll the article a few years back in time to the last "clean" version. Sławomir Biały (talk) 03:33, 21 September 2011 (UTC)

I just felt maybe someone should respond (and I'm bored teaching). I have only undergraduate-level understanding of specical functions, but, in principle, can we deal with this sort of issues in the same way we deal with, say, POV-pushing? That is, demanding "reliable/mainstream" references so forth. -- Taku (talk) 20:40, 21 September 2011 (UTC)

Obviously references for this kind of thing are a must. I'm just wondering whether it's best to nuke this unreliable ORish content, or to plaster it with fact tags on the remote chance that someone will actually try to fix it. (We have always lacked good editors interested in improving special functions articles.) I'm leaning toward the former, although I feel that thus is sort of an unwikipedian attitude. Sławomir Biały (talk) 22:36, 21 September 2011 (UTC)

I went through and added cites for the stuff I could find in A&S. It's the same old story though, when most of the article is unreferenced it's hard to complain about people adding more to the pile. The article could use a rewrite, but I think the best approach would be to start with a good standard reference and build the core of a good article before removing what's there.--RDBury (talk) 02:24, 22 September 2011 (UTC)

Catenary approaching GA standard

I've been working heavily on the catenary article and feel it's nearly ready for a GA review. I removed most of the unreferenced material but there is one "citation needed" left that I'd like to keep, see Talk:Catenary#Simple suspension bridges, citation needed. The article is still incomplete in that there are aspects of the subject that could still be added, but completeness is not one of GA criteria. What I'm looking for is an unbiased pair of eyes to look over the article to verify my assessment of GA readiness, kind of a pre-review review. Comments will be appreciated, please reply on the article talk page.--RDBury (talk) 14:55, 21 September 2011 (UTC)

The Opposites theorem: not notable?

I've just added an {{Unreliable sources}} tag to the page Opposites theorem, since I wasn't aware that this fact had a generally accepted name, and the only source given is self-published. I'm not convinced that it's even notable enough to deserve an article. Jowa fan (talk) 13:04, 22 September 2011 (UTC)

I think that's covered well enough at Even and odd functions. CRGreathouse (t | c) 13:12, 22 September 2011 (UTC)

None of the gbooks hits for "opposites theorem" are related to this fact. It appears to be a neologism.TR 13:23, 22 September 2011 (UTC)

I've now WP:PRODded the article. Jowa fan (talk) 03:38, 24 September 2011 (UTC)

Please could someone check a query on the addition table on the Balanced ternary talk page

Someone has queried the addition table on the Balanced ternary talk page. I believe that the table as given in the article is correct, but another comment makes me think that I have misunderstood the meaning. Please could someone check it. -- Q Chris (talk) 18:19, 23 September 2011 (UTC)

It is OK. +1 + +1 = +2 = +3 + −1 = +1 · 3 + −1. JRSpriggs (talk) 06:52, 24 September 2011 (UTC)

Disruptive editor on Going up and going down

There's an anon editor at 180.216.76.63 who is refusing to reference a statement, and is instead insisting on including his proof in the article. I reverted his changes twice but he rereverted both times. I asked him to view MATH:MOS#Proofs and WIKI:NOR but I only got these classic responses:

• I worked hard on this and the proof is short so leave it be it's an important result you don't know how to welcome new users
• A proof doesn't need a reference you can check it without I will undo your edits and you will not like it leave me alone
• you're probably so mathematically illiterate that you don't understand the proof "rscbnewtic"

Would appreciate if someone else would help remove the proof and keep this guy from reposting. Thanks, Rschwieb (talk) 01:59, 22 September 2011 (UTC)

The same editor is now apparently stalking my edits, since he recently reverted changes I made at integrally closed domain and then rewrote the same portions to his own liking. Can I revert these? The new edits don't correct or contribute anything, they seem to be entirely spite-driven. I would also appreciate any other advice of steps I can take to censure this person, because this is the first time I've encountered such extreme behavior. Thanks again, Rschwieb (talk) 14:17, 22 September 2011 (UTC)

I think at the point at which you're looking for excuses to revert something that didn't do harm to the article, you should take a step back :). Obviously, the random insult in the edit history is there just to goad you -- why let it? (By the way, it is extremely frustrating for new editors to have a correct proof removed for lack of a citation -- I wish that other editors would request the citation first, with and explanation of wikipedia policy on this point and without removing the proof initially. Of course, this doesn't excuse the anon editor's behavior in this case at all.) Joel B. Lewis (talk) 17:05, 22 September 2011 (UTC)

Yeah you're right, reacting to it is obviously what he wants. Actually I think I could make a case that his edits were detrimental, but you're right, it's not THAT important. Months from now when he gives up in frustration/is banned there will be plenty of time to review the page. I wanted to explain the policy politely and in detail but I was hampered by his anon status. I would like to do that via the discussion page, but now I think that would also provoke this person. I would be grateful if someone would attempt to address this person and explain. Here's hoping he fades away... Rschwieb (talk) 17:52, 22 September 2011 (UTC)

"Here's hoping he fades away ..." I wouldn't be surpised if you're the first one to be banned from editing here. But I don't ***HOPE*** that it will happen. I'm a nice guy. You, on the other hand, seem agitated with me and don't want to reason with me. Your edits are bad English style so were reverted. Simple. — Preceding unsigned comment added by 180.216.76.63 (talk) 06:49, 26 September 2011 (UTC)

I noticed using Special:Contributions/180.216.76.63 that several people have accused you of being a troll. I don't think you're a troll. But let me give you some advice (you can take it or leave it): Your style is too abrasive. You call yourself a "nice guy" but you don't come across that way.

When I was in school, I heard one my professors, D., admit that he did not like one of his colleagues. This surprised me, because D. was a very nice person. But D. went on to say that his solution was to not serve on committees with this person. Consequently they never interacted. To this day, I don't know who it is that D. didn't get along with.

I have long taken D.'s example as a model. I suggest you do the same. Ozob (talk) 11:07, 26 September 2011 (UTC)

OK thanks for the advice Ozob. Only two people have accused me of being a troll: rschwieb and kinu so I wouldn't say "several people have accused me of being a troll". You're free to think of "nice guy" as you like but what I mean is that I don't fight with anyone unless provoked. Tell me frankly, Ozob, do you think it's fair for someone (Rschwieb) to say "Here's hoping he fades away ..."/"... when he is banned"? Even a nice guy can only take so much; even the nicest person in the world won't put up with constant harrassment/insults. Now D. (as you call him) only had one person to ignore you see. But many people seem to be against me here. It's hard to ignore people when they're threatening to ban you. I'm avoiding rschwieb but I needed to defend myself here.

At the end of the day, I've got better things to do than to argue with empty matters on a small scale forum. I doubt anyone is going to read "Going up and Going Down" or that anyone here in "Project Mathematics" is actually a mathematician (and even if they are, I highly doubt anyone of some calibre contributes here; and no I don't hold double standards and I'm not claiming I have high calibre either; I'm just someone who likes to contribute math to the world). It's pretty clear that rschwieb is wasting his time with trivialities but hey I'm not one to judge as I'm doing the same here. So I'm not going to comment here anymore I've made my point. I will check for responses to my message and maybe thank you for it but I'm not interested in this discussion. I made an edit and that's all I can do. I can't force people to appreciate me. — Preceding unsigned comment added by 180.216.76.63 (talk) 14:59, 26 September 2011 (UTC)

They've just restored the proof again, but with a more polite and constructive edit summary. Possibly they've glanced at their talk page since last time. It appears that the proof isn't WP:OR, but is by Matsumura. If they can tell us exactly where it comes from (I think Matsumura wrote two commutative algebra books), are you happy to see it remain in the article? Jowa fan (talk) 10:49, 24 September 2011 (UTC)

The irritating thing from my PoV is the lamentable tendency of so many "mathematicians" to want to cram a proof into as tiny a space as possible (as though scared of wasting paper - but the medium is no longer a wartime exercise book, we have as much room as we like). It's unreadable the way it's presented. Needs line breaks in it. --Matt Westwood 11:37, 24 September 2011 (UTC)

Please see Wikipedia_talk:WikiProject_Mathematics/Proofs for a previous discussion and possible solutions. Jmath666 (talk) 14:22, 24 September 2011 (UTC)

The proof doesn't seem especially illuminating to me. The chain of implications "flat"->"faithfully flat"->"surjective morphism of spectra" seems basically to be accepted without comment. The rest of the proof has little content. So I think the article is better off without this proof, although it's possible someone can clarify it to make it worthy of inclusion (Jowa fan, perhaps?) Sławomir Biały (talk) 14:54, 24 September 2011 (UTC)

(Duplicated from Jowa's talk page) "Hi Jowa and 180.216.76.63. I'm glad to see a reference was finally found and that the result can be included, however the main issue still hasn't been addressed. Our Manual of Style directs us to "[not] include them when they serve only to establish the correctness of a result". To keep the article well maintained for everyone (including non mathematicians) the proof should now be at least moved to be a footnote, if not completely removed. The correctness of the proof is irrelevant, this is just a matter of WP:NOTTEXTBOOK.

I'm sorry for the frustration I must have caused you 180.216.76.63, but I wasn't acting without reason. If you took time to read MOS:MATH#Proofs, you would know I was just trying to uphold the set standard."

What opinions do we have on moving the proof? I wouldn't mind compromising it as a footnote. However, the reference really should be enough. It's not the first time a new person accidentally put a lot of effort into something that turned out to be not really appropriate, and that's unfortunate, but it doesn't mean we have to force ourselves to accomodate it. Rschwieb (talk) 15:17, 24 September 2011 (UTC)

Of course, that someone has worked on the material hard doesn't justify its inclusion. In this particular topic, however, I tend to think having some proofs/short arguments might be a good idea. As I understand, the basic question is how to prove going-up/down, not from the pedagogical point view but from the mathematical point view. That is, one (e.g., Kaplansky) often studies whether various conditions are necessarily for going-up/down/inc/lying over. Proofs seem to be integral part of this sort of investigation. One can cite statements with just references, but doing so with giving what techniques/arguments are used is probably more illuminating. Having said, it is possible that maybe a wikipedia article on this topic have to be exceptional (since it's encyclopedia.) -- Taku (talk) 12:45, 26 September 2011 (UTC)

Our manual of style represents a workable compromise that is consistent with the general guidelines. It is best to follow the MOS, particularly when another editor insists on it.

WP:MOS prohibits the use of "hidden" templates on main pages, because of issues with persons with disabilities, I believe. The French WP allows hidden-like templates, which allow readers to skip proofs. (Perhaps we could find a template that was more accomodating to persons with visual impairments?)

It would be best for the IP editor 180.216.76.63 to strike-through his insults, which reflect poorly upon himself.

 Kiefer.Wolfowitz 21:33, 26 September 2011 (UTC)

Matsumura's Commutative Algebra is relatively rare. It would be better to refer to his Commutative Ring Theory, which is widely available. I would suggest following Sharpe's statement and proof, which avoids flat extensions.  Kiefer.Wolfowitz 21:39, 26 September 2011 (UTC)

I second this suggestion, although ideally a proof sketch should suffice. Sławomir Biały (talk) 21:47, 26 September 2011 (UTC)

An Essay towards solving a Problem in the Doctrine of Chances

I just created this page: An Essay towards solving a Problem in the Doctrine of Chances.

I'll add a lot to it unless someone beats me to it. Michael Hardy (talk) 03:44, 25 September 2011 (UTC)

Alternative location for proof at Going up and Going down

Taku's last post suddenly made me realize there is a good alternative to deletion. That proof would be excellent material for Localization_of_a_ring#Applications, since it showcases the exactness of the localization functor. That section I linked could use some more material anyway. This would be a good alternative to deletion!

Secondly, for the record, I have never accused 180.216.76.63 of being a troll. I wrote what I wrote because of the inexcusably rude behavior of 180.216.76.63 at the time. Rather than discuss, they immediately engaged in personal attack and a single instance of edit stalking. I had a hard time believing 180.216.76.63 would ever participate in civil discussion at all. But since then he/she has shown willingness to cooperate, and so it turns out I spoke too soon. I'm sorry 180.216.76.63 for my rash comments, and I generally retract them.Rschwieb (talk) 17:32, 26 September 2011 (UTC)

{{math}} versus <math>

This edit changes almost all the <math> tags to {{math}} -- is this an accepted standard? --Joel B. Lewis (talk) 18:17, 21 September 2011 (UTC)

Edit: sorry, I don't know how to make that link work; it's the 06:39, 20 September 2011 edit by User:No such user to Angle trisection that I'm talking about. Joel B. Lewis (talk) 18:24, 21 September 2011 (UTC)

This edit. --Zundark (talk) 18:31, 21 September 2011 (UTC)

I don't think we've ever come to a real agreement on this. Personally, meaning no offense to the people who worked hard on it, I absolutely loathe the {{math}} template. It's true that it's probably a little better than inline PNG rendering of LaTeX (the <math> tag), because it doesn't have the size disparity that you sometimes see with that. But it dumps serif fonts into the middle of running sans-serif text, which I think looks hideous.

If for some reason people think that we need serif fonts for mathematical text, then either we should always display that text, or we should use CSS to change the entire article into a serif font. --Trovatore (talk) 19:20, 21 September 2011 (UTC)

My impression is that right now, both styles are considered acceptable. As with all such cases, arbitrary changes from one style to the other are discouraged. Consequently I've reverted the above edit. Ozob (talk) 22:54, 21 September 2011 (UTC)

Please stop referring to those edits as "arbitrary". I gave thorough explanation why I made it, and the difference is quite visible. No such user (talk) 14:39, 23 September 2011 (UTC)

I feel as Trovatore does on this matter. CRGreathouse (t | c) 04:50, 22 September 2011 (UTC)

Thangs Zundark. In addition to what Trovatore said, I find the lack of italicization with {{math}} unattractive. Also, it seems to me that if, in the future, some actually decent way of displaying math on Wikipedia is developed, it is more likely to rely on LaTeX than on HTML, so that switching to HTML-based formulae is probably counter-productive in the long-run. Joel B. Lewis (talk) 17:11, 22 September 2011 (UTC)

Well, in this particular case, the ugliness with {{math}} is much more subtle. I don't have personal preference for either style, but having inconsistent rendering within the same paragraph is just awful (see Talk:Angle trisection#Formula style), so, as I noted in the edit summary, I did not change that arbitrarily (and it took some effort to convert). I agree that {{math}} is imperfect, but in this case it is so much better than <math>. If you disagree, I don't mind, but then at least force all formulas in the text into big LaTeX format. Mixed-style is, as anywhere, so unprofessional. No such user (talk) 06:56, 23 September 2011 (UTC)

@Trovatore: "But it dumps serif fonts into the middle of running sans-serif text, which I think looks hideous." -- but that is exactly what <math> does as well, when the formula is rendered small. For me (Firefox 6 on Windows 7), the following two texts look identical, except for spacing and italics, and use the same font:

$4y^{3}-3y-1/2=0$ (as result of <math>4y^{3} - 3y - 1/2 = 0</math>)

4y³ − 3y − 1/2 = 0 (as result of {{math|4y³ − 3y − 1/2 {{=}} 0}})

No such user (talk) 07:05, 23 September 2011 (UTC)

You need to italicise the template to get them the same as in:

4y³ − 3y − 1/2 = 0 (as result of {{math|4''y''³ − 3''y'' − 1/2 {{=}} 0}})

I prefer {{math}} when the math is inline and simple as it doesn't suddenly make things into grotty looking inline pngs on me. (and note what <math> has done to the fraction here, you need extra messing around to get that right) Dmcq (talk) 11:39, 23 September 2011 (UTC)

Well, OK, I'll italicize as necessary, no problem; the amount of wikicode is roughly the same for both versions. I'm not sure I like how that <math> fraction looks like; anyway, we can't have identical rendering, the point is to get it to be acceptable. As for your preference -- exactly my thoughts. No such user (talk) 12:13, 23 September 2011 (UTC)

Earlier you mentioned forcing all inline formulas to render as PNGs. I think this is a really bad idea. In general inline formulas should only very rarely ever appear by default as PNG images. You can use <math> inline, but only for formulas that don't render as PNG with default user settings (the WP:MOSMATH says that this may be used for "very simple formulae"). For more complicated formulas, basic html formatting should be used. (Wrap it in {{math}} if you must, but I don't see this as an essential requirement.) Sławomir Biały (talk) 12:23, 23 September 2011 (UTC)

The formulas are simple, but some of them used <math>60^\circ</math>, producing png $60^{\circ }$, so I converted them all to {{math}} instead. I think that's the best interim solution for the article, because one way or another they should all render equally, not in a text/png mix. Compare this and this. No such user (talk) 14:35, 23 September 2011 (UTC)

I prefer <math> because in works in all wikipedias, which is a plus for people editing outside en.wp as well. Moreover I really dislike the idea of breaking up a unified approach (single method) to deal with all math rendering just to achieve (subjective) "slightly better" display results in eyes of some. Having several methods unnecessarily complicates the handling by humans or machine alike and it breaks the ability to easily deploy future improvements of the rendering process to all math formulas within WP. Also many math editors probably prefer latex notation, since that is the lingua franca of sorts for math formulas anyway. --Kmhkmh (talk) 10:32, 26 September 2011 (UTC)

What WP:MOSMATH says

I think it's fairly clear about the issue, emphasis mine:

“ Having LaTeX-based formulae in-line which render as PNG under the default user settings, as above, is generally discouraged, for the following reasons.

• The font size is larger than that of the surrounding text on some browsers, making text containing in-line formulae hard to read.
• Misalignment can result. For example, instead of e^x, with "e" at the same level as the surrounding text and the x in superscript, one may see the e lowered to put the vertical center of the whole "e^x" at the same level as the center of the surrounding text.
• The download speed of a page is negatively affected if it contains many images.
• HTML (as described below) is adequate for most simple in-line formulae and better for text-only browsers.

”

and later, emphasis mine:

“ Either form is acceptable, but do not change one form to the other in other people's writing. They are likely to get annoyed since this seems to be a highly emotional issue. Changing to make an entire article consistent is acceptable.

However, still try to avoid in-line PNG images. Even if you use <math>L^p</math> throughout the article, use ''L''<sup>&infin;</sup> to get L^∞ rather than using the LaTeX-based <math>L^\infty</math> to get $L^{\infty }$, which doesn't always look good.

”

No such user (talk) 09:27, 26 September 2011 (UTC)

It's talking about inline HTML. It doesn't say anything about {{math}}. My objection is to {{math}}, not to inline wikimarkup/HTML (e.g. using '' to italicize variables). --Trovatore (talk) 09:36, 26 September 2011 (UTC)

I think using {{math}} distinguishes between the English text and the mathematics better and is much more consistent with <math> which I always use for any standalone maths even when the maths is simple. For instance {{math|''a''}} and <math>a</math> give a and $a$ whereas ''a'' gives a. You seem to want to make the maths expressions fade into the text rather than be easy to distinguish so basically what you see as a disadvantage is I think a big advantage. Dmcq (talk) 11:04, 26 September 2011 (UTC)

I'm fine with them being easy to distinguish. That's what italics are for. Don't change fonts though. That's just ugly.

For the moment I think the best advice we can give on using inline math is, if you can possibly avoid it, just don't. Display it as long as the results are not completely ludicrous. It just causes too many problems with the current setup.

I'm not sure what would be better. In an ideal world, maybe I'd like to change the whole of Wikipedia to a serif font, but that's not in the cards. Given that Wikipedia is foredoomed to be in sans-serif, I think we should think about whether mathematics in sans-serif is really so bad. The Beamer (LaTeX) folks don't seem to think so, and Beamer seems to have become the de facto standard for mathematical slide presentations. --Trovatore (talk) 21:11, 26 September 2011 (UTC)

Don't change fonts though. That's just ugly.. Sorry, but that is a bit contradictory, at least with the current setup: both <math> and {{math}} produce the same font. And, as Dmcq, I find it desirable to use the same style for formulas throughout; I don't mind if they differ from the surrounding text by typeface only; on the contrary, I find it even desirable. Just as, for example, in articles about programming we use <code></code> tags for keywords, even when inline.

As for Serif font, here's a tip: if you prefer Serif fonts, you can adjust it in Firefox using Tools/Options/Content/Default font, and for other browsers there is certainly an option too. I set mine to Lucida Sans Unicode (which has an additional bonus that it doesn't distinguish hyphens and en-dashes, everyone's favorite target of edit warring these days). No such user (talk) 10:05, 27 September 2011 (UTC)

They might produce the same font, but <math> is explicitly not supposed to be used inline.

It's not a matter of what I prefer to see for myself. We're trying to get an appealing layout for articles in the project. Mixing fonts inline is ugly, not just on my screen but on everyone's. --Trovatore (talk) 10:07, 27 September 2011 (UTC)

Correction, it is your opinion that mixing fonts inline is ugly. Others clearly disagree.

On a more factual basis, you claim that "I'm fine with them being easy to distinguish. That's what italics are for." Not all math is set in italics, italics are used for variables only.TR 11:46, 27 September 2011 (UTC)

It is my opinion, which is shared by plenty of people. I'm no expert on typography, but "don't mix fonts" is pretty basic, one of the first things they'll tell you in any course. --Trovatore (talk) 19:12, 27 September 2011 (UTC)

Not by me and I agree with talk that uniform handling of all formulas throughout the article is preferable.--Kmhkmh (talk) 01:51, 28 September 2011 (UTC)

It seems there are a number of people who do seem to feel pain or something close to it when different types of font are mixed or there's some problem with the design of the font. I don't get it myself but I try and follow their styles for web pages for instance. I really do much prefer to distinguish the maths from the running text well also I distinguish code from text so they can be handled as separate units rather than mixed in as more words of the running text. I see x as a maths symbol rather than as the letter x in italics. Associating x with x which is as it looks in the standalone maths is associating a letter with a symbol and is extra work for me. There are some font types which have both serif and non-serif forms especially so they can be mixed easily without this bother but we're stuck with the basic web fonts for probably the next five years at least even though most browsers support downloaded fonts nowadays. I think basically the problem boils down to if we are going to have inline maths which of these ways should prevail? And if we want to distinguish the maths is there something that can be done to make it better for people who wince at the difference? Dmcq (talk) 07:53, 29 September 2011 (UTC)

OK, let's take an example: Here's what the top of the e (mathematical constant) article looks like on my screen:

Now, to me, this looks totally unprofessional. Other people can disagree with my aesthetic judgment, I suppose, but I think this will be a common reaction.

I am somewhat curious to know if it looks less bad on other people's screens. I am using the default Firefox on Ubuntu 10.04. --Trovatore (talk) 08:45, 29 September 2011 (UTC)

I will readily agree that using {{math}} in article titles is one step too far. But I find the layout of the lead section, with numerous embedded formulas in Times New Roman, just fine. No such user (talk) 09:15, 29 September 2011 (UTC)

Times New Roman? What's that? Please, considering WP's origin as the "open source encyclopedia", let's not give preferential treatment to proprietary platforms.

I don't see any real difference between the title and the text. The title was just a convenient place to show how bad it looks. --Trovatore (talk) 09:21, 29 September 2011 (UTC)

I agree with Trovatore. e is supposed to be an italicized letter "e". But in e (mathematics) it's not just an italicized "e", it's in a different font; that makes it jump out at you (just like the Weierstrass $\textstyle \wp$). It may be a nice-looking e, but it clashes with everything else. I think the article looks better with everything in the same typeface. Compare the present version to this, where I removed {{math}} from the lead and initial caption. Nothing clashes. I think it's much nicer. Ozob (talk) 11:30, 29 September 2011 (UTC)

I don't think it looks bad at all. Which goes to show that this is simply a matter of opinion/stylistic preference. Long standing tradition on wikipedia is to leave stylistic choices of this type to the judgment of the editors of a particular article, and only require that the editors make a consistent choice within an article. I suggest we do the same here.TR 11:54, 29 September 2011 (UTC)

I think it looks better with the {{math}}. It is the maths constant e rather than the letter e in italic. And at the very least it should be consistent within an article which is what that does. Dmcq (talk) 15:13, 29 September 2011 (UTC)

OEIS templates

I noticed that we seem to have a bunch of different templates for OEIS links, namely {{OEIS}}, {{OEIS2C}} and {{OEIS url}}. I don't really see the benefit of having three different templates for essentially the same purpose. Personally I would like to see a consensus to use only one of these templates and perhaps abandon the other two, but would like to hear what other people think. Thanks. Toshio Yamaguchi (talk) 23:30, 22 September 2011 (UTC)

I think {{OEIS}} is meant to used in normal article text, {{OEIS2C}} is an abbreviation that can be used in tables, and {{OEIS url}} is for when only a link is needed. OEIS2C and OEIS used to be more different than they are now as the {{OEIS}} template was changed recently; it was something like "(sequence  Axxxxxx in OEIS)" but the OEIS part was replaced by an icon. The OEIS url one is rarely used so it could probably be replaced by OEIS2C and retired. OEIS and OEIS2C are used heavily and I think the problems caused by trying to get rid of one of them would outweigh the benefits. The main problem I can can see is for people trying to figure out which is meant to be used when, and the documentation could be improved a bit on that score, but templates are cheap and over all I think having a choice is better than not.--RDBury (talk) 05:18, 23 September 2011 (UTC)

I don't like the name "OEIS2C"; hard to type and not very meaningful in the source. CRGreathouse (t | c) 05:40, 23 September 2011 (UTC)

It appears that back in the dark ages (2005) when the template was created it was intended OEIS2C be used for the second cite and after, which is where the 2C comes from. I don't think it's being used much for that today though. The template is used in several hundred articles though, so moving could be a problem.--RDBury (talk) 12:59, 23 September 2011 (UTC)

It seems the main difference between {{OEIS}} and {{OEIS2C}} is that in the first case the word "Sequence" appears in front of the link. Is that really needed? If not, we should perhaps request a bot task to replace all instances of one template with the other one and then delete the unneeded template. Toshio Yamaguchi (talk) 10:04, 28 September 2011 (UTC)

I think the icon needs to go: (sequence  12345). It's barely decipherable, and looks like a Chinese Unicode character that doesn't render properly. It communicates less effectively than the old link. Moreover, this is a template that is supposed to be used inline; I believe there is something somewhere in the MoS about avoiding inline images. I don't think IAR applies here. Sławomir Biały (talk) 11:06, 29 September 2011 (UTC)

Given that there doesn't seem to be a consensus for this change at all in the first place, I think it should perhaps be changed back to its original appearance (with the simple OEIS wikilink). Toshio Yamaguchi (talk) 11:23, 29 September 2011 (UTC)

Digiarea links

I recently reverted some links to the site digi-area.com, if not spam then at least spammy and from an apparent SPA. Might be a good idea to keep an eye out for similar links.--RDBury (talk) 10:29, 27 September 2011 (UTC)

Consistent Notation For The Euclidian Vector Norm

We have two competing notations for the vector magnitude $\|x\|$ and $|x|$ (ignoring, for brevity, the competing notations for how to identify $x$ as a vector). What would it take to come to a consistent notation across all Wikipedia pages?KlappCK (talk) 15:38, 27 September 2011 (UTC)

I am afraid this is an infeasible task (and indeed, both notations are common in the literature). It would be already a good achievement to avoid the two meeting at the same article. Sasha (talk) 16:29, 27 September 2011 (UTC)

Consistency across Wikipedia is not just infeasible, but undesirable in my opinion. Many areas have good reasons for using different notations. Some notations that make sense in one context would be confusing in others. Obviously, we should strive to be consistent within an article, whenever possible. Sławomir Biały (talk) 16:49, 27 September 2011 (UTC)

Those aren't really the answers for which an idealist would hope. Whatever happened to WP:SOFIXIT? In what context is it confusing to use one over the other?KlappCK (talk) 19:11, 27 September 2011 (UTC)

In applied analysis, the vector norm of (say) the gradient is usually written with one bar, and an energy norm with two. In functional analysis, the norm in an abstract normed space is usually written with two bars. In linear algebra, I've seen both (and even one with three bars) for different matrix norms. Sławomir Biały (talk) 20:30, 27 September 2011 (UTC)

(ec)A change which would affect dozens of article should really have some sort of consensus. In the last month or so we've had discussions on arsinh vs. arcsinh, the definition of limit ordinal and the spelling of Tikhonov; the only thing that was really established is that it's more or less impossible to get people to agree on a choice on things like this. I think a good reasons to be consistent from article to article is to cut down on people "correcting" each other notation when it's really one preference over another. I can see the point about different notations being standard in different areas though. It would be nice to find a compromise though because inconsistent notation occurs in closely related articles as well and is all the more confusing in such cases.--RDBury (talk) 20:35, 27 September 2011 (UTC)

Insisting on a choice of consistent notation for ensuring social harmony seems to have the opposite effect in practice. Sławomir Biały (talk) 13:08, 28 September 2011 (UTC)

Indeed, it tends to lead to yet another spelling/citation/notation war, which is ultimately of little benefit to readers, produces a bad climate between authors and distracts/diverts energy from more important issues such as fixing content (rather than fixing marginal format issues).--Kmhkmh (talk) 13:51, 28 September 2011 (UTC)

I definitely don't want to incite an edit war. Perhaps it would be beneficial to establish a dichotomy (or even a trichotomy, as suggested by Sławomir Biały,) of use cases and attempt to make them use consistent across related pages (as noted by RDBury), or at the very least, use this information to establish some indication of context in our list of mathematical symbols? As of the time of this post, the single bar and double bar notations have overlapping definitions, which, in my mind, would be a source of confusion for a novice mathematician. Of course, maybe I'm just being an idealist, but I believe that this difference in notation is much less trivial than "gray" versus "grey".KlappCK (talk) 14:41, 28 September 2011 (UTC)

Maybe that's possible, but from my perspectuve there is only need for consistency within one article and the meaning of the notation should be "obvious" to readers from the context.--Kmhkmh (talk) 16:34, 28 September 2011 (UTC)

I understand your viewpoint, Kmhkmh, but what is not obvious to (novice) readers, in my opinion, is why the notation changes between pages that cross-reference each other. Article X uses notation A, but internal links on that page to a closely related subject, Article Y, uses notation B. Alas, I suppose I'm fighting a losing battle trying clarify notation for persons who are otherwise unable to infer the meaning from the context of use on each (individual) page.KlappCK (talk) 19:07, 29 September 2011 (UTC)

Robert Berger (mathematician) at AfD

The article Robert Berger (mathematician) has been nominated for deletion. Discussion is at Wikipedia:Articles for deletion/Robert Berger (mathematician).  --Lambiam 20:51, 29 September 2011 (UTC)

Signature of a quadratic form

Hi, Signature (quadratic form) and Signature of a quadratic form have recently been redirected (by AvicBot) to Signature (disambiguation), and I was wondering if they should point instead to a specific article. Thanks, --JaGa^talk 06:32, 30 September 2011 (UTC)

I went ahead and changed the target to Sylvester's law of inertia since that article defines term. Undo or update if it's not the right choice.--RDBury (talk) 11:32, 30 September 2011 (UTC)

Updated to Metric signature as the article on such signatures (and if it didn't exist it would be worth creating).--JohnBlackburne^words_deeds 14:19, 30 September 2011 (UTC)

Such a simple concept as the signature of a quadatric form certainly need not point to an article involving tensors on manifolds. I've added a couple sentences to quadratic form and redirected these there. RobHar (talk) 15:58, 30 September 2011 (UTC)

Hypercomputation article

Hypercomputation article deeply troubles me. It is portrayed as if this kind of "computation" is meaningful from the viewpoint of general applicability. And also, it is a misunderstanding of Turing's oracle machines, that was supposed to be just a theoretical device for proofs. It is not supposed to be a model of a physically plausible machine, a mechanism that requires infinite resources is not a real mechanism, it is a fictional one. That's why it's called an "oracle". I would like to see this point stressed over and over again with the relevant quote from Turing's paper. It does not concern me the least bit whether an article about this was published in Science. Most certainly the author of that paper is an ignoramus in the vein of Copeland, and it does not warrant Wikipedia'a clearance of a metaphysical word salad as if it were a scientifically respectable idea. Exa (talk) 14:08, 30 September 2011 (UTC)

I don't think it's quite so bad, though it does need work. Here's one thing I changed:

So, if machines capable of performing hypercomputational supertasks are taken to be physically realizable, they may be considered pragmatic counterexamples to the [Church-Turing] thesis.

to

So on the Church–Turing thesis, machines capable of hypercomputational are not physically realizable.

These are saying the same thing, but I flipped it around so it was more clear that they're not expected to be physically possible. (I'm not sure I like the paragraph on "they'd take infinite time/energy so they don't exist" since some models of hypercomputation, like CTC, would seem to be counterexamples—though of course we don't think they're possible.)

CRGreathouse (t | c) 18:25, 30 September 2011 (UTC)