Talk:Main Page

Way to synchronize equation numbering in Transcluded text?
I have had to fix up equation numbering problems on several pages (i.e., Definition:Sturm-Liouville Equation, Sturm-Liouville Theory and Orthogonality of Solutions to the Sturm-Liouville Equation with Distinct Eigenvalues) as material was moved from the main article into a Definition. This raises a pertinent question. Are there templates for equation numbering that would solve these kinds of problems? I imagine this synchronization requirement is not limited to the pages I work on. Dan Nessett 16:48, 29 March 2012 (EDT)


 * No there's not, but it hasn't been seen as a problem before. It is rare that a train of thought is so long as to stretch over multiple pages (transcluded or not), as (has been explained before) the nature of this site is more as a dictionary (short pithy entries) than as an encyclopedia (longer discursive entries).


 * TL;DR - If equation numbering breaks under the influence of refactoring, it's just one of those things that will need fixing. --prime mover 16:57, 29 March 2012 (EDT)


 * Maybe this is something that can be fixed; some ideas drip in that may allow for the extension being developed to cover this (but I imagine that it will be hard to cover things like $(3')$ and $(1a)$ which occur now and then. Should I put some more thought into it? --Lord_Farin 17:21, 29 March 2012 (EDT)


 * If you think you have a strategy, then it's worth exploring. For one, I'd suggest a template "eqno" or something equally pithy, which might also contain a means of directly linking back to the original equation in the same / similar way that "eqref" etc. works in a conventional $\LaTeX$ work.


 * But the question is bigger. Pure maths is one thing, where the expositions are short, and there is no need for lengthy pages. However, applied maths and mathematical physics may require that the descriptions are considerably longer (thinking ahead to the delights of the analysis of the behaviour of waves and ripples on the surface of a body of liquid is filling me with anticipation as I type) and so, as with S-L Theory, a new approach will need to evolve.


 * The challenge will be in the crafting of short, self-contained but transcludable, pages like Definition:Sturm-Liouville Equation such that any page referencing it will be able to either link to it or, as necessary, transclude it, without the need to copy-paste or any otherwise repeating material.


 * Another challenge: if several pages are so transcluded, what if the equation numbers clash? --prime mover 17:32, 29 March 2012 (EDT)

Good point, and nice elaboration on the challenges we are coming to face with the advent of more applied systems and research fields. The only possible ways I see to solve this problem are by using eg. an optional unique identifier (like 'eqnaboutblabla') or allowing only for a possible subscript to be added to a number (eg. where 'a' yields $(na)$, and "'" gives $(n')$ with $n$ as appropriate). But these are bound to be fiddly and will put up a wall of syntax for new aspiring editors. Maybe this last point isn't really big because the convention could be applied in a 'only-when-required' fashion. In any case, the amount of documentation I would deem necessary will demand a lot of time, time I seem not to have in the coming few months.

But then, I haven't even spoken about what to do with things like 'Axiom $(2)$' or 'Equation $(3)$ on "somepage"' as references; I haven't got a solution for that yet (maybe we needn't look, as this is of relatively small impact, on crystallised pages). --Lord_Farin 17:45, 29 March 2012 (EDT)


 * I thought about this problem a bit and I now think it will be difficult (but perhaps not imposssible) to provide the requisite functionality even with an extension. What I think is needed is a way for equations transcluded from a page to be tagged with a number based on their context on the referencing (not the transcluded) page. For example, an equation labeled (1) on a source page might require labeling as equation (3) on the referencing page.


 * Achieving this would seem to require global state on the referencing page that figures out where the first reference to the equation occurs and then assigns it a number. That number would then be assigned for each reference to the equation. This is a bit like citations implemented by the Cite extension, but with dynamic numbering.


 * It wouldn't be hard to uniquely identify equations based on a page name and a number on that page, but then to map that into a dynamically allocated number on the referencing page would require MW parser functionality that doesn't exist. In the past I wanted to write templates that did arithmetic on citation numbers for a similar purpose, but discovered that the parser simply doesn't support this. The MW parser is a big mess, but not particularly sophisticated from a computer language point of view. So, achieving the goals of dynamically allocated equation numbering is probably a bridge too far.


 * By the way. In regards to transcluding individual equations from other pages, it might be useful to install the Labeled_Section_Transclusion extension. Just a thought. Dan Nessett 18:46, 29 March 2012 (EDT)


 * Sounds like a good idea to me. This may be particularly useful when we might want to transclude more than one section of a given page - at the moment (or when I last tried it) when you have more than one "onlyinclude" section in a page it doesn't work properly. --prime mover 02:00, 30 March 2012 (EDT)


 * Labeled section transclusion is superseded by the (PW-tailored) extension in development, which will allow for customisation of the header levels under transclusion. To achieve this I am already working with global states; I think it's possible, albeit with a special, to-be-written parser function that outputs $(3)$ (because it's possible that one would like to write $(3)(4)$ to indicate multiplication (though this is disallowed by house style, I think that the distinction should be made clear) and thus simply fetching the occurrences of $(n)$ (and then, which one of the occurrences labels the equation itself? 'see equation $(n)$ below' would cause problems) would be too simple an approach). --Lord_Farin 03:12, 30 March 2012 (EDT)

Laugh and a half
Here's a wally who thinks you can copyright $\frac 1 3 = \frac 1 2 - \frac 1 4 + \frac 1 8 - \frac 1 {16} + \cdots$

http://en.wikipedia.org/wiki/User_talk:WIKI-1-PIDEA#Angle_trisection

How we laughed! --prime mover 15:20, 30 March 2012 (EDT)

Category:Disproofs
Just today, Restriction of Non-Reflexive Relation is Not Necessarily Non-Reflexive was posted. I would argue it belongs in the category Category:Disproofs and maybe some more specialised category linking to Proof by Counterexample. The title could then maybe even be:


 * Disproof:Restriction of Non-Reflexive Relation is Non-Reflexive

I'm bringing this up as the 'not necessarily' in the title shows that it isn't really a 'proof' in some intuitive, emotional sense. What do you think? I haven't bothered practical objections like the linking structure on the site. --Lord_Farin 10:56, 1 April 2012 (EDT)


 * Possibly ... but then there are going to be some borderline cases (can't think of any) which are perhaps proofs of a negative result, etc. Proofs by counterexample may already exist as a category (like "direct proofs" and "proofs by induction") but I've never been a fan of such categorisation strategies so I haven't kept them up to date. --prime mover 14:39, 1 April 2012 (EDT)


 * That's what redirects are for. I noticed that the categories expressing kinds of proofs aren't very popular, and I don't care enough to change that. --Lord_Farin 18:25, 1 April 2012 (EDT)

Source works
Before I just delete the offending line, what's the thoughts of others on a discussion in a maths forum as an appropriate "source work" for a given page? I expect you may be able to guess which page(s) I'm talking about. The forum consists of the contributor raising hypotheses which other contributors to that forum are either disproving immediately or expressing scepticism about. --prime mover 17:58, 4 April 2012 (EDT)


 * I'd rather have no source. --Lord_Farin 18:06, 4 April 2012 (EDT)

Axiom of Countable Choice
As concern had been expressed about the inability to adequately discuss results depending upon the Axiom:Axiom of Countable Choice, I have put together Template:ACC which can be included, in a similar way to Template:AoC, at the bottom of any result which requires the ACC for its validity.

However, I am unfamiliar with the philosophical implications of ACC (they're nowhere near as widely discussed as those of AoC) so can't do justice to the wording.

Is there anyone out there who knows (and is philosophically liberal) enough about this to be able to make a better job of wording it? --prime mover 03:47, 5 April 2012 (EDT)

Editing suggestion
Apparently, nobody noted my suggestion over at Help talk:Editing, but I would like to know your opinions; consider this a gentle push. --Lord_Farin 13:26, 14 April 2012 (EDT)


 * Hadn't noticed it. Have now commented. Have amended the page you talked about it on. Would like to alert users to experiment with nuances of formatting (adding spaces here and there as needed) as MathJax has some shortcomings. --prime mover 15:34, 14 April 2012 (EDT)

Relicensing under CC-By-SA
(This post has been copied into here from my own chat user page. I endorse what this guy is saying.)

Hi prime mover: As we discussed at the MathWikis workshop, I'd like to work with you on getting some or all of ProofWiki relicensed under CC-By-SA. If we're talking about your own entries, all you really have to do is say someplace "I agree to license my contributions to ProofWiki under CC-By-SA", then me (or someone else) can go ahead and find them and download them, and use them under those terms. However, if we're talking about shifting the license on the entire wiki, that means tracking down all existing contributors, and getting them to agree to the same terms.

Basically, CC-By-SA and the GNU FDL are almost equivalent, so in principle there should not be much of a problem. The primary benefit (outside of ProofWiki) to releasing the material under CC-By-SA is that it can then be re-used on sites like PlanetMath and Wikipedia. I'm guessing that broader re-use of the ProofWiki materials would have some benefits here, including more links back to this site (due to the attribution clause of CC-By-SA), and general access to a healthier mathematics ecosystem around the topics discussed here.

For me personally, I'm interested in looking at the proofs you've developed here as a collection of "Worked Examples" for my thesis (http://metameso.org/~joe/thesis-outline.html). That is more or less independent of licensing issues, but a CC-By-SA license would give me the most leverage, I think.

Please let me know how I might be of further assistance in this matter! Arided 17:24, 14 April 2012 (EDT)


 * Everyone: feel free to comment on this - technically we need the agreement of all contributors to allow this change to the copyright licensing, but we can settle with "active contributors", I guess. --prime mover 18:22, 14 April 2012 (EDT)


 * What is not apparent from the 'human-readable' statement but is in fact included in the formal juridical language in which it is cast, is that anything released under the CC-By-SA license is irrevocably released (i.e., I cannot, eg. for the purpose of removing some ludicrous stuff I could have put on PW, demand that such content be removed from PW, and is not to be bound by CC-By-SA any longer (such is specifically prohibited by point 7b (and thereof the part after the last semicolon))) which I consider a possible problem (although unlikely to occur) of adopting this license. I would rather have a license allowing me (or any other editor) to remove certain parts of the made contributions if so desired. However, as long as anything in the 'talk' and 'user' namespace will be amended to have such a possibility (since I do feel that such an irrevocability condition is desirable for bona fide PW entries) of legally allowed removal, I think it is a good idea to implement this licence. But then, GNU-FDL may have already got me there; in any case, such a clause will calm my paranoid mind. Otherwise, I endorse the suggestion.
 * In summary, I think that the actual pages (viz. the main and defn namespaces) are suitable for this licence, while the user-specified pages are only under the condition that it is legally allowed to completely remove them. --Lord_Farin 19:33, 14 April 2012 (EDT)
 * I'm for the CC-SA license - but perhaps the non-commercial license (CC By-NC-SA) would be better? --GFauxPas 21:34, 14 April 2012 (EDT)
 * I also am totally fine with a move to some flavor of CC license - I've never really cared about the subtle distinctions that may or may not exist between CC and GNU/GFDL. I'd pass on the NC addition I think, just cause I don't really see why it would matter (although as I said, I've never bothered to research licenses, I typically release whatever content I put online as un-restrictively as possible). --Alec  (talk) 23:43, 14 April 2012 (EDT)
 * I'm totally against NC because then it means you can't use ProofWiki in the context of commercial writing to contract. That would be silly because this is mathematical proofs and therefore is out there in the real world. It may result in the death of textbooks. --prime mover 01:10, 15 April 2012 (EDT)
 * Okay, I'm pretty neutral on the matter, just thought the issue was worth mentioning. --GFauxPas 08:37, 15 April 2012 (EDT)


 * Hi all, bolded text about CC-By-SA being compatible with PlanetMath and Wikipedia. CC-By-SA-NC would not be compatible w/ those sites.  @Lord_Farin, I don't think it is possible to "revoke" an FDL license on material that has been copied and distributed downstream.  AFAIK the only way would be to delete the "ludicrous stuff" from the upstream site (ProofWiki in this case) and hope that it hasn't spread on to other users!  Cheers, Arided 20:20, 15 April 2012 (EDT)
 * I understand that part; the idea is that I would like to prevent possibly ludicrous stuff on the talk pages from falling under a Licence; rather I would like to see that no implicit approval for citation is given when one puts up stuff on talk pages. Simply deleting the parts which in hindsight aren't desirable will not really work, due to the history-viewing capabilities MediaWiki has implemented. My concern, as I apparently didn't express clear enough, is that users are bound by the Licence, and thence are not allowed to request an administrator to permanently delete a page (for such would be a violation of said Licence), also from the history functionality, when they feel that, in hindsight, a particular contribution is deemed very foolish and undesirable. I deem it undesirable that users are not allowed (whether or not this has been the case in the past) to delete any information they put up on the internet section called ProofWiki (be it under a pseudonym or not). I am not sure how such a thing can be put into effect but I think it is good that users will not be eternally bound by stuff they put up on some discussion page. If this isn't the case already, please point out why. Hopefully I have now more clearly expressed my point. --Lord_Farin 05:41, 16 April 2012 (EDT)
 * What he said - talk pages are (or should be) considered ephemeral and not part of the "canonical" content of ProofWiki. Exactly how to treat the legal aspects of such pages would need to be discussed, but I would suggest: what one says on a chat page should be "owned" by the person saying it at least to the extent that they should be allowed to decide whether it is to be deleted irrevocably. Having said that, this is of course not foolproof because somebody might already have copied what you said into a different place which is outside of your legal control. --prime mover 08:15, 16 April 2012 (EDT)

I am glad at least one person caught on to my points, having spent all those thousands of characters explaining them. I wonder if it would be enough to add a clause to the (now likely soon-to-be-written) Copyrights page stating something like 'ProofWiki and/or its users (maybe: Licensor) prohibits the right to permanently/irrevocably delete any attributed/user-specific content without any further notice.'. --Lord_Farin 10:39, 16 April 2012 (EDT)

Database dump?
While we're at it (see licensing discussion above), a snapshot ("dump") of the current set of articles would make it much easier for me to work with the articles offline. Is there a standard way to request that? Arided 20:32, 15 April 2012 (EDT)
 * Would XML format be okay? I understand that a MediaWiki database (of which this is an instance) can be output in that format - but I've never tried it myself and I am not 100% sure it would do the $\LaTeX$ properly (although this would be hoped). I expect this may be a job for Joe (talk) as he's the one who has been responsible so far for performing admin / maintenance / under-the-hood work. --prime mover 02:39, 16 April 2012 (EDT)
 * Database dump located here . I can set it to dump daily if anyone is interested. --Joe (talk) 07:28, 16 April 2012 (EDT)
 * You're a star.
 * Daily might be too often (I understand it might compromise the ability to edit stuff? please confirm). I suspect that once a week would be plenty enough. --prime mover 08:08, 16 April 2012 (EDT)
 * It will temporarily disable database access for a few minutes. I can just do it at the same time I do a database backup every night, no should even notice (Unless you never sleep). Though in the future I'll probably move them to a better folder (subdomain? Suggestions welcome).--Joe (talk) 08:24, 16 April 2012 (EDT)
 * Good call, there. Usually I'm online by 06:00 UK time, which would be anytime between 10pm and 1am US time wherever you are ... --prime mover 10:33, 16 April 2012 (EDT)
 * I'm UTC−3:30 --Joe (talk) 12:13, 16 April 2012 (EDT)
 * Oh of course, the wonderful Newfoundland. (Or is it Labrador?) Rock on. --prime mover 14:47, 16 April 2012 (EDT)

You're not doing (ahem) a dump now, are you? It's been crashing on me all evening. "Technical difficulties", it sez. --prime mover 15:39, 16 April 2012 (EDT)
 * Well, I was, actually; I am sorry for any problems that have occurred. I will try again at a more suitable time. --Lord_Farin 15:43, 16 April 2012 (EDT)
 * Ah, okay, that explains it. Thx. --prime mover 16:17, 16 April 2012 (EDT)

Can't upload file
On trying to upload a file, I got:
 * "The upload directory (public) is not writable by the webserver."

Can this be sorted? kthxbai. --prime mover 12:42, 17 April 2012 (EDT)
 * On it. --Joe (talk) 12:42, 17 April 2012 (EDT)
 * Try now. --Joe (talk) 12:45, 17 April 2012 (EDT)
 * Gotcha. Thx. --prime mover 12:51, 17 April 2012 (EDT)

Search PW via Google
After a tedious trial and error procedure I have finally found how to simply search PW through Google (thus, without having to type the tedious 'site:proofwiki.org' every time).

Let me point out how to do this in three commonly used browsers.

Chrome:
 * Go to chrome://settings/searchEngines
 * Add a new search engine: name is up to you, as is the keyword (I use pw), the URL is http://www.google.com/search?hl=en&as_sitesearch=proofwiki.org&q=%s

Firefox:
 * Go to Main > Bookmarks > Show all bookmarks
 * Make a new bookmark: name up to you, as is the keyword (I use pw), URL is again http://www.google.com/search?hl=en&as_sitesearch=proofwiki.org&q=%s

Opera:
 * Go to Main > Bookmarks > Manage bookmarks
 * Make a new bookmark: name and nickname (i.e., keyword) as above, URL again http://www.google.com/search?hl=en&as_sitesearch=proofwiki.org&q=%s

In all three browsers, typing eg. pw surjective will let Google search for occurrences of surjective on PW; IMO this is a better (more accurate) search feature than ProofWiki's own (except for brand new pages, which may not have been indexed yet). Hopefully, this helps y'all to find stuff on PW faster. --Lord_Farin 18:23, 19 April 2012 (EDT)
 * Very nice. --GFauxPas 20:03, 19 April 2012 (EDT)


 * Wow - that's pretty good. And more to the point: I have now learned another useful computer technique. Good man. --prime mover 01:25, 20 April 2012 (EDT)

Attack of the spambots
Looks like we're under attack again from spammers. No worries, got it covered. But we might want to review our captcha system. --prime mover 16:21, 24 April 2012 (EDT)


 * ... and we've just had our 1000th user join up. Shame he was a pimping spam-merchant. --prime mover 15:38, 26 April 2012 (EDT)


 * ... and I'm willing to bet a considerable value that the latest 4 users who have just joined are not here to contribute towards the dissemination of mathematical knowledge. --prime mover 02:31, 2 May 2012 (EDT)


 * ... and the latest one just tried to replace this talk page with a spamvert to its website. You can't exactly admire the intelligence of something like that. If it was truly a bot then it needs to be deleted. If it's human then euthanasia (or perhaps extermination of vermin) would be 100% appropriate. --prime mover 02:06, 8 May 2012 (EDT)

I've modified the security question when making an account. Let's see if that makes a difference. --Joe (talk) 12:42, 10 May 2012 (EDT)

Linear Transformations and Matrices
There's a lot of places where a result is proved on the space of linear transformations, and then exactly the same result is being added again but for matrices. As the two are equivalent (i.e. matrices are a tool via which linear transformations are manipulated), this seems to me like a level of redundancy which is not needed. I would argue that this is a different situation from separating out results for $\R$ and $\C$, in that the latter type of result is a genuinely different set of result as they are on a different domain - but as matrices and linear transformations are the same thing, it looks like a lot of duplication. Argue me out of this one, somebody? --prime mover 16:34, 9 May 2012 (EDT)


 * Typically, matrices constitute a special case of linear transformations (namely, they are essentially (up to choices of bases) the finite dimensional linear transformations) and the finite dimensional case is usually where everything will hold trivially (these all being Hilbert spaces, the nicest kind of vector space I know (except for finite dimensional vector spaces...)). As Conway states it: 'Upon introducing a new concept, it is always good to check how it behaves in the finite dimensional case' (IIRC). There is a case for these results as most of the applications work in the matrix setting; it is often convenient to have the result already phrased in this setting. No reason to incorporate such stuff as more than merely a corollary, though; some results get tedious and often very hard to prove when taken out of the abstract functional analytic setting. --Lord_Farin 17:05, 9 May 2012 (EDT)


 * I've been corollarying null spaces under kernels, matrix-vector products under linear transformations, things like that. I have been arbitrarily deciding that some of the theorems "feel different" for matrices and LTs, though. Can you put a mergeto on the pages I made that you think are unnecessary, and I'll work on corollarying some theorems? --GFauxPas 17:28, 9 May 2012 (EDT)


 * I'll get to it. I'm a few chapters away from it in my project to plough through Warner. It won't be for a few weeks yet. --prime mover 17:42, 9 May 2012 (EDT)

Pointwise operations
Taking up this project again, I needed some distraction from building up measure theory. It appears that there are already two strategies cropping up in defining pointwise operations. They are adequately described on Definition:Pointwise Scalar Multiplication of Mappings and Definition:Pointwise Scalar Multiplication of Real-Valued Functions (where the latter approach may also be found on Definition:Pointwise Maximum of Mappings).

Before continuing to streamline (and expand upon) the host of definitions in this range, I want to determine which approach we desire. I have been doing a lot of the second type lately, but I feel that rigour and insight are more served by the first, although I encourage one to look at Definition:Pointwise Supremum which would be hard to convert to the first approach.

So my final suggestion is, that we use the set of all mappings $S^X$ as long as possible, while when only a subset of these mappings applies, we take the more indirect, 'point-by-point' (in this case, 'function-by-function') approach (i.e., the second approach). What do you think? --Lord_Farin 04:42, 31 May 2012 (EDT)
 * What you are doing looks good. I'd suggest: if it makes sense and fits into the strategy you have planned, then go for it. If something does not work too well, then we can restructure it at a later time when the subject has been filled out a bit. In short: I agree with your final suggestion. --prime mover 05:22, 31 May 2012 (EDT)
 * Having thought about it some more, I wonder whether Definition:Pointwise Scalar Multiplication, rather than being a redirect, could be a page in whcih the various instances of pointwise multiplications could appear as transclusions? See (for example)Definition:Rank for the sort of approach I mean. The various definitions are dissimilar enough to need their own pages, but are not so dissimilar as to need a fullscale disambiguation. --prime mover 05:32, 31 May 2012 (EDT)
 * I have reworked Definition:Pointwise Scalar Multiplication of Real-Valued Functions, it is now quite similar to Definition:Pointwise Scalar Multiplication of Mappings. Has this (en passant) resolved the need for the Definition:Rank-analog? --Lord_Farin 03:33, 8 June 2012 (EDT)

I've never liked the tendency in some text books to refer to "addition" and "multiplication" in the context of abstract algebraic structures. If it's an abstract construct, then so is the operation. "Addition" and "multiplication" should IMO be used in the context of numbers only (with the exception that in a ring, the distributand is conventionally called "ring addition"). Separating out the definitions for nothing more (effectively) than a different notation (using "+" sign and juxtaposition) seems a bit "grade school" to me.

What you also see in some books is something like: "If the operation is 'like' addition (or multiplication), then ..." What does it mean for an operation to be "like" addition?

Equally, building two definitions, one for commutative operations and one for not-necessarily-commutative is also overdoing it a bit as well. --prime mover 04:14, 8 June 2012 (EDT)
 * I see your point, and to some extent you are right. But it would IMO be rather awkward to refuse to speak about 'module addition' which by definition behaves like an extension of ring addition. I would rather suggest to restrict 'addition' to numbers, and '(ring-ish) addition' to suitable R-algebraic structures (probably modules). This covers most or even all of the cases in which we are used to talking about addition (like the 'sum' of two vectors); for remaining cases, addition would indeed, as you rightfully state, be a misnomer and will lead readers to tacitly apply certain (possibly false) familiar principles. As for multiplication, it would, continuing this vision on the (non-)use of common names, probably be best to restrict it to numbers only. One generally speaks about 'ring product'. So finally my proposal is as follows:
 * Pointwise Addition of Mappings: transclusion of:
 * Pointwise Number Addition of Mappings (codomain of numbers)
 * Pointwise Addition of Extended Real-Valued Functions
 * Pointwise Ring Addition of Mappings (codomain a ring)
 * Pointwise Multiplication of Mappings (only numbers and $\overline \R$)
 * Pointwise Scalar Multiplication of Mappings: as-is


 * I deem it useful to have a separate page for multiplication because of the explicit setting we put it in - in general it will suffice to consider Definition:Operation Induced on Set of Mappings. It may be best to generalise the current pages for $\R$-valued functions to number-valued functions, while maintaining the $\overline \R$ versions (as $\overline \R$ tends to behave a bit odd). Whilst putting myself vulnerable to critiques on changing my mind so often, I think the abstract-algebraic and number viewpoint are sufficient to cover all cases one would like to consider (at some point we will have to assume the reader has some working knowledge and can instantiate the general induced mapping to any particular case, since the overview is already lost). We can always ad hoc put up particular nonstandard instances (eg. pointwise limit of bounded linear transformations) as we deem fit. Is this strategy acceptable? --Lord_Farin 05:12, 8 June 2012 (EDT)


 * My view is that Definition:Operation Induced on Set of Mappings (possibly renamed) should be the master page here, with various subpages as appropriate, e.g. Pointwise Addition of Mappings. Pointwise scalar multiplication could be a separate page, taking the concept of modules as its basis. If you must have separate pages discussing numbers, then link to the existing pages in (Real) Analysis where the concept is already in place. --prime mover 15:47, 8 June 2012 (EDT)

Concerning Categorisation
I'm having questions about the use of displaying the Category:Disambiguated and Category:Disambiguations categories at the bottom of pages. I would consider putting __HIDDENCAT__ on these respective category pages to suppress their display, yet retain their functionality. Similarly I plead for a category for every book (eg. by ISBN reference) so that every page containing a reference to it will automatically appear in that category. For clarity of categorisation these categories will need the same 'hidden' attribute, yet be accessible via the PW:Books page for it. This will allow an easier search through certain books, which sometimes may be desirable. Another possiblity for naming the category would simply be replacing ProofWiki: in the book's title page with Category: which will probably make it easier to refer to stuff. What do you think? --Lord_Farin 12:17, 5 June 2012 (EDT)
 * If it makes it easier to find stuff, then I'm all for it. As we already have a template for the placement of a citation on a page (several such templates, in fact, borne of my own inexperience with MediaWiki when I put them together, I'd do it differently now) this should not be an impossible maintenance burden. So yes, this all sounds good to me. --prime mover 12:46, 5 June 2012 (EDT)
 * ... all very well, but now look at a disambiguated page, it says: "Hidden category: Disambiguated" at the bottom now. That's no good at all ... --prime mover 12:49, 5 June 2012 (EDT)

One can turn display of hidden categories on or off at one's preferences page. I believe it is default not to see hidden categories; so while you may see it, others (like me) won't. If you so desire, you can of course change the setting. My idea was to put the category link inside the Template:BookReference which is the most common reference method if I'm correct. --Lord_Farin 15:12, 5 June 2012 (EDT)
 * Disambiguation categories have now been HIDDENCATed. As for the book categories, you will have to provide an example so I can see what you mean. Amend the BookReference template if you need to, we can always change it back if it all goes wrong. --prime mover 15:27, 5 June 2012 (EDT)
 * For an (as of now imperfect) example, see Characterization of Integrable Functions. IIRC, there is a way to force that the book ref cat comes after the measure theory category; I will probably think of a neater way to name the category, but that is a concern for later. --Lord_Farin 15:47, 5 June 2012 (EDT)
 * Adjusting the order of display appears impossible; this is a possible downside of the idea. Of course, we could make the categories hidden (eg. only linking from the book page to the category (by for example 'Pages incorporating material from this source can be found in "catname"')). --Lord_Farin 15:58, 5 June 2012 (EDT)
 * We might need to rethink that idea. I'm not dismissing it completely, I just wonder whether there's another way to do it ...--prime mover 16:31, 5 June 2012 (EDT)
 * Same here. But I still think we should make it easier to find pages referring to a particular source work. It makes sense to do such a thing. --Lord_Farin 17:21, 5 June 2012 (EDT)
 * Can't we already see what pages referr to a source work through the "What links here" link on the book page? --Alec (talk) 20:17, 5 June 2012 (EDT)

Entirely correct, thanks for pointing that out.