Talk:Main Page

The use of Q.E.D.
Although considered "traditional" in the field of mathematics, the use of "Q.E.D." is apparently, I believe, considered somewhat archaic nowadays, and a bit (perish the thought) camp. I believe (from reading around the subject and general communications) that a more common way of signalling the end of a proof is by using the symbol "$$\blacksquare$$" (whose LaTeX is \blacksquare) at the far right of the page, and for a subproof (e.g. a lemma proved in the course of proving a particular result) "$$\Box$$" (whose LaTeX is \Box).

What does anyone think? I have consistently not used Q.E.D. in any of my proofs, but then I haven't been using $$\blacksquare$$ either (mainly because it wasn't available when ProofWiki started and I never got into the habit). If we decide that the "house style" is to include Q.E.D. can we agree that it goes in a particularly fancy font, and have a template link in the ProofWiki Specific section?

Happy Hogswatch to all, btw. --Matt Westwood 07:45, 26 December 2008 (UTC)

I'm fine using either one, either the use of Q.E.D. or the squares. Since the use of Q.E.D. is on the way out we should probably use the squares, I'll make a template.

My thoughts are to have it called qed, and have a option for writing say and then it would put a white square, otherwise a black one. Thoughts? --Joe 16:51, 26 December 2008 (UTC)

No objections either way, although I've never been entirely convinced that adding QED at the end of the proof really adds anything (the proof is over, it should be obvious that it's done). That said, if we do use the square, I don't think it should be all the way to the right, I previewed a page with it and was looking for it, and I still missed seeing it the first time around. --Cynic-(talk) 17:09, 26 December 2008 (UTC)

I've noticed that too, maybe we should just have it so that it's put directly at end of last statement.

For example:

Therefore, $$x=\pi$$ $$\blacksquare$$

Thoughts?--Joe 17:18, 26 December 2008 (UTC)

Maybe put in some space before the box: Therefore, $$x=\pi\qquad\blacksquare$$

Unfortunately, putting a spacing command in (\qquad for example) at the beginning of a math section doesn't do anything, so it would be hard to have it be a template. I don't know if you can create your own functions for wiki LaTeX like you can on standard LaTeX, if you can, you could always make a \qed command. Also, don't put periods in after the box, it looks weird. --Cynic-(talk) 21:22, 26 December 2008 (UTC)

"Therefore, $$x=\pi$$ $$\blacksquare$$" works for me, although I wonder whether it might make the looknfeel more consistent to put it on a new line.

"My thoughts are to have it called qed, and have a option for writing say and then it would put a white square, otherwise a black one" works for me as well.

STOP PRESS: I've just got my hands on "Theory of Sets" by Bourbaki (happy xmas, father-in-law) and in the very second line of the mathematical exposition he uses $$\Box$$ as one of the symbols:

"The signs of a Mathematical Theory $$\mathcal{T}$$ are the following:


 * 1) The logical signs: $$\Box, \tau, \vee, \rceil$$.
 * 2) The letters."

Either this is going to have to be translated into a more "conventional" symbolism (goodness, that will take me a day or two, this book is hev-VEE) or we're just going to have to be really careful. --Matt Westwood 23:09, 26 December 2008 (UTC)

Well, as we're dealing with the geometry that's being posted, another issue has occured to me. \Box seems to be the best choice to be the symbol to represent a quadrilateral. We could always use $$\Diamond$$ (\Diamond) but I think \Box works better. Or it might not be an issue, since it would always appear before letters when representing a quadrilateral and on it's own line when representing QED. Thoughts? --Cynic-(talk) 21:13, 30 December 2008 (UTC)

Might not be a problem. The use of \Box for the end of a lemma is going to be rare because it's more usual for such sub-results to have their own pages anyway. In fact that might be a useful general recommendation, i.e. to put all lemmas on their own separate pages, what say? Then the issue wouldn't arise, we'd just have $$\blacksquare$$ for proof endings. --Matt Westwood 22:18, 30 December 2008 (UTC)

I agree. --Joe 01:07, 31 December 2008 (UTC)

WLOG and WRT
Would it be a useful idea to have a page for abbreviations?

Thus one could write WLOG for "without loss of generality" and WRT for "with respect to" and so on.

The initial thought as I started writing this post was to streamline the development of complicated proofs but the counterargument is that it may make the proof less transparent to a noobie. --Matt Westwood 10:10, 29 December 2008 (UTC)

I would make a Symbols:Abbreviations page to put them on, but I wouldn't link them, it'll just make proofs look a lot more complex. Besides, I think anyone who is interested enough to read a difficult proof knows what something like WLOG means. --Cynic-(talk) 16:54, 29 December 2008 (UTC)

I think we could even put them in as definitions. --Joe 16:57, 29 December 2008 (UTC)

I don't see how it would make proofs more complex, you'd just get WLOG appearing in blue. The only added complexity would be to the source code, and that should not really be a concern in this context.

I mention this point because there's already confusion with "iff" which I would have expected undergraduate level mathematicians to be familiar with (I had to uncorrect someone a few weeks ago who "corrected" what he thought was a spelling mistake for "if"). So I'm starting to consider linking "iff" with its def nowadays. --Matt Westwood 18:33, 29 December 2008 (UTC)

Categorization of Images
I think that we should begin to categorize the images before we get too many that get out of hand. I think this would be a good idea especially if you want to go and look to see if particular image may have been already uploaded.

Probably add a new category, called 'Images', then inside that have categories 'Geometry Images', 'Logic Images', etc. Thoughts? --Joe (talk) 01:23, 3 January 2009 (UTC)

Sounds sensible, but will need a word of instruction for those uploading images. Mind, won't most of the diagrams be geometry? --Matt Westwood 06:30, 3 January 2009 (UTC)

Yeah, number theory, for example, is not gonna need a lot of images. I think we need to make sure we have descriptive names for the images too, which would mean we meed to move some of the images we have now. --Cynic-(talk) 02:17, 4 January 2009 (UTC)

What I did with the proofs from Euclid (once I got into the swing of it) was to name the diagram after the proposition number (e.g. Euclid-I-13.png) and in the description field added the name of the link to that proposition (e.g. "Two Angles on a Straight Line make Two Right Angles"). Usually makes sense, before establishing a system for categorization of entities, to gather a load of those entities together first to see what sort of system may be needed. We have something to work with now but hopefully not too much to be too unwieldy to reorganize. --Matt Westwood 07:35, 4 January 2009 (UTC)

Definition
why defintion doesnt have categories??? i tnihk is a good idea.Maybe i can help but there is something that i dont know.. -- Gamma 23:07, 7 January 2009 (UTC)

Good question. It might make sense to have categories, but they would probably be best to have them be separate from the categories for proofs to keep things easy to find. So basically at this point, it's because categorizing them would be a lot of work. --Cynic (talk) 03:52, 8 January 2009 (UTC)

I've wondered about categorization myself, but we need to be more careful (and limiting) about what categories we use, otherwise the site's usability may suffer. --Matt Westwood 06:31, 8 January 2009 (UTC)

Definitions or Proofs?
Say there is a proof which, during the course of that proof, introduces a new term as the result of that proof.

The example currently under discussion between me and Zelmerszoetrop is Euclidean n-Space.

One way to handle this is to add "Euclidean Space" and/or "Euclidean n-Space" as an actual definition, and in it include a link to a theorem "Euclidean n-Space is a Metric Space", or merely to enter "Euclidean n-Space" as a proof, the content of which will (a) defined the term and (b) prove that it is has the purported properties that allow it to be considered as a "metric space".

I have been (fairly) consistently entering such definitions as proofs up till now (not wanting to clutter up the "Definitions" namespace with a lot of what at the time I considered to be extraneous material. Now I'm not so sure, as Zelmerszoetrop's preferred approach seems cogent and sensible.

More I think about it, more I like the way Definition:P-adic Metric has been configured. That is, we put the definition at the top, and then in a separate section any proofs (particularly the one giving rise to the definition in the first place) which are immediately relevant to that definition.

Thoughts, anyone? And if relevant, worth going through and revisiting those "definition by proof" pages and adding a new page for the definition and linking to the proof?

One downside of this (apart from the fact there's a fair amount of work to do, which for me isn't a problem) is that the possible need to split the Definitions page up into separate subcategories may become even more relevant because the number of definitions will grow significantly. --Matt Westwood 13:45, 11 January 2009 (UTC)


 * I really don't have a problem with either way of doing things, but it's certainly something we should discuss and settle on to produce a uniform style to the project. So in response to Matt Westwoods question, if we should go back to the the old "definition by proof" pages and revamp them to a new style, I would say yes, that whatever style we decide upon here should be uniform throughout the project, and I'll do my part to help with that.


 * Now, onto exactly how we should style this. The way I'm doing things, as Matt Westwood mentioned, is to create a definition page which contains as much information about a given concept as a user would need to answer questions they may have about proofs which link to that definition.  Any claims about a given topic can be proven on Theory pages and we can link to those theory pages from the definition page.


 * I understand the objection based on the enormous number of definitions that must be added, but to be frank, I think that is inevitable. At the time I'm writing, there are 1,421 proofs and 574 definitions.  I expect, or at least hope, the number of proofs will expand dramatically, and as new topics are explored (I'm just beginning the massive field of p-adic analysis, and I've gone through about 10 pages of lecture notes in topology, and hundreds of pages of notes to go), the number of definitions will necessarily grow large anyways.


 * Given the inevitability of a very large number of definitions on the way, it seems only reasonable to me that it be split into a variety of sub-categories. Even if the number of definitions was fixed at less than 600, I would endorse this because it is rather a pain to go through the current list and find the definition I'm looking for when writing proofs.


 * I'd be interested to hear anybody else's opinion on this: is there a better way to incorporate proofs of claims made about concepts in definitions? How to best categorize definitions? Zelmerszoetrop 14:06, 11 January 2009 (UTC)


 * I kind of like what we did with types of angles, that is to say define them on a page like Definition:Straight Angle and then link to the proofs of characteristics. And yes, since we can search the database, I don't think it's particularly problematic if it gets big.  --Cynic  (talk) 18:01, 11 January 2009 (UTC)

Heading Style
Would you mind using == Theorem == instead of = Theorem = when you're writing proofs? Just a stylistic issue, we've been mostly doing it that way across the site. Thanks! --Cynic (talk) 18:23, 11 January 2009 (UTC)

I confess I only started doing it like that because of the "Level 2 Headline" box in the boxes at the top of the edit screen. It occurs to me that sometimes one needs to use quite a deep hierarchy and then it pays to start with = Theorem =. Besides, at === and deeper you don't get dividing lines between the sections. So I wonder whether we might want to treat it as a guideline rather than a mandatory requirement. --Matt Westwood 18:36, 11 January 2009 (UTC)

Personally, I think that it the Level 1 Headline looks huge. There is also good precedent for it, since it's what wikipedia does. As usual, it would be a lot of work to standardize every page to level 1 headlines. We could make it a suggestion, but I think it would be better to only use level 1 if we're going to have several levels of subheading. And if you have a lot of subheadings, you'll probably have a Table of Contents, and we could always insert horizontal lines with after a low level subheading if it would be unclear without it. --Cynic (talk) 18:55, 11 January 2009 (UTC)

registration coming up
Hey guys, fee's for ProofWiki are coming up soon and I would really appreciate it if anyone could help out with the cost. I'm planning on switching to a different host, but that won't affect the price. The deal I'm looking at right now is about $80 for a yearly contract. I don't mind paying for it myself but of course would rather not! So if anyone can help out that would be really awesome! If you can go here.

Anyone think it would be too tacky to add a link on the main page to the donate page and see if we can get random donations? --Joe (talk) 18:07, 15 January 2009 (UTC)
 * How's that tacky? Wikipedia just had that huge "personal plea" from Wales on the main page.  I'm all for it.  Now, I'm not sure, but I might be able to throw in about $20 bucks - when do you need it by? Zelmerszoetrop 19:51, 15 January 2009 (UTC)

I can bung you a few quid via PayPal if you like. Email me with details. --Matt Westwood 21:43, 15 January 2009 (UTC)

Awesome, thanks guys! You can donate by paypal at site support. I'm hoping to do the move this weekend, but anytime at all would be fine. I'll just pay for it personally, and just add the difference after. --Joe (talk) 22:15, 15 January 2009 (UTC)


 * Sorry, my paycheck was a little less than I thought, and I'm a college student. 10 was all I could afford right now, but I just sent it out through paypal. Zelmerszoetrop 21:16, 16 January 2009 (UTC)

No need to be sorry, any at all is great help. That's 10 less I have to come up with! Thanks for donating! --Joe (talk) 01:16, 17 January 2009 (UTC)

I tried to donate, but it doesn't seem to like my cards (http://i43.tinypic.com/11hvs69.jpg). Maybe they don't want Americans donating to Canadians or something stupid like that. I sent a complaint to paypal, and I'll try again when they get back to me. Sorry :( --Cynic  (talk) 20:16, 18 January 2009 (UTC)

It's fine for Brits. --Matt Westwood 21:32, 18 January 2009 (UTC)

Worked fine for me, I'm in America. Zelmerszoetrop 00:08, 19 January 2009 (UTC)

Lemmas and Such
Do we want the boxes around the lemmas, or should we set them off some other way? --Cynic (talk) 18:08, 19 January 2009 (UTC)


 * I'm really not sure. I haven't even been consistent myself; I wrote both Fundamental Theorem of Finite Abelian Groups and the still incomplete Classification of Compact One-Manifolds, the latter of which uses the convention on Existence of Non-Measurable Sets and the former of which uses bold type.  It's something that needs settling.
 * In fact, I'm not even sure we should be putting lemmas on pages at all - maybe they should have independent pages of their own. Since this is an issue that applies to all articles that need lemmas and not just this, I'm moving this discussion to the main page. Zelmerszoetrop 18:50, 19 January 2009 (UTC)

This also seems like a good time and place to discuss a single convention on cases, as seen in Ostrowski's Theorem. Zelmerszoetrop 18:55, 19 January 2009 (UTC)

What's the difference between a lemma and a theorem anyway? Surely just a matter of degree? Is it that a lemma is (generally) used in only one proof? There's another page where there's a lemma proved (Lagrange's Theorem I believe) which has a far wider application than just on that page (and in fact has been proved elsewhere anyway). I need to tidy that up. --Matt Westwood 19:03, 19 January 2009 (UTC)


 * There is no formal distinction. A lemma is frequently something which is not used on its own, but rather to prove one or more theorems, while a theorem is something that can be independently applied.  The boundaries are fuzzy.  I like the idea of putting the more important lemmas on seperate pages, and it wouldn't be hard to do. At the same time, take a look at the page that started this discussion, Existence of Non-Measurable Sets.  The lemmas used here are truly specific to the proof, and would be unlikely to be used in anything else.  Breaking the lemma onto a seperate page only serves to obscure the proof and break the flow of thought of the end user.  It would be possible to write these lemmas as integrated parts of the proof, rather than stand-alone lemmas as they are now on that page, but I think that also serves to obscure the proof as having distinct parts.  Zelmerszoetrop 19:59, 19 January 2009 (UTC)


 * I agree that major lemmas should have their own pages. One thing we could do cor minor lemmas is give them a subpage.  For example, we could have Existence of Non-Measurable Sets/Lemma 1 so they are separate for purposes of reading but grouped for purposes of finding them.  I will also note that I find the boxes unpleasant to read from.  --Cynic  (talk) 03:40, 20 January 2009 (UTC)

Another style issue: bold or italic?
When introducing a definition, should it be bold or italic? For example, "a definition is a series of words saying something", as opposed to "a definition is a precise way of confusing people." I've been using italic for some time now (just seemed natural). However, User:Zelmerszoetrop has been using bold for, it seems, better effect. I don't personally like the look of bold, but I admit it does seem to stand out more.

Would it be appropriate to ask for a style ruling while we only have approx 500 defs to go back and alter? --Matt Westwood 20:26, 21 January 2009 (UTC)

Uncategorized Pages
Hey, I'm not sure where to put some of these! --Joe (talk) 18:22, 23 January 2009 (UTC)
 * Took care of it. Zelmerszoetrop 18:53, 23 January 2009 (UTC)

Group Examples
I was looking at, and I was thinking, why not consolidate this category?

My suggestion is three-fold:


 * 1) Make definition pages for a variety of important groups, ie, $$\mathbb{Z}_n, A_n, GL(F,n)$$, etc.
 * 2) Make two pages, one for finite/discrete groups, and another for continuous/lie groups, which contains proofs of group structure for each of the important examples
 * 3) Remove material that is unneeded or extraneous.  Some of the groups in the category are not likely to be used again in other proofs; I'm talking for the moment about this one, this one, and especially this this last one, since it lacks an operation description.

This way, when we begin Lie theory and other really advanced topics, we have a single page to refer to for these proofs. Any or all of these propositions can be enacted separately. Any thoughts? Zelmerszoetrop 02:43, 27 January 2009 (UTC)

I agree with all of these suggestions, although depending on how many "important" groups there are and how much information each one needs, we might want to combine some or all of them onto a Definition:Important Groups page. However, as I consider this, it may be a horrible idea. --Cynic (talk) 04:51, 27 January 2009 (UTC)

I'm very, very, VERY anti the idea of removing stuff, unless it's utterly wrong. Whether a proof is used as a step in another proof is irrelevant. "Let's not bother with a page for FLT, it's not used anywhere else ..."

The "important groups" should have their own special pages, agreed. And there's nothing to stop a separate category being set up called "Lie Groups" or whatever. If they're important enough to have books entitled "Lie Groups" then they're important enough for a category. And as for discrete groups, I anticipate a category (once we get out that far) for all the work contributing towards the Classification project (the one that culminated in the Monster back in the 80's).

However you want to play it, just don't remove any stuff, okay? Not until you've shown that this last one is most definitely not a group! --Matt Westwood 06:35, 27 January 2009 (UTC)

We definitely should not delete a proof, unless it is wrong or is a repeat; even if it has no applications. Saying that I totally understand where you coming from and your points make sense, especially when trying to link areas of math together. I think maybe the best apporach would be though categorization as Matt suggested. --Joe (talk) 10:11, 27 January 2009 (UTC)

Metric Spaces and Analysis
I'm setting myself a new project: to go through all the basic results in Category:Analysis and recraft them in the context of the general metric space.

It would be good if someone were to follow along behind me with a shovel and a bucket and clean up. I'm bound to make mistakes, I haven't actually tried this before. --Matt Westwood 07:34, 2 February 2009 (UTC)