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.

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)

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.

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)

LaTex and other things
LaTeX is finally fixed! Our host had to recompile the program which creates the LaTeX png's so that they are supported. The reason the site was down for a while is because I had no idea where the problem was coming from and it took me several days to figure it out. I noticed that while LaTeX was broken several pages wouldn't load, and would just give a blank white screen. My guess that this was caused by the large number of LaTeX errors on each page, if you notice any pages are like this please let me know.--Joe 18:38, 8 September 2008 (UTC)

Time Zones
Just curious, where do you guys live? Mostly, I'm curious on the time zones based on when you post the most. I'm in Maryland (Eastern Daylight time now, GMT-4:00). --cynic 01:16, 10 September 2008 (UTC)

I'm in Newfoundland, Canada (-3:30,Newfoundland Standard Time(NST)), we have our own time zone! --Joe 02:06, 10 September 2008 (UTC)

I live in California (Pacific Standard Time). --Spoon737 06:21, 10 September 2008 (UTC)

UK - currently UTC + 1 but we'll be at UTC at end of October.--Matt Westwood 06:33, 10 September 2008 (UTC)

nowiki creep
Have you noticed that when you repeatedly edit a page with instances of "nowiki" in it, it adds a line feed before each one? So they creep further down the page and eventually you have to edit the page again to remove the spurious line feeds. Wonder what causes that?

I have noticed that! Happens on wikipedia also, not sure of the cause. It would be nice to know though, I sparsely looked into it, but didn't try too hard, I may have a deeper look this time. Anybody else out there know why this happens? --Joe 23:38, 10 September 2008 (UTC)

Proof of the week suggestion
Anybody have a suggestion? --Joe 21:49, 13 September 2008 (UTC)

Cantor-Bernstein-Schroeder Theorem? --Matt Westwood 22:10, 13 September 2008 (UTC)

Sounds good to me. --Joe 22:31, 13 September 2008 (UTC)

More LaTeX problems
I've noticed that $$\left({R, \circ}\right)$$ is (fairly consistently) not being translated. Same seems to be applying to $$\left({R, *, \circ}\right)$$, which is putting a bit of a crimp on my work on rings. Strangely enough, $$\left({R, +, \circ}\right)$$ seems to be okay. --Matt Westwood 06:39, 16 September 2008 (UTC)

How do you mean not being translated? --Joe 11:47, 16 September 2008 (UTC)

It was appearing as \left({R, \circ}\right) but it must be a function of my machine at home. The one I'm using at work doesn't exhibit the problem. I'll investigate again when I get home.

Try clearing the cache. --Joe 14:50, 16 September 2008 (UTC)

That did the trick. Thx. --Matt Westwood 17:36, 16 September 2008 (UTC)

Are namespaces too complicated?
We currently have to enter definitions with the namespace "Definition:Somedef" and enter them into the "categories" field at the bottom as "Definitions|Somedef".

Having made a couple of fleeting mistakes and completely forgotten to put the "Definition:" bit at the front, and noticed that it seems to work perfectly well without it, I wonder whether it's worth having to have that "Definition:" bit at the front at all.

Same would apply to "Axioms". As long as the entry is in the correct category, specifying its category in its name seems like a bit of overkill (and certainly makes for a lot of extra work).

If we did away with "Definition:" before each def it would mean a fair bit of manic hacking for a bit (there's thick-end of 300 definitions at the moment) but it would make the dictionary look that much cleaner.

If you're okay with this I can get on and start work tidying them all up today ...

If we did away with the definition namespace,it might be tricky to tell how many proofs, since they will be sharing a namespace. We would still be stuck having to add the category either way, although I am working on a bot that can automatically do this. I do agree that it's a lot of work though having the namespace there. What do others think. It's not hard to take the namespace out, provided we'll have to speed a lot of time reorgainzing. We'll have to find a new way to count the proofs though. --Joe 20:08, 16 September 2008 (UTC)

Obviously the definitions would all still be in the "Definitions" category, they just wouldn't have the "Definition:" bit at the beginning.

Would it be possible to count all the entries, then subtract the count of all those in the "Definitions" and "Axioms" categories? Or doesn't it work as smartly as that?

We should be able to figure out something for that. One other question, what will we do if a defn has the same name as a proof? --Joe 20:40, 16 September 2008 (UTC)

My guess would be: in that case either the defn or the proof needs to be renamed, or if the subject matter is in the same area of mathematics, the defn could be merged with whatever is being proved about it that causes it to have the same name as its proof.

Take for example Null Ring in which its definition is in the same page as the proof that it is a ring. If, like this, the existence or method of construction of the thing being defined relies upon a proof, then that to me seems appropriate. I believe that there may well not be any existing instances of the same name being used for both.--Matt Westwood 20:46, 16 September 2008 (UTC)

Okay, I'm fine with getting rid of the the Definition namespace, but it'll be a lot of work, all of the proof pages as well as the help page will have to be updated! --Joe 21:00, 16 September 2008 (UTC)

Right, I'll get on with the definitions and proof pages, over to you for the rest ... ;-)

Okay, I'll leave the namespace intact until we get everything changed over. An I'll put a notice on the main page letting people know. --Joe 21:19, 16 September 2008 (UTC)