Talk:Main Page

Please Post Any Ideas
When writing proofs it would be useful to be able to reference definitions. As well as proofs, then, it would be useful to have a completely different section containing definitions, which could of course themselves contain (or reference) proofs which these definitions rely on.

This leads us on to axioms. Would it be worth adding a page detailing the ZF axioms, and another detailing the axioms of propositional logic? All mathematics can be derived (sooner or later) from these, so we could use that as a basis for this entire operation. I have a 1300-page document sitting on my computer which is an attempt to do just this (it just needs a lot of work to make it web-friendly and wikified).

Having done that, it would be an interesting idea to make sure that every result uses as its basis an existing result, all the way back to these axioms, and we may even be able to create a dependency tree (okay it won't be a "tree" as such, it will have more than one path for most of the proofs, but you see what I mean).

Having done that, we can then make an attempt to rigorously identify which proofs rely upon, for example, the Axiom of Choice and (if we're really ambitious) upon the Law of Excluded Middle.

Category change
What does everyone think about moving the Category Categories to be Proofs, and create a new Category Definitions and and a new one Axioms, then inside Categories, put Proofs,Definitons, and Axoims. I think It'll allow for better organization, all we'll have to do is fix the categories that are now part of Categories to be instead in Proofs. What do you think? --Joe 23:01, 22 July 2008 (UTC)

I've given you something to work on
I've added the definition "Set" and basic pages stating the Zermelo-Fraenckel Axioms are in place.

I have not been able to appropriately set the category of "Set" - can I leave that up to an admin guy?

--Matt Westwood 06:35, 23 July 2008 (UTC)

What category do you want it set to? It shows as belonging to Category: Definitions Should it in something else? --cynic 00:59, 24 July 2008 (UTC)

Oops
I've just realised that I've been consistently spelling Zermelo-Fraenkel wrong. There's no c in Fraenkel.

Would it be worth setting up a page for "errata"? I'm notorious (in certain circles) for making mistakes.

Done, see Proofwiki.org:Errata--cynic 00:59, 24 July 2008 (UTC)

namespace problem
The problem with adding "Definition" or "Proof" in front of the namespace of each entry, is that when you look in the proof index or category index, they all end up under "D" or "P". See what's happened with the "Definitions" category.

Would it be possible for the namespace to be just (for example) "Empty Set" and for the category to be assigned automatically and invisibly?

Or if that can't be managed, put the category (Def/Axiom/Proof) at the end?

I don't think that's doable, but Joe might be able to mess with the settings to hide the namespace for indexing. Don't spend to much time on it though. On a side note, don't put proofs: in front of the proofs, they automatically go into the main namespace, which is where they belong.--cynic 00:59, 24 July 2008 (UTC)

Symbol definition
Would it be a good idea to set up a special page for symbols? We "all know" what $$+, -, \times, =$$ etc. mean, but when we get into the technical details of things like $$\nabla, \varnothing$$ and so on, it would be sweet to have a quickly-accessed glossary page defining all the symbols.

--Matt Westwood 06:31, 24 July 2008 (UTC)

Illogical, Captain
I have set up a page "Definition:Logic" and also tried to set up "Logic" as a category, but I must have done that wrong because it said it entered it in "Category::Category" so I hope I haven't given you too much of a headache to sort out.

No apologies for the number of (seemingly trivial) entries in "Definitions", there is madness to my method.

--Matt Westwood 18:43, 25 July 2008 (UTC)

Hey, I deleted the logic category for now, trying to keep all definitions for now under category definitions. If it gets to the point where we need to organize definitions, then something will have to be thought up, since we can't confuse the categories for proofs and definitions.--Joe 18:51, 25 July 2008 (UTC)

Definitions stuff
I've yet to figure out how to get rid of the namespaces from the definitions category. But I do know how to get it to sort differently, when you add the page to the category do as follows:

If definition is graph, then the box would be

Categories:Definitions|graph this will will give the page a sort key of 'graph', so it will be under G in the categories page. Hope this works/makes sence --Joe 20:26, 25 July 2008 (UTC)

Hmm ... not sure it does (or I'm doing it wrong)
The way I add a new page is to enter its name into the "Search" box and hit "Go" and it will ask me whether to start that new page it can't find. I've studied the docs and I can't figger out how else to start a new page.

But when I enter, for example, "Categories:Definitions|Wibble" and press "go" it won't give me that option of generating the page. Suggestions as to how to go about starting a new page? Or the link that tells me how?

I'll carry on doing what I'm doing at the moment to keep the ball rolling ...

--Matt Westwood 20:59, 25 July 2008 (UTC)

that's how you create a page, but when you put assign it a category, you have to add the | The page name Will still have Definition in front, but on the category page, it will be organzied by what comes after the |.

See this page for an example, and go to the Definitions category too see where its placed--Joe 21:24, 25 July 2008 (UTC)

Gotcha. Cooking with gas now.--Matt Westwood 22:53, 25 July 2008 (UTC)

Uppercase Greek
In LaTeX, uppercase Greek letters that are the same as Roman uppercase letters are not included in the standard language. With this in mind, it appears that some have been very kindly set up on this site.

However, they do not appear in the same format that the other uppercase letters are given in.

For example,

$$\Alpha$$ appears as $$\Alpha$$ (italics), but

$$\Gamma$$ (a LaTeX inclusion) appears as $$\Gamma$$ (no italics).

I believe that for consistency, it would be nice to have

$$\Alpha$$ specified as

$$\textrm{A}$$ which would then appear as $$\textrm{A}$$. There might be an argument for using

$$\mathrm{A}$$ - it looks basically the same: "$$\mathrm{A}$$" but I believe LaTeX treats it differently.

Proof the week
Proof of the week suggestions --Joe 15:59, 2 August 2008 (UTC)

I like this one:

http://proofwiki.org/wiki/There_exist_irrational_a_and_b_such_that_a%5Eb_is_rational

--Matt Westwood 17:06, 2 August 2008 (UTC)

Any suggestions for this coming proof of the week? --Joe 15:33, 9 August 2008 (UTC)

Boy, have you guys got stability problems
I've tried 5 times now to upload the final proof on the Conjunction and Implication page, but it keeps 404'ing on me.

Is there a page size limit? (in which case we have real big problems when it comes to FLT) - or is it just the time of day or something (see time on autosig)?--Matt Westwood 07:43, 3 August 2008 (UTC)

Update: Finally got this to work, but as I say, it took several attempts.

Rats - it's done it to me again! That's 40 minutes of my life I'm never going to get back!

Yes I know I ought to write the entire proof in a separate text editor and copy and paste it in, but that's not the point.--Matt Westwood 18:26, 4 August 2008 (UTC)

I haven't experienced the problem, and the server seems to be working fine. What if you try using the Show preview button, maybe that will help. At least then TeX will be rendered and saved to the site. Might help to decrease upload times when you save a page. I'll try uploading some large things to the sandbox, and see if I encounter and problems--Joe 18:29, 4 August 2008 (UTC)

Yes, that's what I have been doing. Gives me "This page can not be found" or whatever variant. Pressing the "refresh" button gives me a blank text editor. Pressing "back" has a similar effect. The prudent man would control-c the entire posting into his clipboard before pressing those pesky buttons - but sometimes I forget ...--Matt Westwood 19:31, 4 August 2008 (UTC)

Anyway, when you have pressed "Show preview" and seen it looks good, and for the fifty-eighth time in ten microseconds the browser has crashed on you when you press "Save page", how do you recover your edits?

If your browser crashes, there's probably not much you can do. Maybe there could be something wrong with your browser or internet connection? I haven't experienced any problems, and I've check the sever and it doesn't appear to have had any downtime or problems. I recommend checking your browser logs to see why it crashed. --Joe 19:13, 5 August 2008 (UTC)

Hmm ... that's an idea ... I'll have to find out where those live. Such info isn't all that obvious. --Matt Westwood 20:29, 5 August 2008 (UTC)

What browser are you using? If it's firefox, just type about:crashes in the url bar. If it's not firefox, it should be. Try a different browser and see if it helps.--cynic 22:21, 5 August 2008 (UTC)

"If it's not firefox, it should be." It is now! Good call. I ought to have done that ages ago.--Matt Westwood 10:32, 10 August 2008 (UTC)

Update: The link's still iffy - the connection still sporadically resets and times out and so on, but Firefox seems a lot more tolerant of this and pressing "Retry" (sometimes more than once) is acceptably reliable.

I've made another mistake
I've just entered a page called "Definition:Compositon of Relations". Duh. Needs to be changed to "Composition".--Matt Westwood 21:22, 8 August 2008 (UTC)

No problem, all you have to do, select 'move', its a tab near the top. Then delete the page, using the 'delete' label. --Joe 21:36, 8 August 2008 (UTC)

Gotcha. Will do.--Matt Westwood 21:53, 8 August 2008 (UTC)

I've already moved that one for you! --Joe 22:05, 8 August 2008 (UTC)

Been moving some pages around, I've left a few redundant redirects. Haven't been able to find out how to use the 'delete' label. Can you help? --Matt Westwood 07:10, 16 August 2008 (UTC)

What I usually do is go back to the page you moved, and delete that one, then the redirect is no more and that old page is no more. That's what I do, seems to be working so far. --Joe 02:22, 17 August 2008 (UTC)

Yes, that's what I assumed, but as I say, when I'm in that page I can't find an obvious button that gives you a 'delete' option for the page. There's no 'delete' label that you mentioned above. Or do you mean, just remove all content for that page and it will, like, magically vanish?

So I looked it up and apparently only sysops can delete, and since your helping so much with the site, and have a very good feel for where it should be going I'll give you sysop. It'll allow you to edit the main page and other protected pages a well. --Joe 16:25, 17 August 2008 (UTC)

Thx m8, I thought it might be something like that. I will try not to abuse my privs. --Matt Westwood 16:59, 17 August 2008 (UTC)

Small proofs
During the course of establishing a definition, I find it is sometimes a good idea to include on that page some obvious, small proofs which are probably not worth setting up as full-blown pages in their own right. See what I've done, for example, on the page defining reflexivity.

What's the general consensus on this one? Should we enter a fresh page for these simple proofs or would it be better to keep them next to where the definitions are?--Matt Westwood 11:15, 10 August 2008 (UTC)

I would say if it is a proof we might as well make a new page for it. --Joe 14:41, 10 August 2008 (UTC)

Okay no problem - just didn't want to litter the DB with fragments. --Matt Westwood 15:14, 10 August 2008 (UTC)

Another idea
So you're posting up one of your favourite proofs, and the reasoning behind one of the steps escapes you. It was obvious to you once, but no, age takes its toll, it's gone. So you leave a gap in the proof that someone else has the opportunity of doing something about.

Would it be a good idea to have an icon similar to "Stub" or "Proofread" whose meaning is something like "Help finish off"? --Matt Westwood 22:04, 12 August 2008 (UTC)

I was thinking something along those lines, how about something like a clarification ( for lack of a better word), so that people can help fill in things that need clarifying. So I think this is what you were saying, it would be for pages that are done, but for help with steps that need a better explanation? --Joe 22:07, 12 August 2008 (UTC)

That would do, something along those lines. --Matt Westwood 05:51, 13 August 2008 (UTC)

Arrays
My favoured technique for displaying arrays:

\begin{array}{ccc} a_{11} & a_{12} & a {13} \\ a_{21} & a_{22} & a {23} \\ a_{31} & a_{32} & a {33} \\ \end{array} ... doesn't appear to work on this site. How do we do arrays then?

I'm not sure what to do, I'll look into it and try to figure something out. --Joe 20:28, 17 August 2008 (UTC)

Check out this page, it shows all of the features/commands that we have available. Plus it shows how can we align equations without having to use tables. This should make this a lot nicer and clean up some of the mess.
 * http://meta.wikimedia.org /wiki/Help:Formula#Fractions.2C_matrices.2C_multilines

--Joe 20:42, 17 August 2008 (UTC)

If you think that they might be useful to people let me know, or if you want add them to the list of commands below the editing window, its located at mediawiki:edittools --Joe 20:47, 17 August 2008 (UTC)

I've just noticed that some of these things work and others don't. I'll keep looking into it! I didn't realize it but \begin(array) is in the list of things that is supposed to work. --Joe 20:58, 17 August 2008 (UTC)

Sheesh man that is *well* wicked! If only everything worked ... Quite a few things, as you say, don't. "stackrel" is another one I've tried to get to work but gave up on and used a different notational style instead.

How easy is it to add our own amendments? I have several pet ones in my local document area: \tuple{x,y} for \left({x, y}\right), \set{x, y} for \left\{{x, y}\right\}, \ifthen for \Longrightarrow, \bbX for \mathbb{X} and so on. --Matt Westwood 21:16, 17 August 2008 (UTC)

Hmm ... just tried to use "cases" and I got: "Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert)" ... which is promising, it appears that it *is* supported but needs some tweaking. That sort of thing (installation details of this package) is out of my immediate area of expertise, unfortunately. --Matt Westwood 21:21, 17 August 2008 (UTC)

Cases seems to be working for me, what did you try? I'm still trying to figure out why we can't access some functions. --Joe 01:27, 18 August 2008 (UTC)

Aha! So it is for me Definition:Union Relation. It was "\end {cases}" that was throwing it. Should have been "\end{cases}". I suspect that rogue spaces may be the cause of other problems I've had as well. --Matt Westwood 18:26, 18 August 2008 (UTC)

A question about categories
When entering a proof concerned with, say, Relations, one enters it into the category "Relations" which is a sub-category of "Set Theory". A suggestion has been made that we also add it into the "Set Theory" category as well, so that it appears in the global category as well as in the sub-category. (See the discussion in "Union is Associative" proof.) My view is that we ought not to need to add it into "Set Theory" as well (it means a lot more work and a more cluttered appearance to the Set Theory category page. Is it appropriate to ask for a ruling (or even a vote)? --Matt Westwood 21:03, 19 August 2008 (UTC)

I agree, I don't think that we should have it in both categories. Like you said, there's no point clutter. --Joe 21:04, 19 August 2008 (UTC)

What does everyone else think? --Joe 21:09, 19 August 2008 (UTC)

I'll agree to it as well. While we certainly shouldn't aim to copy everything Wikipedia does, I just did a check and they do not include such articles in both categories. At least we know that such a policy isn't unheard of, right? --RickettsAM 21:20, 19 August 2008 (UTC)

Sorry, I've been hogging it ...
I apologise for having carpet-bombed this site with what looks like hundreds (literally) of "trivial" (and some not-so-trivial) proofs which all seem a bit mundane. There is method in my madness. I am working towards an axiomatic definition of the natural numbers. To do that I am making sure that the chain of reasoning is rock-solid. (Work is still in progress.)

Might it be worth putting a sub-category together to hold all this "scaffolding" which is in danger of obscuring the "real" proofs that this site looks as though it is going to be the best in the world at?

It's awesome that you've been doing some much work, keep it up! What do you have in mind for the new sub-category idea? It sounds it might be a good. --Joe 14:45, 23 August 2008 (UTC)

Difficult question. I wonder whether we can have a sort of a loose "importance" hierarchy: "theorems", "lemmas", "results", the latter being things like the majority of what I've been adding in support of the major important theorems and stuff. And even a level more important than mere theorems, namely, named theorems.

Wonderful opportunity to have stimulating discussions as to which level to put which entries ... "No! You can't put FLT into the lemma category!" and so on.

Also I think we might want to categorise the definitions, it's beginning to look a little unwieldy.

Just something to think about before we get too far down the road ... but then it's something we can take our time looking at before making an arbitrary decision. --Matt Westwood 18:11, 23 August 2008 (UTC)

I've added a new category: "Named Theorems". I've been using it to put: a) Theorems and results named after particular people (e.g. "Cantor's Theorem" - contender for POTW?) and also b) theorems and results which have specific names, e.g. "Quotient Theorem for Sets" and so on. --Matt Westwood 11:32, 24 August 2008 (UTC)

Good idea! --Joe 14:04, 24 August 2008 (UTC)

Page naming and page redirection
For pages that have multiple names, do you think we should still leave the old page's there and just redirect them to the new one? --Joe 21:27, 24 August 2008 (UTC)

I think we should follow the Wikipedia approach to page redirection.


 * Allow access in the case that a pagename is provided:
 * which is an alternative term for the subject
 * which is a term for a subtopic (in this case one may use a redirect to a section)
 * which uses alternative capitalization and hyphenation
 * which uses alternative spelling
 * which has a common misspelling
 * Provide a way of conveniently going to a page (shortcut).
 * Keep links to a page active after it has been moved (even if internal links are updated, this still applies for links from outside).

I agree, since that works well and it is what people will expect of a wiki. Is there some way to make it automatically check alternate capitalizations so we don't end up with two versions of the same theorem the way we did with the Squeeze Theorem? If not, I propose that all theorems have the first letter of every word in the title (other than prepositions, articles, and the like) capitalized to avoid confusion.--cynic 16:48, 27 August 2008 (UTC)

Okay, I agree lets do that. I'll check and see if there is a way to see if a page has already been named.--Joe 17:12, 27 August 2008 (UTC)

I'm all up for renaming a page and deleting the original one if (a) the original page name was misleading or mis-spelled or inaccurate in any way and (b) the page is still pretty new and part of a field of maths which is still being expounded on this site.--Matt Westwood 17:50, 30 August 2008 (UTC)

I agree, pages should only be deleted if the name is wrong/misleading, or in an incorrect namespace. --Joe 17:53, 30 August 2008 (UTC)

Progress so far ...
Just a note to explain a bit about where I'm going and where I've been ...

I haven't gone near formal languages, so the work on propositional logic is not as 100% rigorous as it might have been.

I still have to work out how I'm going to approach predicate logic. The most important omission so far are the laws regarding the usage of "for all" and "there exists", references to a couple of the (so far non-existent) results are still outstanding.

I've put down as much basic Set Theory as I'm likely to, including basic truths about relations and mappings.

I'm hacking my way through abstract algebra at the moment, trying to rationalise some of the basics before I get into rings and ideals.

Next on my list of things to do:
 * Cartesian products in the context of algebraic structures
 * Homomorphisms
 * The embedding theorem
 * Inverse Completions
 * Groups and rings (very basic stuff at this stage)
 * Factorisation in integral domains
 * Fields
 * Ordered structures

Then it's number systems:
 * Naturally Ordered Semigroups
 * The creation of the set of natural numbers from what-all's gone before
 * Introduction to the difference between finite and infinite
 * Sequences
 * Integers
 * Rationals

... and that's about as far as I go on "basics", although I may try and introduce the real number system if I don't get too bogged down in Cauchy sequences.

Later on I plan on doing some introductory results for modules, vector spaces and ideals (all of which were outside any of my formal training so I may be on dodgy ground).

Then there the results which give a formal justification for calculus.

Once I've done all that I may well take a short break ... --Matt Westwood 19:25, 30 August 2008 (UTC)