Talk:Set Equation: Union

I don't know if pages like this are allowed.

I wanted to stop in case it was a waste of time.

Please give me a heads up so I can put it in my user pages before it's deleted.

--Jshflynn (talk) 23:04, 6 October 2012 (UTC)

It's something which needs to be thought through. It would be easy to plaster up a colossal quantity of examples of equations and their solutions in all areas of mathematics without any consideration of the structure of the categories to hold them, and that could cause existing categories to clog up with examples to the detriment of the basic results.

How to structure categories for examples is something I haven't spent much time thinking of (mainly because I have things to do that are of higher priority: others show more keenness to start setting up categories for "examples") except that I believe they should be separate from the existing "definition" and "proof" spaces.

On an unrelated note, you might want to examine the format of the page you have generated here, and compare it to that of any other page on the wiki, and amend it to make it match in style. One of the things for which this site has been commended (there aren't many, published reviews of ProofWiki generally sneer at it) is that its format is uniform and its look-and-feel are of a high quality. If that's the main thing we're good at, then that's what I want to make sure is maintained. --prime mover (talk) 05:28, 7 October 2012 (UTC)

I understand. Every page should really being saying something. I felt uncomfortable posting some pages on B-Algebras for that reason. I intended to use these results to study "systems of set equations". I think it would be best if I developed any little niche of interest I have in my user space before I put it with the main body of results. So feel free to remove this page.

And yes, I am one huge appreciator of the internal consistency of this site so I will heed those words of yours in the future.

Oh and about "examples". Formally, what is an example really? All examples of X mandate justification that they actually are examples of X and so would have an associated theorem. Perhaps it would be best to call the Example Space: "Example Subspace". 8) --Jshflynn (talk) 21:48, 7 October 2012 (UTC)

"What is an example really?" I found myself asking that as a philosophical question while typing the above earlier, and I can't come up with a rigorous definition. Best I can come up with is: an example is a result with no applications. I don't know. What I've been doing is posting up published results on the grounds that the contexts they appear in can be picked up from the text. And in those circs, the "examples" are sometimes useful results and sometimes "exercises" which have no general use beyond their ability to exercise the definitions. Are instances of order $n$ groups "examples", for example? Or are they just part of the larger theorem that details all finite groups?

I don't like either "Example Space" or "Example Subspace" because there are already mathematical terms called "Space" and "Subspace" - what confusion! You really want to go there? --prime mover (talk) 22:10, 7 October 2012 (UTC)

In my opinion an example is a theorem of the form: $$\vdash X \in Y$$ Instinctively, one urges to add sections on the motivation for a concept, finite examples, applications but that's not what ProofWiki's about. It's very difficult to know to do. One example I picked up on by just browsing the other day was the string of theorems: Identity of Group is Unique coming from Identity of Monoid is Unique coming from Identity is Unique. Having all 3 is good in some respects and undesirable in another.

Striking a balance between cluttering redundancy and comprehensive accessibility will be an unending struggle for the editors here. I will follow by example (see what I did there :D ). --Jshflynn (talk) 22:42, 7 October 2012 (UTC)

What was helpful to me was the distinction between a class of examples (like "Permutation groups $S_n$) and actual examples (like $S_{20}$). You probably noticed my activities in the category theory section, where I tend to get cluttered every time with a bunch of examples, which intuitively are clear but need formal backing. I encourage some sort of a brainstorm session to determine how to process examples in general; it will be an important part of the site, so we'd better think it through thoroughly in advance. --Lord_Farin (talk) 07:33, 8 October 2012 (UTC)