Talk:Main Page

We've gone social.
I've just setup a Twitter and FaceBook accounts for ProofWiki. If anyone is interesting in helping out with the facebook page let me know. --Joe (talk) 15:40, 4 October 2012 (UTC)


 * We've already had a comment on Twitter appreciating our Template:Handwaving ... Sheer class. --prime mover (talk) 16:53, 4 October 2012 (UTC)


 * Should anyone find or post locate something worthy to share with the world, don't hesitate to request a tweet. I for one have just posted about Group Example: inv x = 1 - x. --Lord_Farin (talk) 21:04, 10 October 2012 (UTC)

Spam

 * Changed to use reCAPTCHA. Hopefully this will solve some spam issues. --Joe (talk) 11:14, 10 October 2012 (UTC)


 * ... and instantly a spam posting appears.
 * Interestingly the precise same message from the precise same username (Jeremykippler728) has just been deleted by me from another website I assist in moderating. That website has a horrifically bad problem with spammers, and (mow I think about it) may be a major contributor towards my chronically bad temper. --prime mover (talk) 20:13, 11 October 2012 (UTC)

I'm not sure what else to be doing to stop the spam. --Joe (talk) 20:15, 11 October 2012 (UTC)


 * Can you go back to what we had before yesterday? It was considerably more effective than reCAPTCHA which is showing the same weaknesses as I'm having serious problems battling elsewhere. --prime mover (talk) 22:30, 11 October 2012 (UTC)

I think I've mitigated the spam problem for the time being. Changing the question we were asking seems to have done the trick. It's not a question anymore, just a copy the following "blah...." into the provided box. --Joe (talk) 01:37, 22 October 2012 (UTC)

Xymatrix
Allow me to draw your attention to this fantastic package again. Through the hard work of sonoisa, the xymatrix commutative diagram drawing package is now implemented.

A few months ago, the more powerful (but also more difficult and cumbersome) back-end language for xymatrix, xypic, was introduced, which I have employed several times.

But now, with xymatrix, I feel that most PW users should be able to draw the CDs they need. Documentation for xymatrix is easily located through a web search, but I find http://www.jmilne.org/not/Mxymatrix.pdf to be a good source.

The package can be used inside a xy environment, like so:

$\begin{xy}\xymatrix{

//xymatrix code here

}\end{xy}$

I have adopted the convention to precede such diagrams with two colons :: so as to place it a bit more centered in the flow of text.

In case you find functionality of xymatrix that is not yet supported by the implementation, notify me; I'll pass it through to sonoisa. That's all for now - happy editing. --Lord_Farin (talk) 19:52, 20 October 2012 (UTC)


 * I'm currently not in the area of mathematics which requires me to use this - but I will give it a workout once I need to. What I see of its results looks good. --prime mover (talk) 05:23, 22 October 2012 (UTC)


 * Should the basic reference above be insufficient for your purposes, then check out this, or as a last resort (very technical but complete) this. --Lord_Farin (talk) 17:35, 22 October 2012 (UTC)

Equation template amendment
I have amended the eqn template to put the "ro" column to the left of the "r" column so as to be able to build multi-line expressions on the right with greater effectiveness. See this in effect on the $> 1$ proof in Minkowski's Inequality for Sums (incidentally up for a major refactor). --prime mover (talk) 11:23, 4 November 2012 (UTC)

Axiom namespace
It occurs to me that Definition:Group Axioms, Definition:Open Set Axioms and also potentially the axioms for a Definition:Synthetic Basis should perhaps all be somewhere in the Category:Axioms namespace.

Of course, that will mean the Sysyphean task of changing Definition:Group Axioms to Axiom:Group Axioms and all the appropriate pages (and also for Open Set Axioms but there are little links for that yet).

Anyone else think that's a good idea? Oh please say no, my fingers hurt. --prime mover (talk) 22:38, 5 November 2012 (UTC)


 * I'd say no. Almost every concept defined introduces its "axioms". You have probably noticed yourself referring to them as "conditions" as well. I can't craft a definitive argument, though. It seems so natural to have Peano's axioms in the Axiom namespace. It also feels natural (to me) to not include the "totally ordered field axioms" there. Maybe the benchmark is that a certain axiom system should be more-or-less universal, or at least universally accepted as a possible axiomatisation (like e.g. Hilbert style deduction axioms for PropLog). Abstract algebra and topology seem to be less suitable for such axiom systems. --Lord_Farin (talk) 22:55, 5 November 2012 (UTC)


 * As is apparent from my answer, there is a case for this change. However, I think that we're better off tidying proofs, refactoring pages and eviscerating stubs than letting our fingers bleed for such an ultimately aesthetic change. --Lord_Farin (talk) 22:58, 5 November 2012 (UTC)


 * I have an idea PM if you're quite serious about your fingers hurting. Perhaps make something that could take "[ [D:Set union] ]" and turn it into "[ [Definition:Set Union] ]" (that could of course be extremely difficult I don't know).
 * I am quite confused as to what an axiom is in any given context due to conflicting sources. Some sources call proof rules axioms, others make no distinction between an axiom and an axiom schema and others further still call the defining properties of a class the axioms of some theory about that class. I understand all these senses and that the essential quality they have in common is that they are starting points but I wish there was a bijection between words and concepts. I will have to leave it up to you. --Jshflynn (talk) 01:29, 6 November 2012 (UTC)


 * No I'm sorry, you've lost me again: why would I need to turn [ [D:Set union] ] into [ [Definition:Set Union] ]? It already does say [ [Definition:Set Union] ] thruout. --prime mover (talk) 06:16, 6 November 2012 (UTC)


 * As far as I'm aware when creating an article you have to type [ [Definition:Something] ] over and over when you want to refer to a definition page. It might be easier if upon saving a page some program could turn [ [D:Something] ] into [ [Definition:Something] ] (you know like \R instead of \mathbb{R}). The idea being that it would do the transformation once you press the save page button (so people in the future would still see it as [ [Definition:Something] ]). It is just an idea though and may save no time at all to someone such as yourself. --Jshflynn (talk) 09:46, 6 November 2012 (UTC)


 * Interesting that you say that. I suspect it not to be too hard to implement this; I'll discuss it with Joe. In fact, MediaWiki already supports a similar feature, which I happily use: if you type, say  Definition:Set Union </tt>, that becomes Set Union. Make use of it :). --Lord_Farin (talk) 13:12, 6 November 2012 (UTC)


 * On the note of making shortcuts, if it is simple to implement them, can we make one for \operatorname? --GFauxPas (talk) 14:26, 6 November 2012 (UTC)


 * I see that the shortcut LF mentioned works for other namespaces too (even nonexistent ones should you need to implement them in future). How delightfully efficient :)

Changing letters
I have recently seen that some editors prefer the use of the symbols $S$ or $A$ rather than $X$ to denote topological spaces and the like, because "$X$ tends to denote an unknown." I have no objection against this, but I cannot comprehend why this is an improvement. Would anyone mind to explain this (somewhat) more thoroughly? --abcxyz (talk) 00:06, 18 November 2012 (UTC)


 * Whim. --prime mover (talk) 08:45, 18 November 2012 (UTC)


 * It's good to have consistency of presentation in a wiki. When the topology work was started, a lot of the original work had $X$, a lot had $A$ and a lot had $S$, depending on who posted up what. Either we leave it like it is, with lots of different symbology, or we make an attempt to bring it into line. I've been working hard on generally trying to bring consistency to the site, and it cna be frustrating to find that what I'm doing has been undone. --prime mover (talk) 09:13, 18 November 2012 (UTC)


 * Fair enough. I haven't bothered to go through all the topology pages and see which symbols are more common than others.
 * Also, I have a question about linking to redirects (such as  Definition:Neighborhood of Point </tt> as opposed to  Definition:Neighborhood (Analysis)/Topology/Point </tt>). Would anyone mind to explain why this is done? I just don't understand it. --abcxyz (talk) 19:13, 20 November 2012 (UTC)


 * It is mainly for two reasons:


 * 1) Prettier text when hovering over a link
 * 2) In the case a page gets refactored in the future, only the redirect needs to be adapted; this saves mountains of work


 * I'm sure you understand now. As far as I'm concerned, the second argument is the more important of the two. --Lord_Farin (talk) 19:38, 20 November 2012 (UTC)


 * Thanks; I hadn't thought of that. It appears to be a good idea. --abcxyz (talk) 21:10, 20 November 2012 (UTC)

clock
Any chance of getting the system clock reset? It's 5 minutes or more fast. --prime mover (talk) 23:05, 19 November 2012 (UTC)
 * I shall see what I can do! --Joe (talk) 22:23, 20 November 2012 (UTC)
 * Fixed. --Joe (talk) 13:25, 21 November 2012 (UTC)
 * Much better. I no longer panic when I see the time on a page I've just edited. Thx. --prime mover (talk) 08:29, 22 November 2012 (UTC)

Of vs. for (moved from Talk:Equivalent Definitions of Direct Limit of Sequence of Groups)
We now have Equivalent Definitions for T5 Space and this page [ Equivalent Definitions of Direct Limit of Sequence of Groups, LF]. There are various other names for this kind of page (e.g. "Equivalence of Definitions of ..."). We need a consistent convention. What will it be? I like "Equivalent Definitions" better than "Equivalence of Definitions" (it's shorter). --Lord_Farin (talk) 18:22, 26 November 2012 (UTC)
 * Pedantically, "Equivalence of Definitions ..." is more accurate, as "Equivalent Definitions ..." suggests that the definitions themselves are being introduced on that page - whereas the definitions themselves are in fact elsewhere. I confess I have not thought it through; but were we to use the latter it ought to be "Equivalent Definitions of ..." not "... for ..." (when I was refactoring over the weekend, "for" felt wrong) but I'm not in the mood to change them all at the moment.


 * If someone else were to volunteer to do the work, then making everything either "Equivalence of Definitions of..." or "Equivalent Definitions of..." would work for me. --prime mover (talk) 18:50, 26 November 2012 (UTC)


 * The new structure with definitions on subpages makes it much easier to have these pages adhere to a common standard, and to ensure that updates on the def. pages get reflected properly on other pages. --Lord_Farin (talk) 13:55, 27 November 2012 (UTC)

What to do about bad work
Some of the work on this site is shockingly bad. This has got to stop.

I recommend that people who post up unacceptable pages get punished for it. I recommend a fine of up to and including 1000USD and a ban from posting for up to and including life.

That's the only way we can get the quality of submissions up to a decent level. --prime mover (talk) 07:09, 27 November 2012 (UTC)


 * I don't deem it commendable to expel new enthusiasts adding a proof for a previously stubbed article because their writing style is not as we demand it. I do however agree that users notorious for posting substandard material (not that I know many) should be warned and if necessary restricted to their own user page until they demonstrate to know how to make stylistically bearable contributions. I fear that a too repressive regime (and I'd say we're already pretty relentless, only not finding the time to display it) would scare off (highly desired) new contributors, thus limiting the influx of information unnecessarily. --Lord_Farin (talk) 13:55, 27 November 2012 (UTC)


 * Bad formatting and lack of attention to appropriate writing style is not a problem. It's bad mathematics that I was suggesting needs to be eliminated. --prime mover (talk) 19:41, 27 November 2012 (UTC)


 * Would you care to give a rather more objective description of what you consider 'bad'? Plainly false, or incoherent, or phrased in specialists' language? --Lord_Farin (talk) 19:47, 27 November 2012 (UTC)


 * In particular, invalid arguments like affirming the consequent. Incoherent as well. Specialists' language is fine, it just needs someone to come in and say "This means ..." and so on. --prime mover (talk) 20:17, 27 November 2012 (UTC)

Repeating the hypotheses
When I was at school and my perspiring perpetually-defeated teachers tried vainly to bludgeon the basics of mathematics into the solid lump of bone that passes for my skull, one of the rules actually caught hold. That one is: when you're answering a question, it makes sense to repeat the basic facts of the question at the top of your answer so you have a precise grasp of your hypotheses.

In this context, I believe it does no harm to repeat the hypotheses of the theorem within the body of the proof (at the top) in order to clarify the statements which hold at any particular time.

It does no harm to repeat the hypotheses in the proof. OTOH, I think it would be bad to insist that "All hypotheses need to be repeated at the beginning of all proofs and all new work is to be abandoned until every proof adheres to this commandment". But there's a case for saying: if a hypothesis has been repeated at the top of a proof, it does not necessarily improve the proof by removing it just because you can. --prime mover (talk) 19:48, 1 December 2012 (UTC)


 * Fair enough. I'll take this bullet. --Lord_Farin (talk) 20:10, 1 December 2012 (UTC)


 * OK, fair enough. I removed the phrase to make the proof easier to read; it was at the end of a rather lengthy sentence. (Not that you said I "removed it just because I could", but this is why.) Moving it to the beginning of the proof also does the job. --abcxyz (talk) 21:57, 1 December 2012 (UTC)


 * Same thing happened somewhere else I think, I misremember exactly where. No worries. --prime mover (talk) 22:30, 1 December 2012 (UTC)

Differentiation and integration
Is there already a proof that the derivative of the integral of $f$ is $f$, i.e., that differentiation and integration are inverses? — Timwi (talk) 12:29, 3 December 2012 (UTC)


 * Cf. Fundamental Theorem of Calculus (first part, I think). --Lord_Farin (talk) 12:31, 3 December 2012 (UTC)

On results for concepts that have multiple definitions
We have recently decided to try and treat all (sourced) definitions for a concept on equal footing. An example of how the site is progressing can be found at Definition:Connected (Topology)/Topological Space. In time, Definition:Exponential will go through a similar remodeling, and I hope to add other descriptions of a Definition:Boolean Algebra. This brings me to the following point, concerning how results on such "multi-defined" concepts should be structured. As it stands, we have pages like Exponential as Limit of Sequence; this will of course become irrelevant given that we may define the exponential in terms of this limit. Such pages therefore naturally move to the associated Equivalence of Definitions result.

Up to now, such has not posed a problem. However, in the case of Boolean algebras, we have results of the kind Meet is Commutative, or, more relevantly, Join Distributes over Meet. In order to prove that a BA may equivalently be defined as a complemented, bounded, distributive lattice, it is then required to effectively prove Join Distributes over Meet to establish the equivalence. OTOH, given that a BA is a distributive lattice, the result is not even a result, but plainly imposed. Because there are rather a lot of such results involved in proving equivalence of the definitions, there are two, both unappealing paths that I see:


 * Firstly, that the pages remain in place, and have a "this is by definition" one-line proof (which seems rather irrelevant).
 * Secondly, that the pages become lemmata on the Equivalence of Definitions page, thereby unnecessarily lengthening that page (and I can foresee it will already be quite comprehensive from itself).

Of these options, neither of which is satisfying my elegance standard, I'd prefer the first, if one were to be chosen. We are also approaching a similar issue with the natural numbers. There are a lot of results which either prove basic facts about certain paradigms, or prove partial equivalence of definitions, or prove things by means of one paradigm that are trivial in another (without mentioning the equivalence).

It will benefit the consistency and completeness of ProofWiki if we pursue a meta-structural approach that treats, to the extent possible, definitions on an equal footing. In the long run, this will:


 * Make proving stuff easier, because the paradigm(s) most suitable to a typical can be invoked to achieve results that are nearly infeasible to prove directly from other definitions.
 * Make ProofWiki more appealing to all mathematicians, since there is no need for abandoning preferred frameworks and mindsets.
 * Make the site easier to navigate, and make it easier to locate what one is looking for; to this end, the "Also known as" sections should be as comprehensive as possible.

While I am convinced (as is apparent) that this is the situation ProofWiki should pursue, I think it is of the utmost importance that all editors are aware of, and should be able to comment on, this new direction, before we start rolling back each other's edits and create a hostile environment where the covering of mathematical knowledge is no longer the paramount goal of every editor. Thus, please comment. --Lord_Farin (talk) 14:10, 4 December 2012 (UTC)


 * Completely agree.


 * There are two types of definiend here:


 * One, e.g. Connectedness, which is one particular concept which can be treated monolithically; equivalence is proved "in one step", so to speak.


 * The other type of definiend exemplified is that of natural numbers, which is defined by means of an axiom schema - and in this case there are several approaches. In this case, what is done is for separate threads to be established, each one aiming towards the "defining properties" of the natural numbers - and indeed, some of the proofs along the way may be trivial.


 * The transition from the definition-and-equivalences to the multiple-definitions paradigm can be fraught with trouble if other editors are simultaneously trying to "correct" stuff which is still in the process of being developed, but if we are rigorous about using (and respecting) templates indicating work in progress / refactoring / etc., and perhaps adding a field for a username to those templates which do not have them, then inter-editor friction should be kept to a minimum.


 * I would also exhort newer editors to learn the ropes before being too strident in their opinions of how they think things ought to be. Many of the structural conventions have evolved over time and (despite appearance to the contrary) do actually make sense. Some MediaWiki tools and MathJax constructs, for example, are specifically not utilised because they have been shown to cause problems (although with more recent releases of the s/w some of these may well have been resolved).


 * In short, if new editors find their work is being systematically altered, tagged, refactored etc. etc. then treat it as a learning experience as to how pages are to be styled rather than as a challenge to their creative abilities. They are invited to take note of the changes being made and adjust their style accordingly. There are reasons. --prime mover (talk) 15:03, 4 December 2012 (UTC)


 * As to that last point of PM, I'd like to stress that anyone who doesn't understand a certain edit is urged to ask the relevant editor for a justification. In this way, we are both ensured that people get the rationale behind paradigms such as house style, and that such rationale continues to exist in the first place. All editors are invited to put up examples of possible changes/advances in house style or otherwise on their user sandbox, and invite others to comment. This seems to me like the appropriate way to try and nudge the rules and regulations for editing in one's preferred direction (as opposed to simply posting pages in the newly desired format in the main wiki). --Lord_Farin (talk) 22:13, 4 December 2012 (UTC)