Wikipedia talk:WikiProject Mathematics/Conventions

message: 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)
thread_title: Algebras

message: 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)
replies: text: 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)
replies: text: Lie rings don't have units (and I don't think that anybody would really want to ajoin a unit to a Lie ring just for kicks). So, is a Lie ring a ring? --Ramsey2006 (talk) 01:42, 20 March 2009 (UTC)
thread_title:  Rings being unital 

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

message: I believe the suggestion is only what we currently do (see category theory). Charles Matthews 11:48, 28 October 2005 (UTC)
replies: text: Agree. Move to adopt as no one has objected. -- Fropuff 03:46, 6 December 2005 (UTC)
thread_title: Hom-sets

message: 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)
replies: text: 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)
replies: text:  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)
replies: text: 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)

text: 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)
thread_title:  Italic constants 

message: 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)
replies: text: 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)

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

text: 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. --KSmrqT 22:22, 23 January 2006 (UTC)
replies: text: Isn't a "variety that isn't irreducible" just an algebraic set?  -lethe talk 03:24, 24 January 2006 (UTC)

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

message: "Directed sets are preordered sets with finite joins, not partial orders as in, e.g., Kelley (General Topology; )."
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)
thread_title:  Troublesome reference to Kelley 

message: 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 , 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)
thread_title:  Bipyramid vs. Dipyramid 

message: * (Notational) Subset notation: \subseteq should mean subset, \subset should mean proper subset.
** (Counter-proposal) \subseteq should mean subset, as above, but \subsetneq should be used for proper subset, and \subset should not be used at all.
**(Counterproposal): \subset should mean subset, \subsetneq should mean proper subset. \subseteq may be used for emphasis or clarity, and will mean subset.
** (Synthesis proposal) Subset is denoted by \subseteq, proper subset by \subsetneq. The symbol \subset 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, A\subset B might be given as the hypothesis of a theorem whose conclusion is obvious in the case that A=B). All other uses of the \subset symbol should be explicitly explained in the text.
- recorded by Gauge 02:52, 28 June 2006 (UTC)
thread_title: Saved copy of various proposals for subset notation

message: 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)
thread_title: Some new remarks

message: 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
:\Pr[X=x]
:\Pr(X=x)
:P(X=x)
Also, there is the probability of event X occurring:
:\Pr[X]
:\Pr(X)
:P(X)
Finally, there is the expected value of X:
:E(X)
:E[X]
:\mathrm E(X)
:\mathrm E[X]
:\mathbb E(X)
MisterSheik 19:25, 16 February 2007 (UTC)
replies: text: 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)
replies: text:  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)

text:  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 Hoeytalk 18:48, 30 April 2007 (UTC)
thread_title: Probability

message: 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)
thread_title:  Different type of convention 

message: I don't see why it's necessary to prescribe how many items need to be written down in a sequence. It depends on the context and, in my opinion, can thus be better left to individual authors. I certainly disagree with the proposed convention, because it does not allow the common idiom
: a_i = \text{bla}, \qquad i=1,\ldots,n. 
I don't think it's necessary or helpful to write i = 1, 2, 3, …, n as is proposed. -- Jitse Niesen (talk) 12:30, 20 February 2009 (UTC)
replies: text: I have to agree.  This seems like a terrible convention. Thenub314 (talk) 18:10, 21 February 2009 (UTC)
thread_title:  Sequences and series 

message: From Talk:Linear code#Notation for Linear vs Non-Linear codes, there was a discussion on who gets () and who gets [].  Consensus appears to have been reached to use () for non-linear and [] for linear.   They asked where to document the convention, so I mentioned here was a good place, and copied it over. JackSchmidt (talk) 22:18, 21 February 2009 (UTC)
thread_title:  Code parameters 

message: The pages linked to from  currently differ a bit in their display of formulae. Some add the integration constant C at the end, whereas some leave it out. What is the current convention on this? You know, I find it pretty confusing having it on some pages, but leaving it out on others. --The Evil IP address (talk) 13:18, 17 August 2011 (UTC)
thread_title:  + C in the solution of integrals 

message: Hello,
Is there a manual of style or a list of conventions for geometry-related articles? In particular, I am thinking of the article for pentagon. The article content is clearly skewed towards regular pentagons, however, the equilateral pentagon (often used as the symbol for a house) is just as commonly encountered. In fact, there are as many types of 5-gons as there are polygons. Are the articles for the more well-known types of polygons supposed to be skewed towards their regular forms? Else, I should think that there should be a separate heading for each kind of pentagon, with more detailed information at their respective articles. Can anyone point me in the right direction? 8bitW (talk) 23:41, 28 January 2016 (UTC)
replies: text: I don't think there's any convention on this. If you want to add content about non-regular pentagons, go right ahead. To start, it should be in its own section in the article. Eventually, when there's enough content, the article can be split into a regular pentagon article and something else (irregular pentagon?).  Ozob (talk) 01:01, 29 January 2016 (UTC)
thread_title:  Manual of Style / Conventions for Geometry 

message: I successfully helped a sibling, in a matter of a few days, avoid flunking out late in his Calculus I course. I am working on v:Calculus I and I would appreciate feedback on conventions and stuff. Please let me know if there is a better place for this notice. Thanks in advance.--Samantha9798 (talk) 13:36, 19 November 2016 (UTC)
thread_title:  Calculus I