Wikipedia talk:WikiProject Mathematics/Conventions

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Contents 1 Algebras 2 How to standardize? 3 Rings being unital 4 Quasi-compact 5 Cyclic groups 6 Dihedral groups 7 Hom-sets 8 Italic constants 9 Semidirect product 10 Subset notation 10.1 Literature survey 11 purpose of the conventions page 12 Infinity notation 13 Algebraic variety 14 Troublesome reference to Kelley 15 Bipyramid vs. Dipyramid 16 Saved copy of various proposals for subset notation 17 Greek letters 17.1 Some new remarks 18 Notation reform 18.1 Probability 19 Transpose 20 Different type of convention

[edit] Algebras

It would be nice if our conventions for algebras (cf. algebra over a field, associative algebra) matched our conventions for rings, i.e. they should be associative and unital. It would then be appropriate to have a page on nonassociative algebras, etc. Of course, by our conventions for rings we are already forced to assume that algebras over a ring are associative and unitary. This makes for the somewhat akward situation that an algebra over a field is not necessarily an algebra over a ring!?! -- Fropuff 13:32, 2005 Apr 23 (UTC)

Yes. There was some early distortion, I think, in order to fit in the Cayley numbers. Let's not get into the politics. No, maybe it's better to be upfront, and say that there is a strand of theoretical physics and its needs that determined, AFAICS, the idea that our algebras aren't associative. This can change, of course. The real issue is quite a small one, it seems. As long as we have the convention that division algebras are not assumed associative, very little need to change. So that division algebra is not the intersection of ring and algebra over a field, and not a subset of division ring; but a separate kind of object, like Lie algebra or Jordan algebra.

So, with perhaps a small change, we could take all algebras to be associative.

Charles Matthews 14:15, 23 Apr 2005 (UTC)

I think that's probably the right thing to do. Things are just confusing as they now stand. I'm a fan of octonions myself, but I don't see any reason to change the definition of an algebra to encompass them; they form a rather exceptional mathematical structure.

What about the existence of a unit? Do you forsee any major headaches if we declare that algebras must have one. What important examples are we excluding? -- Fropuff 14:04, 2005 Apr 24 (UTC)

[edit] How to standardize?

Well, okay, someone has gone and switched all the sign conventions on the Clifford algebra articles. I have half a mind to switch everything back as I am partial to the other convention and most of the Clifford algebra references I have use that convention. I guess more to the point is how should these conventions be decided? Is convention decided by the last person to edit the article (as seems to be the case here; the new convention is listed here as standard). What happens if I switch everything back? Can I then declare my preference to be standard? In other cases, conventions seem to be decided by the first person to edit the article; all changes being reverted to the original. Maybe we should vote. If so, who gets to vote? -- Fropuff 15:17, 2005 Apr 26 (UTC)

Just to be clear, I am not going to make an issue with the particular choice of Clifford algebra convention. But we should think about how these things should be decided in general. -- Fropuff 15:58, 2005 Apr 26 (UTC)

[edit] Rings being unital

I'm not an algebraist, but from looking through my algebra books (c. 1970), it seems to that defining rings as being unital, may be convenient, but is probably not customary (see: talk:Ring (mathematics)#Definition: some references, remove unit element?). Since we are an encyclopedia and not a textbook, it seems we should be more constrained by the former than the latter. Does anyone have any references for Rings defined as unital? Paul August ☎ 18:10, Jun 1, 2005 (UTC)

As Charles says, the only obvious argument for removing this requirement is so that ideals become subrings. Are there other arguments for? Besides ideals what nonunital rings arise naturally or frequently in mathematics? There are arguments against as well. Ring homomorphisms between unital rings are not necessarily morphisms of unital rings, so it becomes necessary to say unital ring homomorphism all the time.

Of the abstract algebra books I own, they are split about 50/50 as to whether a ring should have unit or not.

(Why didn't mathematicians bother to give two different names to rings (with or without unit) and unital rings as they did for semigroups and monoids?? Then these sorts of issues wouldn't arise.) -- Fropuff 18:50, 2005 Jun 1 (UTC)

One can always add a unit (cf. adjoint functors page discussion) making the old ring a two-sided ideal. The modules are the same, except that if you happen to have a unit and don't require the unit acts as 1 on a module it acts as an idempotent - so there are possibly some modules with stuff in them that is just there to be 'killed off'. So really, unless you want those strange modules, the loss is only not being able to call the two-sided ideal a subring. Of course there are plenty of things like convolution algebras where the added unit looks a bit artificial. Charles Matthews 19:03, 1 Jun 2005 (UTC)

Jacobson calls non-unital rings rngs, without the i. He clearly considers this almost a joke, but then goes on to explain adding a unit and never mentions them again. Septentrionalis 18:36, 24 September 2005 (UTC)

[edit] Quasi-compact

Why do we assume that compact spaces are not necessarily Hausdorff? The purpose of introducing the widely-used terminology quasi-compact was to clarify exactly this point. All of the texts in algebraic geometry that I've seen use this terminology. Has there been a discussion regarding this topic? - Gauge 02:08, 21 August 2005 (UTC)

Because the definition is simpler, and many properties are true in general. Compact Hausdorff space is not that hard to type. Perhaps there should be a convention of stating usage in articles where it matters; maybe even a template saying By convention, we do not require compact spaces to be Hausdorff. (I haven't dabbed the last three links.) Septentrionalis 18:29, 24 September 2005 (UTC)

Quasi-compact was a Bourbaki neologism, and not I think standard. Charles Matthews 21:13, 24 September 2005 (UTC)

It was a neologism, as are most (all?) new mathematical terms; I don't see that as a strike against it. Robin Hartshorne uses quasi-compact in his book Algebraic Geometry, so it should be quite widespread by now. If one were to tell an algebraic geometer that a variety was compact, she might assume automatically that you mean Hausdorff, simply because the term "quasi-compact" was not used. "Quasi-compact space" is also not that hard to type, and is less ambiguous than "compact space", especially if some writers on Wikipedia tacitly assume that their spaces are Hausdorff and use this when stating certain results. - Gauge 00:34, 25 September 2005 (UTC)

Yes, it got into algebraic geometry via EGA, and occurs in phrases such as fpqc (don't ask ...). But that is quite a localised area, and we can easily explain that quasi-compact scheme is so called for a good reason. Charles Matthews 13:19, 27 October 2005 (UTC)

[edit] Cyclic groups

I'd like it if we could agree on whether the cyclic group on n elements is denoted as Z_n or as C_n. My own preference is for Z, which I believe is more common. Does anyone else care? -- Dominus 18:13, 21 September 2005 (UTC)

I think the Z_n (or better IMHO: Z/nZ since Z_p is often used to denote the p-adic integers) is the more common notation. There are other notations that make use of the C_n, notably: degrees of chain complexes, and I heard something just today about C being used to denote "group completion", although I will have to look into that. Also, the standard inline wiki notation for the complex numbers is C, and the notation C_n may be interpreted as the field C(ζ) where ζ is an nth root of unity. - Gauge 01:54, 22 September 2005 (UTC)

Can we agree on C_n or Z/nZ? I like the symmetry of C_n and D_n, and I would naturally read Z_n as the ring, or the p-adic. Septentrionalis 18:44, 24 September 2005 (UTC)

C_n is OK for me, but I think Z/nZ, as a mild abuse of notation, is the standard usage (around number theory and other subjects where Z_n will cause confusion). Charles Matthews 21:11, 24 September 2005 (UTC)

An advantage of changing the notation of the abstract group C_n would be that the same notation for the isometry group type is no longer ambiguous (there are more isometry group types of the same abstract group type).--Patrick 22:19, 23 October 2005 (UTC)

However, the notation Z / m Z is rather cumbersome for such a simple and common group, and sometimes even requires parentheses, as in:

Dih_mn / (Z / m Z) ≅ Dih_n

Patrick 10:56, 24 October 2005 (UTC)

Therefore, in contexts where there is no confusion with p-adic integers, I like Z_n. The fact that is has additionally ring structure does not matter. Compare with using R, one sometimes uses its ordering, sometimes not, etc.--Patrick 14:20, 24 October 2005 (UTC)

I much prefer C_n for cyclic groups; I have never written one as Z_n in my life. By the way, the whole question of notational conventions is a little different from terminology conventions. For notation, everyone is talking about the same thing; from the point of view of terminology, people are referring to different objects and the position is more serious in a way. So perhaps the project page needs to clarify the difference. Charles Matthews 13:07, 27 October 2005 (UTC)

Actually, that's not right, in the phrase Z₂-graded, I suppose. Anyway, I have now edited the project page to suggest that terminology and notation questions are on different levels. Charles Matthews 11:36, 28 October 2005 (UTC)

I've bolded the set of intergers in the Terminology conventions. I hope no one objects. At least until were allowed to use blackboard bold as in ℤ_n (or, heaven forbid, MathML). -- Fropuff 02:34, 15 December 2005 (UTC)

[edit] Dihedral groups

I think the subscript should be the order, so that D₈ is symmetry group of the square rathern than the regular octagon. Charles Matthews 17:36, 23 October 2005 (UTC)

From what I have seen the subscript is more often half the order. Also it is already for some time a well-established convention in many Wikipedia articles.--Patrick 21:49, 23 October 2005 (UTC)

That doesn't make it a good convention. As User:r.e.b. has pointed out, the 2n convention is more common. I treat what he says as authoritative. Charles Matthews 21:57, 23 October 2005 (UTC)

He says "in finite group theory". There is also geometry and crystallography.--Patrick 22:05, 23 October 2005 (UTC)

A reason for changing the notation of the abstract group could be that the same notation for the isometry group type could be made unambiguous (there are more isometry group types of the same abstract group type; one of them of order 2n is denoted D_n; see Point groups in three dimensions). However, the notation would have to be changed to something else than D with an index, otherwise there will be only more confusion. Perhaps Dih(Z/nZ), although that is rather long.--Patrick 22:29, 23 October 2005 (UTC)

Dih_n as a Wikipedia convention wouldn't be too bad. D_n is already a Dynkin diagram. Charles Matthews 07:41, 24 October 2005 (UTC)

Dih_n, i.e. Dih not in italics, seems better, otherwise it may look like a product.--Patrick 12:13, 24 October 2005 (UTC)

I think this is excessive carefulness. Can anyone construct a sentence in which a dihedral group and a Dynkin diagram are both meaningful?

I can think of only one paragraph that would include both: and that rather boring statement should be expressed:

The symmetry group of D_n is the symmetric group S₂, except for D₄, which has S₃.

Septentrionalis 06:26, 12 January 2006 (UTC)

Well, since you asked... The discrete subgroups of Sp(1), the group of unit quaternions, fall into an ADE classification (referencing the root systems). The type D root systems correspond to the double covers of the dihredral groups in SO(3) in the double covering Sp(1) → SO(3). So there is a direct correspondence between the D_r root systems and the dihedral subgroups of SO(3). I'm not using this as an argument for anything. Just an interesting bit of trivia. Incidently, this trivia is highly non-trivial as the reasoning for the ADE classification is made clear by considering orbifold singularities in string theory -- Fropuff 06:58, 12 January 2006 (UTC)

Humphreys denotes the dihedral groups by I_n. I'm not sure how standard the convention is, but there's precedence, and therefore reference (James Humphreys, Reflection groups and Coxeter groups, Cambridge). 10 June 2007

[edit] Hom-sets

I believe the suggestion is only what we currently do (see category theory). Charles Matthews 11:48, 28 October 2005 (UTC)

Agree. Move to adopt as no one has objected. -- Fropuff 03:46, 6 December 2005 (UTC)

[edit] Italic constants

There is (and has been for a long time now) a discussion about whether the constants e and i, and the differential d, should or should not be italicised at Talk:Complex number, of all places. As far as I know it was effectively concluded that they should be. But it seems optimistic to suppose that everyone with an opinion would have found it, so I'm adding it as a proposal. —Blotwell 12:58, 18 December 2005 (UTC)

I don't exactly see this conclusion, but I guess you could conclude it from counting up the votes. More importantly, I don't see why we need to have a convention on this. Is there any genuine possibility for confusion if you use italic in one article and upright in the other? -- Jitse Niesen (talk) 14:26, 18 December 2005 (UTC)

I would not support a convention on it right yet. However, if I see an editor in the future doing mass conversion of italic e, i, and d to roman one, I will revert. :) Oleg Alexandrov (talk) 19:13, 18 December 2005 (UTC)

I recently started to prefer using upright d when discussing differentials, but I think e and i should be italicized to make them stand apart from the rest of the text (in the same way that a variable a would be italicized). I have seen many people use dx instead of dx in mathematics papers. The former looks better, IMHO. - Gauge 05:29, 19 December 2005 (UTC)

IUPAC has published directions on this. An extract from from I. M. Mills and W. V. Metanomski; "On the use of italic and roman fonts for symbols in scientific text"; IUPAC Interdivisional Committee on Nomenclature and Symbols; December 1999. (Accessed from [1], 2003–05–08.):

Scientific manuscripts frequently fail to follow the accepted conventions concerning the use of talic and roman fonts for symbols. An italic font is generally used for emphasis in running text, but it has a quite specific meaning when used for symbols in scientific text and equations. The following summary is intended to help in the correct use of italic in preparing manuscript material. 1. The general rules concerning the use of an italic (sloping) font or a roman (upright) font are presented in the IUPAC Green Book [1] on p.5 and 6, and also p.83 to 86 in relation to mathematical symbols and operators (see also p.75, 76, and 93). These rules are also presented in the International Standards ISO 31 and ISO 1000 [2], and in the SI Brochure [3].

Also:

Symbols for mathematical operators are always roman. This applies to the symbol [...] d for an infinitesimal difference (in calculus)[...]. The symbols π, e (base of natural logarithms), i (square root of minus one), etc. are always roman, [...].

Some of the previous respondents seemed to argue that dx isn't right because 'd' doesn't "operate" on x, but rather dx is a variable in its own right. In this case you'd think that the variable should be defined, and you'd also wonder why a single (large) pronumeral wasn't used. And you'd be open to define dx (say) as an infinitesimal part of variable y! Arguing that dx can't be a variable doesn't follow for me: that the leading character is roman should not preclude this; consider for example x_{a small bit} — evidently a variable, representing (apparently) a small bit of x. Another correspondent wrote that writing the integral was ugly with no space — well, "yes", it would, but not spacing the differential from the argument is equally wrong with italic 'd' — in such a style would xyz be a product or a variable! Omitting spaces is laziness, and not an argument against (or for) italic 'd'.

Personally I support the IUPAC conventions. The only fundamental reason for an italic 'd' that seemed to make sense to me in the WP discussions I've seen was elucidated by User:KSmrq at Wikipedia_talk:WikiProject_Mathematics/Archive_20#Symbol_for_differential ...although I'm not a pure mathematician.

— DIV (128.250.204.118 10:00, 31 August 2007 (UTC))

The IUPAC guidelines are quite different than the conventions in mathematics, where the constant e and the complex number i are almost universally italicized, and it is very common to use no upright lowercase Greek at all (for example, Knuth did not provide upright lowercase Greek in his original TeX package, which was written to professionally typeset mathematics books). The differential is an issue to itself. In any case, we can't expect a Chemistry style guide to be authoritative for issues of typesetting of mathematics in the field of mathematics, although it may be reflective of the mathematics practice in Chemistry journals. — Carl (CBM · talk) 13:01, 31 August 2007 (UTC)

[edit] Semidirect product

The proposal regarding the semidirect product symbol is a result of discussions held at Talk:Semidirect product#Semidirect product symbol. The notation K ×_φ Q is preferred both because it avoids a choice of which side the bar goes on as well as forces the author to explicity specify the map φ. The bar notation K ⋊_φ Q is discouraged because

• there appears to be no consensus as to which side the bar should go on (the normal side or the opposite)
• the wiki TeX software doesn't support the AMS symbols \ltimes or \rtimes.
• the Unicode symbols ⋉ (U+22C9) and ⋊ (U+22CA) may not display correctly on many browsers

References using the bar on the non-normal side (which is what we advise) are:

1. Rotman (1995), An Introduction to the Theory of Groups, 4th ed., p. 167.
2. Alperin and Bell (1995), Groups and Representations, p. 20.
3. CRC Standard Mathematical Tables and Formulae, 31st Edition, p. 187.
4. Dummit and Foote (2003), Abstract Algebra, p. 177.
5. Cameron (1999), Permutation Groups, p. 9.

I am unaware of references using the bar on the normal side but am assured that they exist. -- Fropuff 01:32, 12 January 2006 (UTC)

I support this proposal. - Gauge 01:44, 12 January 2006 (UTC)

In many contexts the map φ is implicit, but it is certainly the case that no semidirect product is singled out until a map is chosen. I would have no strong objection to using ×_φ instead of ltimes or rtimes. --KSmrq^T 05:11, 12 January 2006 (UTC)

I oppose the additional proposal: "The semidirect may also be written K ⋊ Q or Q ⋉ K (with the bar on the side of the non-normal subgroup) with or without the φ. The bar notation is discouraged for reasons outlined on the talk page." It contradictions the Unicode notation described at semidirect product. --KSmrq^T 05:20, 12 January 2006 (UTC)

I agree with Ksmrq; the alternate symbol doesn't display on my browser, and therefore wo't on other readers. Septentrionalis 06:13, 12 January 2006 (UTC)

As I stated above we are discouraging the use of the symbols ⋉ and ⋊ in favor of a subscripted times. With regards to the Unicode names, I am well aware of these, but in recommending one convention over the other I feel that we should stick with prevailing mathematical convention (as demonstrated by the listed references) rather than the recommendations of a non-mathematical organization. -- Fropuff 06:38, 12 January 2006 (UTC)

We've covered in talks the fact that the Unicode names were in the AMS specs prior to adoption in Unicode. Given the display problems and the lack of consensus on which side gets the bar (as noted in some of the references), it seems wiser to not "take sides". (Sorry, I couldn't resist the pun.) --KSmrq^T 15:59, 12 January 2006 (UTC)

I agree with Fropuff on this. - Gauge 08:20, 12 January 2006 (UTC)

I oppose "The semidirect may also be written K ⋊ Q or Q ⋉ K", since the symbols do not display for many users. I recommend using images.--Patrick 09:20, 12 January 2006 (UTC)

I wouldn't have a problem with amending this statement to use LaTeX instead of Unicode if most users can't render these symbols. I'd first like to understand how widespread this problem is, though. - Gauge 02:57, 13 January 2006 (UTC)

Wikipedia's variant of LaTeX doesn't recognize the barred symbols, ltimes and rtimes. --KSmrq^T 15:53, 13 January 2006 (UTC)

With IE this only works with the Arial Unicode MS font. See also Talk:Orthogonal_matrix#Special_characters.--Patrick 10:58, 13 January 2006 (UTC)

Are you seriously claiming that the Code2000 font, which covers even more characters, won't work? Or that the STIX fonts, when they become freely available in June, will not work? Not to be insulting to you or Microsoft, but this sounds like a preposterous assertion. --KSmrq^T 21:21, 14 January 2006 (UTC)

Let's see whether the symbols display once they exist. If this would require that readers download a font to read our articles, I would find that regrettable. Not everyone will; not everyone can. I'm using a library computer right now myself. And why is it preposterous to suggest that MicroSoft will not cooperate with shareware? ;-> Septentrionalis 17:12, 17 January 2006 (UTC)

It is a fact of life that mathematics has its own repertoire of characters, just as do various languages (Hebrew, Cherokee, Devanāgarī). Therefore, until every computer has a universal free Unicode font with complete coverage, mathematics display problems will arise. As for Microsoft cooperation, or lack thereof, even MS is unlikely to tie a browser to one specific font — especially one that has been withdrawn from free distribution. --KSmrq^T 05:28, 18 January 2006 (UTC)

We can also use {{unicode|⋊}} and {{unicode|⋉}} giving ⋊ and ⋉. That template is specially for solving this problem.--Patrick 11:10, 13 January 2006 (UTC)

Assuming this works properly, I am okay with promoting this workaround when people choose to use these symbols instead of the preferred notation. - Gauge 05:53, 14 January 2006 (UTC)

The unicode template is a good idea (although some users will still have problems I'm sure). But all techical issues aside I think it is a good idea to recommend a convention regarding usage of these symbols. Even if there is no clear consensus in the mathematics community, I would rather we recommended one usage and stick with it. It will always be impossible to please everyone when it comes to arbitrary conventions like this. But can we at least agree that internal consistency is desirable? -- Fropuff 06:30, 14 January 2006 (UTC)

You mean like British versus American spelling? Or period versus comma as a decimal separator? ;-)

Agreed, consistency is a good idea in the abstract, but if it doesn't exist in the wild we want to be careful about artificially forcing it. This kind of issue comes up time and again for terminology as well as symbols. (Does a ring have an identity? For Wikipedia, yes.) We can't assume that an arbitrary reader looking at an arbitrary page will simply know all the conventions we have adopted. So, as always, I strongly recommend that each article take responsibility for informing the reader of the choices it makes in such matters, regardless of whether they are Wikipedia conventions or not. This is much more beneficial than merely adopting a convention and stating it on an obscure page than most web surfers will never see. --KSmrq^T 21:38, 14 January 2006 (UTC)

Yes, but I'm rarely confused when I see colour instead of color or 3,14 instead of 3.14. Mathematical notation is a different beast; it carries semantics. Besides, we seem to already be in the habit of adopting conventions for which is there is not universal agreement. As you mention, we state that rings have units. There is hardly consensus for this among mathematics. I would argue (and the mere existence of this page would argue) that consistency is a better thing than universal agreement. Of course, all of these conventions are only advisory anyway (the notational ones more so). An article may well break with convention if it has a good reason. I see this as a good thing. -- Fropuff 00:51, 15 January 2006 (UTC)

Support: I agree with the original proposal, and it seems to me that if someone wants to use ⋊ in either manner they need to explicitly say so in their article. As with all Wikipedia conventions, we're not exactly saying that you have to use them, only that if you're going to use a different convention it needs to be stated explicity in your article (which as was pointed out, is probably a good thing to do for any ambiguous notation anyway). Meekohi 13:19, 17 January 2006 (UTC)

Oppose Wikipedia is inconstent. That is one of its virtues. It always will be, because this page is obscure; and the practice of going around forcing consistency on articles should be deprecated. I support having a page of conventions in case editors ask; I would support enforcing the graph theory practice of saying: in this article, graph means [whatever] (but this may vary from article to article). Septentrionalis 17:12, 17 January 2006 (UTC)

Nobody is forcing anything. This page is a list of suggested conventions so editors have something to go by. Nothing more. Nobody is asking for consistency across the board. Do you agree with the suggested convention? It is and always will be only advisory, not mandatory. -- Fropuff 17:19, 17 January 2006 (UTC)

The original proposal on top of the section, including the alternative of the {{unicode|⋊}} and {{unicode|⋉}} workaround, is acceptable. I would add: Whichever is used, the notation should be defined as the semi-direct product in the article, and which group is normal should be specified.Septentrionalis 17:33, 17 January 2006 (UTC)

I completely agree. -- Fropuff 17:43, 17 January 2006 (UTC)

I support the new modified proposal. - Gauge 03:46, 18 January 2006 (UTC)

[edit] Subset notation

This is already quite standard in WP, but it has been argued that probabilitists use for subset, and that therefore articles in probability theory should use this convention. I want to make sure we all agree to use consistently. --Meni Rosenfeld 09:38, 17 January 2006 (UTC)

• Support: I agree absolutely. Since the probabilitist notation is more relaxed than the usual mathematical notation, it should not cause them any distress to see when they expect . In fact, if they aren't familiar with this convention it'd probably do them good to learn it ;) Meekohi 13:08, 17 January 2006 (UTC)
• Half agree, half disagree. I absolutely agree that should be used for the default notion, that of not-necessarily-proper subset, but is a bad notation for proper subset, precisely because a significant part of mathematical literature uses it the other way. If you mean proper subset, you should use . (Is there a Unicode for the latter?) --Trovatore 15:50, 17 January 2006 (UTC)
• I agree with Trovatore, there is a substantial part of the literature using ⊂ () for not-necessarily-proper subset, e.g. Algebra by Serge Lang. If it is important that to restrict yourself to proper subsets, you should use , which is ⊊ (⊊) in Unicode. -- Jitse Niesen (talk) 16:45, 17 January 2006 (UTC)
  • The unicode doesn't display in my browser (Mozilla 1.7.8) with the font set I'm using (which I don't know what it is, nor how to find out; presumably it's what comes by default with Debian Sarge). --Trovatore 17:15, 17 January 2006 (UTC)

This unicode character, like many others, do not display on my browser either - though admittedly, I don't understand much about character sets. In either case, the symbol, while unambiguous, looks to me too clumsy, and in fact is very similar to , which can be confusing (to the eye at least). Perhaps it would be better to use after all, and add a reminder that we mean proper subset, at least once in an article. --Meni Rosenfeld 18:47, 17 January 2006 (UTC)

The character isn't beautiful in the current PNG rendering, but that's a technical issue that will eventually be resolved. The problem is that has no standard meaning, whereas does, and is universally understood. --Trovatore 18:53, 17 January 2006 (UTC)

I am fairly certain that is used far more often. Since it is also much more elegant (both visually, and in analogy with < and ), I think it should be used. Anyone in doubt can always check what convention is used, and we could add a header to every article that uses (which I'm not sure are very numerous) which clarifies its meaning. I think this will make WP much more readable. And it will also help to promote a notation which I think is by far superior. --Meni Rosenfeld 19:13, 17 January 2006 (UTC)

I have the opposite impression. In set theory, at least, is completely standard, although it usually appears with a slash through an equals sign below a sign (that is, two parallel lines with a slash, not just one line). On the other hand really is genuinely ambiguous; there simply is no consensus as to whether it is to mean "subset" or "proper subset". --Trovatore 19:29, 17 January 2006 (UTC)

I'm not sure I agree that is standard; and I agree with Meni Rosenfeld that is more elegant. In addition, in measure theory, there are the additional concepts of subset up to a set of measure 0, subset up to a set of measure 0 with the difference set of measure > 0, etc. Perhaps some of those concepts have symbols in the appropriate articles. Arthur Rubin | (talk) 02:21, 18 January 2006 (UTC)

I prefer as it is certainly less ambiguous than ⊂ for denoting proper subsets. As for elegance, this is a problem that will be solved for us in due time; I think the first priority should be with keeping things unambiguous. As for measure theory, I don't know if there are any standards for such symbols in the literature, but I would be interested to know what they are. If there aren't any, then we may as well use whatever symbols are most convenient for us here. - Gauge 03:46, 18 January 2006 (UTC)

Please allow me to reinstate that any ambiguity is dissolved by a simple reminder in an article. Besides, I guess most articles that use "proper subset" also use "subset" so it will be clear which is which. --Meni Rosenfeld 05:41, 18 January 2006 (UTC)

The symbol is an archaism; the trend is to do away with it because no one can be sure how it will be read. It's true that you can state what you mean by it, as you can do for any nonstandard notation for that matter, but why not just make the notation unambiguous in the first place? That way you don't have to worry that the reader will miss your notice. --Trovatore 05:45, 18 January 2006 (UTC)

The usage standard I was taught (not so very long ago), especially in the fields far from mathematical logic, was that was not-necessarily-equal and the other two were only to be used for clarity. I should prefer not to have it called archaism, if Trovatore doesn't mind. Septentrionalis 06:02, 18 January 2006 (UTC)

In the large part of mathematics remote from mathematical logic which uses inclusion casually, as part of a proposition talking about something else, not-necessarily-equal is overwhelmingly more common, and should have the simpler symbol. It requires proving one proposition, instead of two. Septentrionalis 06:02, 18 January 2006 (UTC)

I assume that by "not-necessarily-equal" you actually meant "necessarily-not-equal", i.e. proper subset? --Meni Rosenfeld 06:07, 18 January 2006 (UTC)

No, I meant If x is in A, x is in B, without any mention of y is in B, but not A; i.e. not necessarily equal and not necessarily proper. Septentrionalis 06:17, 18 January 2006 (UTC)

BTW since we can't agree which is more common, I think it will be useful if several users will tell us which they have encountered more often. --Meni Rosenfeld 06:09, 18 January 2006 (UTC)

And I've just noticed Pmanderson's suggestion. Needless to say, I absolutely disagree. --Meni Rosenfeld 06:14, 18 January 2006 (UTC)

How about a simple statement of the meaning of and; followed by Use of should be clear in context? Septentrionalis 06:21, 18 January 2006 (UTC)

Oh, I've just realized that you are pmanderson. In that case, "not-necessarily-equal" is pretty much meaningless, since in either case it is not necessary for the sets to be equal. There is only one symbol that implies that the sets are necessarily equal, and that is = . What you should have said to make yourself clear is "possibly equal", or "not-necessarily proper".

As for your first suggestion, in this sense is just not common enough (and with good cause) to be a standard.

As for your second suggestion, this is similar to Trovatore's, my uncomfort with which I have explained. We need to see what other people think. --Meni Rosenfeld 06:30, 18 January 2006 (UTC)

Since I object strongly to Trovatore's suggestion, I doubt they are similar. Septentrionalis 06:40, 18 January 2006 (UTC)

My experience in formal set theory is that is commonly used for subset, and is sometimes used for proper subset. I'd never seem before, but many of my reference books are before TeX. (As an aside, looking through my parents' books on set theory and the axiom of choice, I've seen some constructed symbols which aren't in our restricted TeX or in Unicode. I guess cardinal number theory was on the cutting edge of typesetting.) I've often seen and it's mirror (I'm not going to look it up) used in less formal works and in logic, but the concept of proper subset isn't used in those articles. My vote would be to define the term for proper subset in all articles where it's used, leaning toward use of , but I could go either way. Arthur Rubin | (talk) 07:23, 18 January 2006 (UTC)

I'm mostly with Septentrionalis here. Firstly, I've never thought about it, which indicates that in most cases, either the difference between a not-necessarily proper subset and a proper subset is not very important or it is clear from the context which one is meant. My gut feeling is that both and are used for subset and that if one needs a proper subset (which is not that often), no special symbol is used but one says "X is a proper subset of Y" or .

However, I have not read much in set theory and logic, so it could well be that they use a different convention there. So, my convention would be something like "The symbol is ambiguous and should not be used when the difference between not-necessarily-proper subset and proper subset is important and not obvious from the context" (which is not really a convention, actually, and about the same as Septentrionalis proposed above). I don't care if somebody tacks on a bit about usage in logic and set theory, if we can come to a consensus about that. -- Jitse Niesen (talk) 13:26, 18 January 2006 (UTC)

I guess I'm OK with Septentrionalis' formulation as well; I would continue to use myself, but that's allowed by his proposal. (For me is the default symbol and I use it even if I know the inclusion is proper, as long as it's not important to say that it's proper.) When it is important to say that it's proper, I think it's clear that doesn't accomplish that goal and (or an explanation in words) is necessary. It's probably less common that it's important to convey the fact that the two sets may be equal; in that case is surely necessary, because isn't going to get that idea across either. --Trovatore 15:11, 18 January 2006 (UTC)

Agree with Trovatore (and Septentrionalis by implication, I suppose). The ⊂ would be fine to use if the meaning is clear from the context or is not important, but otherwise I prefer and for clarity. The ⊂ symbol should never be used when it is important that the subset be proper, unless the meaning is clear from the context. - Gauge 15:56, 18 January 2006 (UTC)

It can be fun to discover what you don't know. For decades it always seemed obvious to me that "⊂" was analogous to "<" and "⊆" was analogous to "≤", so that the former should be used for a proper subset. On reflection, it has never bothered me if the authors of some books chose the simpler character for all uses, not needing properness; part of mathematical maturity is coming to grips with diversity. I have rarely seen (and never used) the more sophisticated "⊊" symbol for proper subset, but its meaning is immediatedly obvious to me. It would be a pity to abandon use of the clean and natural "⊂" symbol and its visual relationship to "<", but given the apparent risk of misinterpretation it appears that the only safe Wikipedia convention — if one is to be adopted as a suggestion — is to either avoid it or explain it. --KSmrq^T 18:51, 18 January 2006 (UTC)

I've codified the above two paragraphs in a "synthesis proposal" on the main page. --Trovatore 15:20, 19 January 2006 (UTC)

Well, since there isn't going to be consensus supporting my original proposal, I will have to (reluctantly) support Trovatore's new suggestion. -- Meni Rosenfeld (talk) 16:38, 19 January 2006 (UTC)

I strongly support the original proposal. My general philosophy regarding these issues is that we shouldn't avoid a very common mathematical notation simply because it is not universally agreed upon. There are always those who will use a different notation. By trying to please everyone at once, we get forced into adopting some convoluted mixture of notation that no one in the real world actually uses. Some amount of mathematical sophistication is needed in reading mathematics articles and this includes checking the subset article to see what notation is being used here. If a particular set of articles wants to use and rather than and it is their right to do so as long as the meanings are clearly stated. -- Fropuff 20:49, 19 January 2006 (UTC)

It's true that for proper subset is "very common", but it's also true that it's very common for just-plain-subset. (I think we all agree that just-plain-subset is the "primitive" notion and proper subset the "derived" one, and surely was the original symbol, so it must have meant just-plain-subset.) As far as the pair and being something "no one actually uses", that's just false. --Trovatore 21:06, 19 January 2006 (UTC)

Well, not exactly no one, but I think for the most part people are in one camp or the other. No one disagrees about what the primitive notion is—that's not really the point. I'm not objecting to use of the symbol if maximum clarity is needed, but neither do I think we should change the subset article in any substantial way. -- Fropuff 21:15, 19 January 2006 (UTC)

I think the subset article should at least warn the reader that the use of as distinctive for proper subset is not universal, and perhaps not even the majority usage. I was looking through the texts I could easily put my hands on, and not a single one uses that convention. --Trovatore 21:28, 19 January 2006 (UTC)

On the contrary, I think that the subset article should introduce the notation that is actually preferred in other articles, so that the [[subset]] tag in an article points to a gloss of the notation that readers will see. Explanations of variant and historical uses, and why modern authors tend to avoid them, are good material for a section of the subset article, but not the lead. This applies to more than subset—WP links that point to articles that lead with different conventions are a real problem, and this page is the best hope for addressing the problem.–Dan Hoey^talk 15:44, 21 June 2007 (UTC)

Hm, it may be a problem; I'm skeptical that this page can solve it, but it can be tried, as long as we keep its limitations in mind. If we want to have a go of it, following your idea about the lede, then the symbol should be removed entirely from the lede of the subset article and its "Definitions" section, preferring the unambiguous pair and . Or, since "proper subset" is a less important notion, maybe it shouldn't be mentioned in those two sections at all, and the discussion deferred to later.

I do actually think that the claims made so early on in the subset article are seriously problematic, given the large number of authors who use to mean just-plain-subset rather than proper subset, and this does need to be fixed one way or another. It's not really acceptable to have the early part of the article contradict such a large segment of the literature. --Trovatore 09:08, 22 June 2007 (UTC)

Certainly the subset article should mention alternative notations that are used. I'll check some of my set theory books when I get the time. -- Fropuff 23:12, 19 January 2006 (UTC)

I looked over the subset article; there's a section on "notational variation" that attempts to address the article, but it's seriously problematic in two ways: First, it doesn't mention that some authors use and , dispensing with entirely. Second, the symbol for used is a Unicode that doesn't show up for me. Finally, it violates WP:ASR by making a claim about the convention used by "Wikipedia". Articles should not attempt to establish conventions for other articles; we can try to agree on that, here, in Wikipedia space, but even then articles should not be written assuming that the reader knows what we've agreed on. --Trovatore 02:13, 20 January 2006 (UTC)

Well, I think I've revised my opinion after looking through a bunch of books. The symbol ⊂ seems to be used for subset much more often than proper subset. Perhaps we should recommend this usage instead. I added to your literature survey and listed the results below. -- Fropuff 01:23, 21 January 2006 (UTC)

Trovatore's synthesis proposal agrees with my opinion, but it basically says that we do not have a convention. I don't really see what purpose it would serve to include this on the Conventions page. -- Jitse Niesen (talk) 13:29, 21 January 2006 (UTC)

Well, it would be a reminder to editors that the potential for confusion exists, and that they need to be clear about it; probably that's the most important thing the Conventions page can usually do anyway. And in the wording I gave, it at least encourages the doubly-unambiguous convention, which I think is the best one. --Trovatore 15:27, 21 January 2006 (UTC)

Agree with Jitse, that if we don't assign some preferred meaning to there isn't much point in listing it here. If we're going to have a convention we should say one way or the other, or recommend avoiding it's use altogether. -- Fropuff 16:31, 21 January 2006 (UTC)

It appears to me that there's not going to be a consensus for any of those options (though for just-plain-subset is the one with the best chance). If there is no consensus on any specific recommendation, I still think it couldn't hurt to put a note on the Conventions page about the ambiguity, for the benefit of editors who may not be aware of it, and as a record that the issue has been discussed. --Trovatore 16:41, 21 January 2006 (UTC)

I agree with Trovatore. To prevent ambiguity and inconsistency in articles, we should state a convention to use and and avoid . -- Meni Rosenfeld (talk)

[edit] Literature survey

• Uses for subset. No special notation for proper subset.
  • Folland, Real Analysis.
  • Kunen, Set Theory.
  • Jech, Set Theory.
  • Halmos, Naive Set Theory.
  • Halmos, Measure Theory.
  • Rotman, Group theory.
  • Lang, Algebra.
  • Hungerford, Algebra.
  • Quigley, Manual of Axiomatic Set Theory.
  • Willard, General Topology.
  • Lipschutz, Set Theory and Related Topics
• Uses for subset and for proper subset.
  • Munkres, Topology.
• Uses . No special notation for proper subset.
  • Kechris, Classical Descriptive Set Theory.
  • Riesz and Sz-Nagy, Functional Analysis.
• Uses and .
  • Moschovakis, Descriptive Set Theory.
• Uses for subset and for proper subset.
  • Devlin, The Joy of Sets.
  • Suppes, Axiomatic Set theory.
  • Stoll, Set Theory and Logic.
  • Just and Weese, Disovering Modern Set Theory.
  • Takeuti and Zaring, Introduction to Axiomatic Set Theory.
  • MathWorld

[edit] purpose of the conventions page

The main page says

This page is to collect up various standard conventions used in Wikipedia. Where there is not complete consensus in the mathematical literature, we have to use one consistent terminology (rather than explain each time).

I think that overestimates what this project can do. Encouraging the use of a consistent terminology is a good thing, but it's not a substitute for making ourselves clear in each individual article. I suggest rewording to indicate that our goal is stylistic consistency across articles, not the creation of a repository of definitions with which readers may be assumed to be familiar. --Trovatore 15:20, 20 January 2006 (UTC)

Took a crack at it. --Trovatore 15:34, 20 January 2006 (UTC)

Well, things have moved on a little since that was written; but not much. We still don't want some articles assuming rings have 1s, and other articles not, in a random way. It is well worth having a reference page that says the default is that rings have 1s. The fact that notation problems have threatened to dominate the discussion is just one of those things. Discussion over notation is not like serious work or anything like that; but it attracts people. The 'mission statement' got refined by the mandatory/advisory distinction. Charles Matthews 16:02, 20 January 2006 (UTC)

I certainly agree with your two sentences about rings, and I'm perfectly happy with having a guideline for editors that says we've agreed that rings have 1s. What I'm saying is, if an article might confuse a reader who doesn't know we've made that agreement, then the article should mention it, for example by writing "ring (with unity)" at the first occurrence of the word "ring". --Trovatore 16:06, 20 January 2006 (UTC)

Of course, a reader is always free to click on ring and note that they have a unit. Readers will probably assume the encyclopedia to be self-consistent, even if it isn't. For that reason it is more important to state deviations from the conventions listed here.

Yes, it is unfortunate that the notational issues are proving to be such a time sink. But I don't see a way around it. People are bound to have strong opinions on such issues. In the end I suppose its better to take the time to hammer it out once rather than have the argument rekindle every couple months or so. -- Fropuff 16:14, 20 January 2006 (UTC)

A reader is free to click on the link to ring -- but if he knows what a ring is, why would he? Yes, he might be aware that there are two possible definitions, but if he's thinking that deeply about it, he probably also realizes there is no practical way to enforce consistency in a project like Wikipedia, and therefore that he can't rely on the conventions in ring being the same as in the article he's reading. Whereas by adding two words at the top of the article, we could have cleared the whole thing up. --Trovatore 16:19, 20 January 2006 (UTC)

I think the specific point here is that ring theory specialists are the people who push the non-unital convention. But for commutative algebra you absolutely must have unital rings, or the subject makes no sense. The loss in making rings (rather than algebras) unital is mathematically tiny. You will get some outraged ring theorists, but we shouldn't have the convention that pleases them and lets the bottom drop out of algebraic geometry. Charles Matthews 13:58, 23 January 2006 (UTC)

That's all fine--I'm in favor of the unital convention. I just think it should be mentioned in each article, if there's a realistic chance of confusion from not mentioning it. Takes twelve bytes. --Trovatore 14:49, 23 January 2006 (UTC)

No, why bother discussing it at all, then? Take the example of graph theory: in the old days they used to have to start each talk by stating whether graphs had loops, repeated edges. Now they have the good convention understood. At least wait until someone raises the point in a talk page. Charles Matthews 15:06, 23 January 2006 (UTC)

Well, I said if there's a realistic chance of confusion. Maybe there's not, among people who would understand the article anyway. But I think the fact that we've discussed it should be completely ignored when calculating what readers will understand. Most of them won't know we've even made a convention, unless they're editors in the math project themselves. And any article that won't be understood outside the WP context violates the spirit of WP:ASR.

So to summarize, agreeing on a convention so that editors use it consistently, good; assuming readers know we've made that agreement, bad. --Trovatore 15:14, 23 January 2006 (UTC)

Least bad solution might be to have a universal template warning that conventions are in place, and referring to the conventions page. Charles Matthews 15:20, 23 January 2006 (UTC)

Why isn't the least bad solution just to make ourselves clear in each article? In the cases we've discussed it requires very few words, and while they might be a little unaesthetic, I think a template would be much more so. --Trovatore 15:59, 23 January 2006 (UTC)

I agree with Travatore here. I don't we should have links to this page from the article namespace. Paul August ☎ 22:40, 23 January 2006 (UTC)

So I suppose one possibility would be to have one template for each convention (It's not like there are that many of them) that actually states the convention on the template, rather than linking to this page. For example {{math-conv-ring}} might expand to a little blue box that says convention: rings are assumed to be unital., and appears on the right-hand side of the page. That would take care of the self-reference problem; the only question is whether it's more or less undesirable than just adding that text to the article. --04:16, 24 January 2006 (UTC)

Well, I'm not finding much to agree with here. 'No' to a template per convention: those will soon mount up (ring of functions on a compact space is two already). 'No' to adding to each article about rings the unital convention: undesirable overhead and should be designed out of the system. And why make the conventions we use hard to find, for those few who want to know them? Charles Matthews 14:01, 24 January 2006 (UTC)

I think having individual templates or a catch-all template is unnecessary. I don't really see a need to link to this page from the article namespace either. If a reader wants to know our conventions about rings, he goes to ring (mathematics), or to note that compact need not mean Hausdorff he goes to compact space. If an editor wants to remind the reader of the conventions being used inline as Trovatore suggests that's great, but I don't think we should require it. As for making this page easy to find for editors, we already have a link on the project page. I can add a link to the mathematics portal if you think it will help. -- Fropuff 15:50, 24 January 2006 (UTC)

It would not even occur to me to look at the article on rings to see if WP has a convention on rings. I would go to the article on rings only if I wanted to know about rings; if I think I already know about them, it just wouldn't happen. I think Charles's idea that our agreements on conventions can be made systemic is just unrealistic. It may be that the unital convention doesn't need to be mentioned in each article because it's what readers with the background necessary to understand the article, will be expecting anyway. But if that's not the case, then this page is not a substitute, and can't be made a substitute without violating fundamental WP notions. --Trovatore 16:50, 24 January 2006 (UTC)

Why would you not look at the ring (mathematics) page to see what convention was in use? Sorry, but this is a reference work; it assumes that people will find what they need, by referring to relevant articles. And if they are once informed that our rings convention is in the rings article, will they not look at th Clifford algebra to see our Clifford algebra convention, our graph theory article to check what we do about graphs?

We should (a) give readers credit for intelligence, and (b) do what the whole world outside mathematics and the legal profession does, which is not to let discussions on definitions dominate things. It is not unrealistic to centralise conventions. I have no idea what is 'violating fundamental WP notions' about having one forum in which conventions are debated and noted. Charles Matthews 17:34, 24 January 2006 (UTC)

As I understand it, one of the fundamental notions is that articles are supposed to be severable and stand on their own. That's why the idea of subarticles was junked, right? And it's the motivation behind WP:ASR. As I interpret this, it means that an article using the notion of rings should be understood correctly without having to go to specifically WP sources to see what we mean by a ring. --Trovatore 17:44, 24 January 2006 (UTC)

Well, I don't think that's right. We shouldn't use bizarre notation which we define in a semi-secret place. That's clear enough. I think we can perfectly well have a few conventions implicit. An analogy is dates in history, where there is the trouble caused by calendar changes and year-end changes. Most of the history articles won't have to mention those matters. Those that really need to bring up Julian and Gregorian calenders and all that can note what is going on, in an ad hoc fashion. Charles Matthews 17:55, 24 January 2006 (UTC)

If I were reading a history article and weren't sure whether the dates were old-style or new-style, I don't know where I'd look, but it wouldn't occur to me to look in a WP article called date. Who knows if the person who wrote that article had anything to do with the article I'm reading? And I know what a date is.

I think most of the time the reader doesn't really need to know that we've picked a particular convention; either it will be clear from the way the article is written, or it just won't matter. I'm not saying the word "unital" needs to appear in every article that mentions rings. But in those instances, perhaps rare, where there is a genuine chance of confusion, then no, the fact that the ring (mathematics) article explains the convention is just not sufficient. IMHO, obviously. --Trovatore 19:21, 24 January 2006 (UTC)

I think I agree with Trovatore. For example, there should definitely be a mention that rings are unital in kernel (algebra) (there currently isn't), since without that, that article is wrong. -lethe ^talk 20:05, 24 January 2006 (UTC)

[edit] Infinity notation

See also original discussion on the topic. -- Meni Rosenfeld (talk) 08:45, 23 January 2006 (UTC)

If this means should be written , I'm against. Fredrik Johansson - talk - contribs 11:54, 23 January 2006 (UTC)

I think that discussion that Meni links to shows that many people think it is unnecessary in at least some situations (and I agree with them). -- Jitse Niesen (talk) 12:16, 23 January 2006 (UTC)

Agree. Having a convention on ±∞ seems quite unnecessary. Use +∞ only if there is a significant chance for confusion. -- Fropuff 17:06, 23 January 2006 (UTC)

The sum and integral conventions are unnecessary (with one exception, below). I would support a convention to distinguish between the (one sided) and the (two-sided) .Septentrionalis

• If the normal integration/summation convention (that the lower limit is less than the upper one) has been violated in the same article, then of course one must be careful; but this comes under {sofixit}, not a convention. Septentrionalis 19:39, 23 January 2006 (UTC)

Okay, I agree that doesn't look very good on the summation and integration symbols. But what about limits? Should we have a convention about them? Perhaps not a convention, but just a recommendation? (I will fix such things if we agree that it is desirable). -- Meni Rosenfeld (talk) 20:37, 23 January 2006 (UTC)

Support as above; noting that all these conventions are recommendations. Septentrionalis 17:00, 23 March 2006 (UTC)

[edit] Algebraic variety

This is being discussed on Talk:Algebraic variety, where it is said that the assumption of irreducibility is the common one but not universal. These days I think it is common to talk using scheme theory language about objects not assumed irreducible. Carrying around irreducible every time one mentions the dimension of an algebraic variety is fairly intolerable. Charles Matthews 09:39, 23 January 2006 (UTC)

I familiar with irreducible algebraic varieties, but then again I use Hartshorne as my reference. I think sticking with this usage is best unless there is evidence that this is no longer the norm. -- Fropuff 17:06, 23 January 2006 (UTC)

Harris and Reid also require irreducibility. -lethe ^talk 21:10, 23 January 2006 (UTC)

I can live with this. However, in computer graphics applications, for example, the varieties encountered in practice may not naturally come irreducible, and there is some danger that a naive reader may not be aware of the common mathematical assumption. If some place, say the algebraic variety article, there could be a prominent notice that most of mathematics assumes irreducibility, that would be helpful. --KSmrq^T 22:22, 23 January 2006 (UTC)

Isn't a "variety that isn't irreducible" just an algebraic set? -lethe ^talk 03:24, 24 January 2006 (UTC)

This is a good convention as far as I am concerned. - Gauge 03:17, 24 January 2006 (UTC)

There is no accepted convention about what an algebraic variety is. You could follow Hartshorne's Ch. I convention of it being a quasi-projective variety over an algebraically closed field. Or you could follow his Ch. II def'n of it being an integral separated scheme of finite type over an algebraically closed field (hence, in particular, irreducible). These are the schemes that correspond exactly to Serre's "abstract algebraic varieties". In Qing Liu's textbook, an algebraic variety is any scheme of finite type over a field, not necessarily algebraically closed. Everybody is well aware of the varying definitions of this term, so everybody expects a definition each time it is used, usually in the form of "scheme" with appropriate adjectives. I think the term should be given a brief definition on Wikipedia every time it is used in a way that calls for that degree of precision. I do not believe any convention should be adopted on this point. Joeldl 00:59, 23 April 2007 (UTC)

[edit] Troublesome reference to Kelley

"Directed sets are preordered sets with finite joins, not partial orders as in, e.g., Kelley (General Topology; ISBN 0-387-90125-6)."

Kelley defines directed sets in terms of partial orders, but he does not mean partial order in either of the usual senses: "An ordering (partial ordering, quasi-ordering) is a transitive relation. A relation < orders (partially orders) a set X iff it is transitive on X." I would advise against referring to Kelley for anything involving orders. It might, however, be a good idea to have one or more articles on variation in mathematical conventions. Dfeuer 00:42, 16 March 2006 (UTC)

[edit] Bipyramid vs. Dipyramid

I added the following proposal:

• (Terminology) The term "bipyramid" should be preferred over "dipyramid".

"Bipyramid" is more commonly used (per Google at least). Unfortunately, it is not consistent with the Greek prefixes used in many geometric objects (I made a mistake in my edit summary at [2], by the way). I therefore have no strong personal preference, although I lean toward "bipyramid" because of general Wikipedia naming conventions. Perhaps, then, my entry should have been

Google hits for "triangular dipyramid" outnumber those for "triangular bipyramid" by 7:1. -- Dominus 17:36, 19 August 2006 (UTC)

• (Terminology) Should "bipyramid" or "dipyramid" be the preferred term?

Ardric47 00:19, 28 April 2006 (UTC)

• Google hits for "bipyramid" outnumber Google hits for "dipyramid" by 9:1, but it's also true that Google hits for "triangular dipyramid" outnumber "triangular bipyramid" by 3:1. Perhaps this terminology should be left to the discretion of individual editors. Jim 23:25, 24 September 2007 (UTC)

[edit] Saved copy of various proposals for subset notation

• (Notational) Subset notation: should mean subset, should mean proper subset.
  • (Counter-proposal) should mean subset, as above, but should be used for proper subset, and should not be used at all.
  • (Counterproposal): should mean subset, should mean proper subset. may be used for emphasis or clarity, and will mean subset.
  • (Synthesis proposal) Subset is denoted by , proper subset by . The symbol may be used if the meaning is clear from context, or if it is not important whether it is interpreted as subset or as proper subset (for example, might be given as the hypothesis of a theorem whose conclusion is obvious in the case that A = B). All other uses of the symbol should be explicitly explained in the text.

- recorded by Gauge 02:52, 28 June 2006 (UTC)

[edit] Greek letters

I paused here before renaming Mu operator to μ operator. Does that violate the capitalization rule in [[WP::NAME]]? ( Is User:CMummert/π relevant?) There are already nonalphanumeric article names such as C*-algebra and π (the latter is redirected in the wrong way). I can't find any discussion in the project archives.

I want to learn if there is consensus on when to use the typographically and culturally correct Greek symbol instead of the (incorrect) spelled out version. Note that there is no article Enn Pee-complete! There are lots of math articles that could use Unicode titles: Zero sharp, Gamma function, and so on.

My proposal: always use the Greek version as the proper name and put a redirect using the spelled out version. I remark that the Greek symbols are always used in print, so this proposal says we would be following the convention that exists outside of Wikipedia.

Remark There is some policy about names like Wierstrauß. I think that this issue is relevant, although the policy does not explicitly cover phrases such as Γ function where the Γ is not a letter in a word but rather a symbol like *. If the wikipedia policy prohibits naming an article Γ function, there is little we can do until wikipedia is fixed.

CMummert 23:23, 15 July 2006 (UTC)

There was much discussion about the naming of Pi, resulting in consensus on the place. Even with the present character representation, it is possible that μ or π or Γ will fail to display on some computer; there is also a certain efficiency in making the typeable version the article. Edvard Benes is wrong; but what is positively wrong with Gamma function? Septentrionalis 00:59, 16 July 2006 (UTC)

I scanned the archives for Pi briefly, and only saw brief discussion. There is nothing more wrong with Pi than with Ell-Function or Enn Pee-complete. Spelling out the letters may be necessary for technical reasons due to wikipedia, but it is universally avoided in print. It is embarrassing to put a wrongtitle template on so many pages. is there general objection to a wrongtitle templte on Pi? CMummert 01:13, 16 July 2006 (UTC)

I would think Pi is better than π, as it is easier to type and to link to. Although I must confesss I created an article called ∫ (which should have been integral sign I guess). Oleg Alexandrov (talk) 02:01, 16 July 2006 (UTC)

It's good you asked before moving. We get enough heat for special characters within articles, despite the advent of Unicode and UTF-8. To introduce a non-Latin character in a article title would definitely provoke controversy. (The NP-complete comparison is silly, because all its letters are Latin.) One argument against Greek letters is that they are much more difficult for most readers to type; frankly, few readers would ever succeed. (Don't even think about it for Weierstrass's elliptic functions!) This would force redirects, which are an extra burden on the servers. And never forget that this is an English-language encyclopedia, with innumerable defenders of the faith. So stifle those typographic urges when staring at the title and get busy improving content. --KSmrq^T 05:29, 16 July 2006 (UTC)

I ran into this issue in the middle of improving content; there are plans to merge computable function with recursive function and add an article on Mu-recursive functions. I looked for a guideline on how to add the last page, but it was difficult to find any clear instructions. If Latin letters must be used, this should be noted in the Math conventions document, at least, so that it is easy to find out. What about the following paragraph:

Article titles Some article titles contain Greek letters or other symbols. Wikipedia policy WP:NAME requires that the article titles be spelled out using only English alphanumeric characters, although a redirect from the symbolic version of the title to the spelled out version is allowed. Additionally, each title must start with a capital letter. The template code {{wrongtitle|title=Correct title}} can be inserted at the top of the article to explain what the correct title should be. An example can be found at π.

I would like to add that to the conventions page. I think that is a reasonable stopgap until Wikipedia cleans up their act regarding article titles. CMummert 13:50, 16 July 2006 (UTC)

Generally fine by me; I would even use recommends instead of requires. And Pi should not have {{wrongtitle}}; that's for cases like eBay; or like Edvard Benes before we could use diacritics. It's not worth changing; but it's not a good precedent. Septentrionalis 19:40, 16 July 2006 (UTC)

Well, that's the rub. If it is not required to use Mu operator then I would be correct in naming the article μ operator. My reading of WP:NAME seems to indicate that I am required to use the Anglicization. As to {{wrongtitle}}, it seems applicable to me. It's not like the difference between Greece and Ελλάδα, where the natural choice is obvious. The English word for Γ-function is not Gamma Function; the reasons given for using the second one as an article title are limitations of wikimedia software and limitations of web browsers. That is certainly a technical difficulty, and {{wrongtitle}} lets readers know that we are aware of it. Moreover, articles like pi and lambda calculus and zeta function should be lower case, another technical problem. CMummert 19:58, 16 July 2006 (UTC)

Although it's been awhile, I'd like to point out that I'm pretty sure redirects are not burdensome to the servers. Ardric47 01:11, 29 July 2006 (UTC)

It's been over two weeks since the last comment. Recent events at Pi and Mu-recursive function illustrate the utility of having a convention in place. If there are no objections, I'll put the following into the conventions page soon:

Article titles Some article titles contain Greek letters or other symbols. Wikipedia policy (WP:NAME WP:UE) states that article titles should be spelled out using only English alphanumeric characters, possibly with diacritic accents attached. Letters from non-Latin alphabets, such as Greek and Arabic, and symbolic characters are discouraged in article titles. Additionally, each title will automatically be capitalized by the Wikimedia software. A redirect from the symbolic version of a title to the spelled out version is allowed. The template code {{wrongtitle|title=Correct title}} can be inserted at the top of the article to explain what the correct title should be. An example can be found at π.

CMummert 11:26, 19 August 2006 (UTC)

The pi article may not be the best example. Even the Greek letter is wrong, because it is capitalized, making it read as a symbol ("∏") with a completely different meaning: product.

It's also important to understand that without a Greek keyboard most users will not be able to type π and other Greek letters in the search box. Even if it is technically possible using an entity name (try typing &thorn;), they won't know to do that. So we must always have at least a redirect from an easily-typed title.

Lastly, I feel somewhat uncomfortable having the mathematics community define its own conventions about article titles rather than clarify (or reshape) the implications of Wikipedia-wide conventions. Your statement of "English-only" characters would imply that "Paul Erdős", which uses a Hungarian character (that's no umlaut!), should be a redirect to "Paul Erdos". In fairness, the proper choice has been the subject of some debate. However I find no debate about Kurt Gödel, which uses a German character. (Can you spell "inconsistent"? I knew that you could!) --KSmrq^T 15:25, 19 August 2006 (UTC)

Support. Anything that helps keep this from coming up again is a good idea. I don't mind "requires" here, as it is clear in WP:NAME that policies are only recommendations (and hence only required if one chooses to follow them). Michael Kinyon 14:15, 19 August 2006 (UTC)

The remark by KSmrq about Paul Erdös was apropos. I have edited the paragraph above to distinguish between Latin letters with diacritics and non-Latin letters. I also changed the language to clarify that these are recommendations. I don't feel that the goal of this paragraph is to make a different policy for math; the goal is to clarify that current consensus (such as it is) in writing. My impression of the overall consensus is that Greek, Arabic, east Asian, and other foreign alphabets are discouraged in article titles, and diacritics are a subject of discussion. CMummert 12:51, 20 August 2006 (UTC)

[edit] Some new remarks

So first of all I think this discussion is in the wrong place. It's a manual of style issue, not a conventions issue. It should go at the talk page for WP:MSM or WP:NAME; I'm not sure which.

That said — I really don't buy the point that the genuine article title should be easily typed. Why should it? The performance issue with redirects is utterly negligible. Just have the easily-typed redirect, and put the article title at the commonly used name, even if that means unicode. (We've really got to get on the developers' case to remove the uppercasing for initial letters when they're not Latin. The uppercasing is supposed to be so you can use an article title in a sentence with its natural capitalization. That makes no sense at all, on English WP, for non-Latin letters.) --Trovatore 05:57, 6 September 2006 (UTC)

[edit] Notation reform

Math notation represents a un-wiki aspect of Wikipedia, where particular symbols rendered in a LaTeX image cannot be themselves linked, unless they are described. Since there are countless topics in math and physics which use math notation - some of these in a way which is ambiguous with other forms - I propose a rule that every canonical formula be accompanied with a clearly stated explanation of the formula. This will benefit anyone from the beginner to the expert - An advanced explanation might work at K-theory (physics). A beginner's explanation might be something as simple as that at standard deviation.

(Standard deviation equals the square root of E ... equals the square root of E times the square of X minus the square of E times X).

This might be a bit redundant with articles that are well written, and thus link to most of the relevant material. But it will address the basic operations required to handle it - at least to remind editors to include a descriptive. Antipating any groaning, this could even be hidden in a collapsing div, if people are squeamish and think this would be blightish. The accessibility of any article is far more important than "concerns" of blight. -Ste|vertigo 03:49, 6 September 2006 (UTC)

Incidentally, the above "explanation" of the standard deviation definition is completely wrong, because E is the expected value operator; it is not "multiplying" anything. --KSmrq^T 09:21, 6 September 2006 (UTC)

I think you're trying to solve a problem that doesn't exist. Wikilinking is correctly used in moderation; you shouldn't link things just because you can. I see no justification for even trying to wikilink something in the middle of an equation; I'd say it's a good thing that this is impossible. --Trovatore 04:13, 6 September 2006 (UTC)

You have misunderstood my argument perfectly. -Ste|vertigo 07:45, 6 September 2006 (UTC)

Every time someone proposes to add links to equations, it seems we have to explain yet again why it's a bad idea. The example given above is especially bad, because if we must explain what "equals" means we have no hope of conveying "standard deviation"! Anyway, the correct approach, as always, is simply better writing, with any vital links in the text. Note that we already have a guideline in the WP:MSM that says prefer words over symbols in elementary circumstances. --KSmrq^T 04:37, 6 September 2006 (UTC)

I agree with the elementary argument that asserts a certain minimum competency is implied in reading any math article. An explanation of the arithmetic symbols is almost always unncessary. Nor do I think that the complete rules for algebraic factorization need to be explained.

But I dislike the way this idea of "minimum competency" is stated as if it were an natural law. Doubly so, when its spun with an elitism that belies both the whole point of an open encyclopedia and the fact that any article is an entry point for any reader: In the WP context, its quite easy to link from one article in one field to another field altogether, thus making it even more important to be explanatory. All I am proposing is that, within certain reasonable confines, a textbook-like "reading" accompany one or two central formulas in an article.

Further, I dislike any method which states a preference for "words over symbols" in "elementary circumstances." The addition article for example was fine when it treated every thing from arithmetic to complex summation. Its not good to be either too expert or too elementary - beginners as well as experts should be able to read any article without feeling like it has been "dumbed down" or made "inaccessible" by its complexity. If you like, you can take a crack at K-theory (physics), and prove me wrong. -Ste|vertigo 07:45, 6 September 2006 (UTC)

[edit] Probability

I think that we should standardize the statistical notation between pages. Does anyone else think so?

Right now, I think many pages use one of the following notations. The probability that X takes the value x is

P(X = x)

Also, there is the probability of event X occurring:

P(X)

Finally, there is the expected value of X:

E(X)

E[X]

E(X)

E[X]

MisterSheik 19:25, 16 February 2007 (UTC)

No matter what notation we use, we will still have to explain it in English, because we can't expect readers to know the notation. But once we have explained it in English, it doesn't matter what notation is used, so long as each article uses some standard notation and is internally consistent. So I don't see the need for a convention. Really, this argument covers most of the conventions here. CMummert · talk 15:34, 3 March 2007 (UTC)

Hmm... I agree that explaining things in english is good practice, but I think that seeing things presented in a consistent manner makes things easier to understand more quickly.--MisterSheik 16:28, 4 March 2007 (UTC)

I strongly disagree with CMummert's comment about internal consistency being sufficient. An article links to another so that a reader can get background information on concepts used in the first article. If a page with one notational convention links to a page with a different convention, the process of obtaining background is at least inconvenient and sloppy-looking; in worse cases, it can lead to incomprehensibility or misinformation. So consistency across articles is a very important consideration, at least within the same general subject matter. There is a problem, though, in that <math> tags are widely seen as inappropriate for inclusion within paragraphs of text. So as much as possible, there should be a pair of standards, depending on the rendering environment. I suppose mathml will be a third environment to consider, but I haven't used it. –Dan Hoey^talk 18:48, 30 April 2007 (UTC)

[edit] Transpose

I've seen a number of different conventions, sometimes in the same article. My suggestions:

Text: X^T or X^T, not X^T or X^T

Equations:

1. 
2. 

   but not

3. 
4. 
5. 
6. 

But I'm open to suggestions. — Arthur Rubin | (talk) 16:24, 1 June 2007 (UTC)

My convention has been M^T ("''M''^T") in text, and ("M^T") for displayed TeX using <math> tags. A little inconsistent, yes; but so is using \mathbb for reals and the like in displays and boldface in text (Q versus ). Anyway, a user is free to change a stylesheet, so that the body text is set in a serif font (like Times Roman) rather than the default monobook sans-serif. (They could actually choose any whacky font they like.) I try to remember to explicitly state that "·^T" denotes transpose, because a variety of conventions can be found in the literature. --KSmrq^T 00:45, 2 June 2007 (UTC)

[edit] Different type of convention

Would it be possibly more prudent (and informative) to have a specific notation standard throughout a single article then put sort of disclaimer-thing on the top (or anywhere else relevant -- maybe a See Also section or such) with a link to any relevant pages on the specific notations used (i.e. what are they, why someone might prefer one notation over the other, which are standard, etc.)? Foxjwill 06:31, 12 June 2007 (UTC)