Talk:Reflexive Closure is Idempotent

May I suggest this be a subpage of your proof that reflexive closure is a closure operator? It's a lemma.... Lord_Farin, however, will be able to tell for sure. --Dfeuer (talk) 07:51, 5 March 2013 (UTC)


 * Perhaps I'm not seeing what you're seeing. I think it already is. --Jshflynn (talk) 07:53, 5 March 2013 (UTC)


 * I don't see the need to rid this page from its descriptive name. I do see the need to bring the notation in line on this page and its direct family. &mdash; Lord_Farin (talk) 07:55, 5 March 2013 (UTC)


 * I also do see the need to refrain from transcluding it if it's not a subpage, because otherwise we have the stupid QED spacing problem. --Dfeuer (talk) 08:01, 5 March 2013 (UTC)


 * Are you suggesting to replace it with links or to move the argument? I can see the former happen, the latter is not appealing to me. Too many times I've struggled to nicely present some commonly used pieces of mathematics (i.e., not repeating ad nauseam). Just remember that one can hack around it with the $\LaTeX$ commands  $\Box$ and   $\blacksquare$. Alternatively, place the qed invocation on the same line as the transclusion call. &mdash; Lord_Farin (talk) 08:10, 5 March 2013 (UTC)


 * I didn't know about those hacks. Nice trick. I had thought it should just be a link. As for why I don't really like it and all its brothers and sisters being independent pages: I have already put up proofs that reflexive and transitive closures are closure operators using a very different technique. I don't really want to have to add a second proof to each of these .... --Dfeuer (talk) 08:17, 5 March 2013 (UTC)


 * Correct me if I'm wrong but I think you are saying: "I don't really want to do a Reflexive Closure is Closure Operator/Proof 2 style proof for Transitive Closure is Closure Operator". If that's the case then I will have a go of doing it. --Jshflynn (talk) 08:22, 5 March 2013 (UTC)


 * We're not in a hurry. Nobody is forcing you to do only boring stuff :). I see where you're coming from not longing for adding many a fortiori proofs, but there is no harm in having this set-up. &mdash; Lord_Farin (talk) 08:25, 5 March 2013 (UTC)


 * No, Jshflynn, that's not what I was saying. What I'm saying is that there should be a second proof of Reflexive Closure is Order Preserving that invokes my proof of Reflexive Closure is Closure Operator. I'll let Lord_Farin's ruling stand without argument. Side note to Lord_Farin: I am starting to disagree with you on increasing vs. order-preserving in the special case of closure operators. Using the word increasing makes all three properties start with the letter 'I', which I for one find mnemonically helpful. --Dfeuer (talk) 08:34, 5 March 2013 (UTC)

Hm, this mnemonic is indeed appealing. Oh well, feel free to change it. On the page considering the general ordering it isn't necessary to stress the order perspective anyway. It is a fortunate synergy from different sources that we have found these terms (since "inflationary" was something else at first on the closure operator page). Almost as if all these discussions could have some value for the casual reader :). &mdash; Lord_Farin (talk) 08:44, 5 March 2013 (UTC)


 * Absolutely no need for any action on this page. The only issue I do have is with Reflexive Closure is Closure Operator/Proof 2 where transcluding the subproofs is a structural direction which is contrary to the structure of proofs that has been developed so far. Similar pages merely provide a link to the proof itself: "Idempotence follows from Reflexive Closure is Idempotent" and leave it at that. By insisting on the full transclusion of the page, complete with having to manage the structural complexity that ensures that the correct part gets included, along with the rest of the baggage that goes with this style of presentation (e.g. fussing and faffing over renaming the page) is contrary to the site philosophy. --prime mover (talk) 08:52, 5 March 2013 (UTC)


 * From the eyes of an outside user I would say it is easier to read Reflexive Closure is Closure Operator/Proof 2 with all the pages transcluded in it as opposed to being presented with 3 "follows directly from" lines. That is just my opinion. --Jshflynn (talk) 09:02, 5 March 2013 (UTC)


 * We will leave well alone on the grounds that this page is visually appealing as it is. Once the concept beds in of presenting such a page in this form, we may want to experiment with trying it out on other pages which are composed of proofs like this. The Fundamental Thingy of Partitions or Equivalence Relations has been done similarly, IIRC. --prime mover (talk) 21:34, 6 March 2013 (UTC)