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
Any suggestions on what our next proof of the week should be? --Joe 23:16, 26 July 2008 (UTC)

Dunno ... it's so difficult to top that Pythagoras proof for elegance, simplicity and memorability. I'd offer up a few myself but I want to get the field of PropLog sorted out first (I'm still on the pesky definitions).--Matt Westwood 23:24, 26 July 2008 (UTC)

Well, I'm partial to the Law of Cosines, since its short and sweet, and is kind of a logical followup. Alternatively, we if we can upload .sfw (flash) files and display them, we could use a flash I borrowed from the USAMTS website (http://www.usamts.org/Gallery/G_Gallery.php). As long as we credit them, it's probably okay. My favorite is the sum of the first n odd natural numbers one, but if others like the idea and prefer one of the other proofs, I can download another easily enough. I don't know if the site even supports flash, but we could try.--cynic 02:41, 27 July 2008 (UTC)

Ok, I'll put up Law of Cosines for now, should we start our week or Sunday or Monday? --Joe 02:54, 27 July 2008 (UTC)

Doesn't matter, as long as we're consistent.--cynic 02:57, 27 July 2008 (UTC)

Okay, I'll go Sunday