User talk:Dfeuer

Welcome
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Cheers!


 * --Your friendly ProofWiki WelcomeBot 16:40, 29 November 2012 (UTC)

BPIT
I note that you're enthusiastically banging in the BPIT template all over the place in pages which in several cases already have AoC etc. templates in them. I have reservations about this for several reasons:

a) It has not completely been established exactly what BPIT actually is. Yes, there is a partial proof in place, but it might or might not work, but at the moment it is unfinished and, ultimately, incomprehensible because we don't even know what a prime ideal is yet.

b) Places where the BPIT already exists do not indicate exactly where it is used, and why it is relevant, and what the point is. If you look at existing pages using AoC (where the work has been done properly, of ocurse) you will see that there is a specific point in the proof where it is invoked, or if not, in the use of the template there is an indication of which result in that proof does use the AoC (e.g. "... by Zorn's Lemma" etc.). The BPIT work does not.

c) Even when we have sorted all that out, the philosophical significance of BPIT remains obscure. It's couched in technical language about a collection of objects that need considerable work to understand, and even when you do understand them all, it's like: so what? The AoC is a short, pithy fact that can be put into a single sentence's thought and therefore means something. The BPIT in consequence just looks like something clever-sounding that we read off the internet and include because it makes us look smart. Personally I don't think it *does* make us look smart.

Thoughts? --prime mover (talk) 06:24, 14 December 2012 (UTC)


 * Most set theory is pretty strange, but the set theorists keep making it anyway. The Boolean Prime Ideal Theorem is really no stranger than Zorn's Lemma. It apparently has several forms, some of them simpler than the one I started the page on, which all turn out to be equivalent (somehow), the simplest of which that I've seen is the Ultrafilter Lemma. It appears to have been studied extensively at least since the 1960s (and the Ultrafilter Lemma since the 50s), so there's plenty of source material out there—it's not some new experimental axiom that only a handful of specialists have heard of. Personally, I enjoy how it's helping me explore set theory some more to try to understand why different bits relate to each other in certain ways. I don't see how acknowledging on a page that a proof from weaker principles is possible and we'd like to have one makes us look stupid. As long as ProofWiki is a work in progress and not a finished product to be shown off in a library that seems fine to me. --Dfeuer (talk) 07:45, 14 December 2012 (UTC)


 * It would be a good idea to at least indicate that we are still looking for proofs from e.g. BPIT. This can be accomplished by amending the template. Upon establishing more relevant context for the BPIT it will be torn out of obscurity; and if not, there's always the statement that it is a consequence of AC so that any willingly ignorant visitor can content himself with accepting AC and not bothering. For the interested visitor, who may be pleased by accepting a varied assortment of axioms these sections contain valuable and interesting information. There should be more rather than less, IMHO. --Lord_Farin (talk) 12:14, 14 December 2012 (UTC)


 * What might be useful is a "overview" page like we have for, for example, Definition:Separation Axioms in which the various axioms and their relative strengths are presented and explained briefly. Extracting that brevity may be a challenge. In the meantime I recommend we complete the train of thought which goes towards the proof of BPIT (including the definition of the various objects - Prime Ideal comes to mind) and make an attempt to justify the claims that are made in its name. Finally, there are various pages which state "This theorem depends on BPIT" without any indication as to which particular point in the proof it is needed. IMO this is of paramount importance.


 * Demonstrations of relative strength and weakness of the axioms should ultimately be illustrated by examples of objects / constructs which are satisfied by one axiom but not another, proving that while A --> B there are objects that are B but not A. Again, this will be challenging, but should ultimately just be a literature search.


 * I understand the drive to raise the reader's awareness of these things - they fit into the strategy of where we want ProofWiki to go - but without making a solid attempt to justify the underlying foundations there's a danger of the information on this site becoming disconnected. In the extreme would fall into danger of becoming an alternative wikipedia - a conglomeration of cherry-picked interesting / important / noteworthy theorems with no solid underpinning. --prime mover (talk) 14:23, 14 December 2012 (UTC)

Page deletion
For the record if you want a page deleted, please invoke the "delete" template. --prime mover (talk) 09:16, 16 December 2012 (UTC)

Thank you
Thank you for recovering my extension of the Schur's Theorem (Ramsey Theory). That was very nice of you, and skillful!

BTW, why can't one edit a fragment only, why this necessity of editing the totality of the text?! It's ridiculous. Can it be true?!

Best regards, Wlod (talk) 02:27, 26 December 2012 (UTC)


 * I refer you to Help:FAQ --prime mover (talk) 09:41, 26 December 2012 (UTC)

Supremum of Suprema
I replaced your work with essentially a new page. This was easier for me at this hour of the day than the tedium of rewriting your sentences. No offence intended - it was simply quicker. --Lord_Farin (talk) 23:31, 2 January 2013 (UTC)


 * I don't generally mind, but could you explain what made mine so horribly awful that it needed such treatment? Also, I'm not a big fan of mathbb for general purposes (it tends to make me think some "standard" set like $\mathbb C$ is intended. Would you mind switching to mathcal or mathscr? --Dfeuer (talk) 23:36, 2 January 2013 (UTC)


 * Nothing wrong with mathbb. It looks a lot better than mathscr, which is nearly as bad as fraktur for impracticality. Reverted to mathbb. There is a precedent - several pages already use mathbb for subsets of the power set of a set. --prime mover (talk) 06:17, 3 January 2013 (UTC)


 * Would you mind if I switched it to mathcal? --Dfeuer (talk) 06:22, 3 January 2013 (UTC)


 * I tried mathcal but $\mathcal T$ is too similar to $T$. --prime mover (talk) 06:26, 3 January 2013 (UTC)


 * Changed to mathscr per suggestion. Changed it because I felt uncomfortable with the choice of letters and other symbols, and the amount of detail skipped. On a different time of day I might have simply tidied your version. Nothing special. --Lord_Farin (talk) 23:50, 2 January 2013 (UTC)


 * Thanks --Dfeuer (talk) 23:45, 2 January 2013 (UTC)


 * Unrelatedly, we need infimum of infima, and we need right distributive implies left distributive, and all results about ideals and prime ideals in ordered sets need their duals for filters and ultrafilters in ordered sets (which are related to, but not the same as, filters and ultrafilters on sets, and blah blah. There's got to be some way to deal with these duals without duplicating all the text and then struggling to keep them matched s they're edited. Even the cop-out approach of having a proof do little more than link to another strikes me as more practical.—Dfeuer (talk)


 * This stuff is pretty high on my wish list for new schemes. I have a feeling that we can do little more than put up both results because they may arise in very different contexts. If you have ideas on this I'd be very eager to hear about them - don't worry too much about practicality at this point. --Lord_Farin (talk) 23:49, 2 January 2013 (UTC)


 * Well, I already mentioned the impractical option of writing these theorems as templates parametrized by the relevant sensitive words, but I suspect that would lead to much confusion. --Dfeuer (talk) 23:52, 2 January 2013 (UTC)

Category and links
I understand about your physical infirmities, and I appreciate the fact that the page Strictly Positive Integer Power Function Unbounded Above‎ is barely started yet, but as a matter of courtesy to other editors it is good to get into the habit of adding the category for every page you write, as you start it rather than as an afterthought at the end, and also, as you proceed through the writing of it, to link to each concept as you go. --prime mover (talk) 06:26, 3 January 2013 (UTC)


 * I don't have terrible physical infirmities, but I sometimes have technological ones, and sometimes I don't know the right category to put something into. --Dfeuer (talk) 06:27, 3 January 2013 (UTC)


 * If you don't know the category to put something into, then I suggest you explore to see what categories are available. If nothing else it will increase your familiarity with this site, and if you plan on sticking around it's more than just a good idea that you get to grips with how the site is structured - and indeed what is already up on the site. As for "technological restrictions", I suggest you get access to a computer with a decent sized screen and a proper keyboard. Then you'll be able to use accessibility tools to expand the size of the font so you'll be able to see it better. --prime mover (talk) 06:31, 3 January 2013 (UTC)

sandbox
It is suggested that work which is in process of being developed be done in your sandbox. This can be set up as the page User:Dfeuer/Sandbox. Only when your work is complete and you have a page which is presentable (by this meaning that the argument is complete) would it then be deployed to the wiki proper. (See User:GFauxPas/Sandbox for a model instance of how these things are used.)

This does not mean to say that a "stub" page should not go onto the wiki as a placeholder (this is perfectly acceptable practice), but so that a whole series of half-developed proofs do not clutter up the history page, and potentially confuse or irritate users of this site. Basically, it keeps it neater all round.

It would also be hoped that the links would also be complete by this time, and (dare I say it) the house style would be adhered to.

Please feel free to evaluate the above to determine whether it fits in with your own strategy for contribution towards this website. --prime mover (talk) 09:59, 3 January 2013 (UTC)


 * Notwithstanding the above (which contains valid nudges towards being a better contributor), it be mentioned that we highly value the time you devote to ProofWiki. --Lord_Farin (talk) 16:19, 3 January 2013 (UTC)


 * Thanks, Lord_Farin. I just created User:Dfeuer/Product of Positive Element by one Greater than One. Do you think you can check the math and suggest a better name? Or is this theorem already on ProofWiki somewhere I haven't found yet? --Dfeuer (talk) 16:23, 3 January 2013 (UTC)


 * Proof correct; a better (since more consistent with other pages) name may be "Product of Positive Element and Element Greater Than One". There is a lot of house style violation left on that page - you may want to try to sort that out yourself, though. --Lord_Farin (talk) 18:08, 3 January 2013 (UTC)


 * I did some tidying and moved it to the main space. Next up: User:Dfeuer/Strictly Positive Power of Element Greater than One Not Less than Element


 * Again, proof correct, style not so. Please try to tidy and add a tag before moving to main. --Lord_Farin (talk) 19:20, 3 January 2013 (UTC)

spambots
No, that's not what we do. We wait for one of them to do something illegal.I don't see why it would make you nervous. In the grand cosmic scheme of things it's a low-priority concern. Deleting someone's account just because they don't use it is fascism. --prime mover (talk) 06:06, 9 January 2013 (UTC)

Reflexive Reduction of Ordering
It would appear that we can do a better job than introducing $<$ as the reflexive reduction of $\le$ every time. I'm thinking along the lines of a definition for this concept specifically tailored to orderings. Maybe Definition:Strict Ordering of Ordering. --Lord_Farin (talk) 10:28, 9 January 2013 (UTC)


 * I'm open to suggestions. I've been trying hard to cut down on the boilerplate, but I may well have missed opportunities. The trouble is that whether you're basing it on a compatible relation or an ordering, you still need to invoke the theorem that the "strict ordering of ordering" or the "reflexive reduction of the relation" is compatible if the original relation/ordering is compatible. --Dfeuer (talk) 10:34, 9 January 2013 (UTC)


 * An alternative, of course, is to prove the ordered group theorems from preceding ordered group theorems, rather than from the compatible relation theorems. That's less boilerplate, but more actual repetition. --Dfeuer (talk) 10:35, 9 January 2013 (UTC)


 * It was accommodation to the reader's intuition ("... surely $<$ is the strict ordering corresponding to $\le$? Why don't they call it that?" which could easily lead to "This site sux, I'm outta here.") that made me propose this. Indeed, it does not resolve reference issues but it does allow to use one name for a concept. Such allows for reading and searching convenience. --Lord_Farin (talk) 10:41, 9 January 2013 (UTC)


 * Gotcha. I'll be glad to work on that, but I should have been asleep hours ago..... --Dfeuer (talk) 10:43, 9 January 2013 (UTC)

Congratulations
You've surpassed me in number of edits over the last thirty days. I think such hasn't occurred since I started to contribute significantly, approximately one year ago now. Keep it up :). On a side note, it'd be interesting to see how many characters a user contributed rather than how many edits. However, that metric is not available atm... Who knows what the future brings? --Lord_Farin (talk) 22:51, 9 January 2013 (UTC)


 * Thanks, Lord_Farin! I don't think it's the most meaningful metric, but I'll take what I can get! On the other hand, this use of the word "metric" doesn't match the mathematical one, so we should probably use another name. Measure, perhaps? --Dfeuer (talk) 04:44, 10 January 2013 (UTC)


 * The name "measur" doesn't match "the" mathematical one either. "Metric" is perfectly good, it's just a case where the word has tw separate meanings. I suggest that as this is an informal use of the term we do not atm add a disambiguation page. --prime mover (talk) 06:09, 10 January 2013 (UTC)


 * I do hope you realize I was joking. --Dfeuer (talk) 06:10, 10 January 2013 (UTC)


 * No I didn't. It wasn't obvious. --prime mover (talk) 11:20, 10 January 2013 (UTC)

New categories
You have enthusiastically created a bunch of new categories with associated definition categories. Two remarks on that:


 * I had intentionally put lattices and bounded lattices together because they have a huge overlap. Arguably that was a bad call on my part, so I've chosen to go with the way you organised things.
 * Putting e.g. Definition:Distributive Lattice only in the category Category:Definitions/Distributive Lattices is not the correct practice. You may note that many categories do not have an associated def category. This is because the def category is intended to be used for definitions specific to the notions the main category is about.

I may have more points occurring to me later, but that's it for now. --Lord_Farin (talk) 09:27, 10 January 2013 (UTC)

Please keep in mind prime.movers comment about creating virtually empty categories (especially definitions categories). Some of them may well be superfluous because there are no (well-known) concepts defined specifically for a certain structure. --Lord_Farin (talk) 11:20, 10 January 2013 (UTC)


 * I'll bear that in mind. It does seem likely sensible for definition categories. I guess I got a bit over-eager. --Dfeuer (talk) 11:24, 10 January 2013 (UTC)


 * Useful constructs around generation of categories are Template:Subcategory, Template:LinkToCategory, Template:CategDef, Template:DefsLink. I hope most of them have some explanation on the page. --Lord_Farin (talk) 11:26, 10 January 2013 (UTC)

On Definition:Distributive Lattice
I have finally found a quite satisfactory and good-looking approach. See Equivalence of Distributive Lattice Definitions as well. If you agree, I'll delete the pages on join and meet distributing (I've already flagged them for deletion). --Lord_Farin (talk) 16:13, 11 January 2013 (UTC)

double redirects
I have gone through and cleaned up all the double redirects except those from your own (and Lord_Farin's) pages - this is to alert you that you might want to sort them out. --prime mover (talk) 07:50, 17 January 2013 (UTC)


 * Argh! I've tried to fix those as I move pages. Sorry I've missed some. I hope there weren't too horribly many. --Dfeuer (talk) 07:51, 17 January 2013 (UTC)


 * You're all right, just a handful. You can find them via the "Special pages --> Double redirects". --prime mover (talk) 08:10, 17 January 2013 (UTC)

Sandbox
Could you take a look at the new section of User:Lord_Farin/Sandbox? Literature seems to distinguish between Boolean lattice and Boolean algebra (with resp. without ordering) and is mostly vague on the connection between the two. I posted a connecting definition at Definition:Boolean Lattice and want to verify that it is correct before proceeding further with the refactoring (and, incidentally, resuming with Givant/Halmos). TIA. --Lord_Farin (talk) 22:27, 17 January 2013 (UTC)
 * I can look at the math, but I can't tell you if the definitions are standard. If the only difference is whether or not you impose the natural ordering, that hardly seems worth worrying about. --Dfeuer (talk) 22:30, 17 January 2013 (UTC)
 * It's the math; your sentiment about the ordering seems to be bon ton among authors. --Lord_Farin (talk) 22:32, 17 January 2013 (UTC)
 * Incidentally, it provides a really nice way of recovering the lattice ordering (since neither distributivity nor complements are used in the proof). Might consider adding that to Definition:Lattice (and it's a quite nice conclusion of my pondering "what can we say of an ordering compatible with $\vee$?"). --Lord_Farin (talk) 22:34, 17 January 2013 (UTC)
 * I had some trouble figuring out what was going where. As soon as you have a semilattice you have two orderings. If you have two semilattices on the same set that obey the absorption laws, then if you label one a "join" and the other a "meet" semilattice, they induce the same ordering and you have a lattice. I thought we'd already dealt with how you recover the ordering...--Dfeuer (talk) 00:02, 18 January 2013 (UTC)

Category theory
You expressed contemptuous ignorance of category theory in a post to another contributor soon after your joining this project. Now you're making fundamental architectural changes based on your noticing the similarity between the words used to define two completely different concepts. Give over, already. Can you undo all the work you have done in this area? I really have better things to do with my time. --prime mover (talk) 06:12, 18 January 2013 (UTC)


 * Fundamental architectural changes? Most of what I did was put definitions of different kinds of isomorphisms into a category. I would frankly be astonished if I miscategorized more than three pages in total. I need to go to bed now. --Dfeuer (talk) 06:20, 18 January 2013 (UTC)


 * There's a good pageful of changes that relate to what you've done in this area. --prime mover (talk) 06:21, 18 January 2013 (UTC)

Categories
Please curb your enthusiasm for creating categories for entities until they have at least been defined - and preferably until there are enough things to go into them. Is there really a need for a category called "topological division rings"? --prime mover (talk) 06:01, 30 January 2013 (UTC)


 * Obviously, that category is unlikely to have many things in it that won't go in topological fields. But if we have topological fields and not topological division rings, then any stray topological division ring theorems will get stranded in the topological rings category, which is too general for them. One might argue, then, that we should instead drop the topological fields category instead of the topological division rings one. But then that's crazy. So I don't really know. I don't feel very strongly about it. What I am much more concerned about is that the Continuity category is structured upside down. There should really be a "continuous functions" category as a subcategory of both "analysis" and "continuous mappings", but instead all the continuous functions are in Continuity, and Continuous Mappings is a subcategory of that. --Dfeuer (talk) 06:09, 30 January 2013 (UTC)


 * Even so, my request stands. Please refrain from creating categories until there is a need for them.


 * "One might argue, then, that we should instead drop the topological fields category instead of the topological division rings one." Certainly - that sounds like an excellent idea. Drop them both, till it has been demonstrated that there exists a need for either.


 * "I don't feel very strongly about it." In that case you will see the wisdom in following the suggestion (which has in fact been made to you before) to hold back on your category creation activities.


 * I concede that the Continuity category may be considered by some to be suboptimal, but I don't see it as "crazy". As it is, it's convenient. I just see it as something which has evolved in a particular direction. Categories are groupings of convenience only. Bad move to structure them into a form that makes them difficult to find things in. If there are too many categories it becomes difficult to find stuff in them.


 * And there should be no need for "continuous functions" to be a subcategory of "continuous mappings" - a function is a mapping. How confusing and pointless would that be? --prime mover (talk) 06:21, 30 January 2013 (UTC)


 * I personally see no reason whatsoever to distinguish mappings from functions, but since that is a point on which you stand very strongly I think we need to fit it into the structure properly. What we have now is that continuous functions go in Category:Continuity, and continuous mappings that are not about numbers go in Category:Continuous Mappings, which is a subcategory of Category:Continuity. My own view is that the "natural" structure is something more like this:
 * Topology > Continuous Mappings > Continuous Functions
 * Analysis > Continuous Functions
 * Why should I have to dig deeper to get to more general theorems about continuity? I think if we are to have a Continuity category at all, it should be to cover any notions of continuity that may or may not exist (I don't know) that don't correspond to topological continuity. --Dfeuer (talk) 06:28, 30 January 2013 (UTC)


 * "if we are to have a Continuity category at all" - feel free to delete it if it causes you pain. --prime mover (talk) 09:15, 30 January 2013 (UTC)

feelings of being ridiculous
"I feel ridiculous every time I use the name Definition:Continuity/Topology/Open Sets."

What you need to do, when you find a definition which has / in them, is to do a "what links here" to see what pages redirect to the page in question. If there is more than one, use the most popular one (it's probably superseded a less optimal one).

In this case, the link you want is Definition:Continuous Mapping (Topology). --prime mover (talk) 09:05, 30 January 2013 (UTC)


 * Why not MOVE Definition:Continuity/Topology/Open Sets to Definition:Continuous Mapping (Topology) and let the one with fully two slashes in it be the redirect to this incredibly important definition? --Dfeuer (talk) 09:07, 30 January 2013 (UTC)


 * So that the subpage structure is not violated. Simple. --Lord_Farin (talk) 09:10, 30 January 2013 (UTC)


 * Here's a big problem with the structure as it stands: this key concept can be defined in MANY ways (any topology book will have a collection). Open sets, closed sets, bases, subbases, various things about closures and interiors, etc. Our current primary name is "open sets", which doesn't actually describe all of these things, and does not gracefully leave room for multiple equivalent definitions. --Dfeuer (talk) 09:14, 30 January 2013 (UTC)


 * I agree that there is ample room for improvement here. I don't think that moving the page to somewhere else is improvement; how that will be approached is not up to me - basic topology isn't as close to my heart as some of its subfields. --Lord_Farin (talk) 09:18, 30 January 2013 (UTC)


 * In order to gather all the various threads together that define "continuity": in the various fields (topology, metric spaces, the various number fields and (arguably) most importantly on the real numbers, a certain amount of compromise had had to be accepted. It is important that all the definitions are available to be accessed immediately from a "common" core page from which all definitions are presented. It is also necessary that for individual fields of mathematics (e.g. real analysis) a definition of continuity is available directly (therefore the redirect page from, for example, Definition:Continuous Real Function to Definition:Continuity/Real Function, which itself has subpages definition subtleties of definition). This is how it is, and it has evolved into that format through four years of gradual refinement, via various techniques which have been tried and have failed, to what we have now which is perfectly adequate.


 * Continuity is usually defined in a topology text by its "open set" property. This is easy to state and completely unambiguous and rigorous. The fact that it can equally well be defined based on closed sets is equally valid, but rarely done as a primary definition because topologies are themselves "usually" defined based on open sets. And the fact that they too can also be defined in terms of closed sets is equally straightforward, and there is indeed a link to where they are so defined and that the definitions are mutually equivalent.


 * There is indeed room for multiple definitions of continuity in topology, and in due course all these can and should be added, and proofs be developed to demonstrate their equivalence.


 * But the original question was that linking to Definition:Continuity/Topology/Open Sets made you feel "ridiculous". Stong word that - in other words you think you're being laughed at. I am at a loss to understand what your problem is: if you don't like that particular definition, why not link to one of the definitions that you do like? What is wrong with using Definition:Continuous Mapping (Topology)? This is after all (as has been pointed out by L_F on another thread and in another context) mandatory in order to comply with house style.


 * If you particularly need to access a different definition of the concept then there should be no difficulty in constructing the actual definition that you need - but in the context of the basic definitions you are putting together that should not be a concern. --prime mover (talk) 09:52, 30 January 2013 (UTC)

categories again
You're doing it again. Please refrain from creating categories for things that do not yet exist. I mean that. It's not just an idle whim. Your personal predilections are in danger of reducing the usability and therefore quality of this site. --prime mover (talk) 09:55, 30 January 2013 (UTC)


 * On a more explanatory note, the approved method (when not advancing into a completely uncovered field of mathematics - *not* a subfield) is to first populate categories, then as they have grown sufficiently, the operation of creating subcategories may be started with. In that light, your efforts on separating results about continuous functions from the Category:Continuity are valued, while your creation of new and empty categories is not. I confess to have created some of these in the past as well, but I have come to the conclusion that it's not a good idea. --Lord_Farin (talk) 10:00, 30 January 2013 (UTC)

If you folks are talking about the uniform continuity category, there are loads of pages up already that need to go into it. --Dfeuer (talk) 10:06, 30 January 2013 (UTC)


 * My response is intended to apply in general, at least the first sentence. Please take it to heart. --Lord_Farin (talk) 10:07, 30 January 2013 (UTC)


 * So is the category "uniform continuity" or "uniformly continuous mappings"? And is it general, or is it specifically for metric spaces? Methinks this can do with being thought through a little bit more - and if you get obvious redlinks on your usage of the templates, suggest you need to go back and fix what you did wrong before continuing. As it is there is a danger of fragmenting the categories so much that material is going to get seriously lost. --prime mover (talk) 10:11, 30 January 2013 (UTC)


 * Sorry, I got that mixed up. For now I want uniformly continuous mappings and uniformly continuous functions. --Dfeuer (talk) 10:12, 30 January 2013 (UTC)


 * Or should I call that first one Category:Uniformly Continuous Mappings (Metric Spaces) to leave room for uniform spaces? --Dfeuer (talk) 10:15, 30 January 2013 (UTC)


 * Not at this point. If and when we get to it, a refactoring operation will be instigated. --Lord_Farin (talk) 10:16, 30 January 2013 (UTC)


 * I reiterate: the "correct" assignation of categories is not a primary concern. Too many fragmented categories causes it to be difficult to find stuff. Please stop creating categories. Whether they are or are not useful is at this stage beside the point - the fact is your judgment on this matter is up for question. --prime mover (talk) 10:22, 30 January 2013 (UTC)

Editing conduct (again)
With over 2k edits in the last month, you are to be considered a regular contributor (to say the least). It makes me sad to see that you still refuse to try and adhere to the style rules for e.g. linking (and another style rule I will not mention so as to avoid another rage against it). You seem not even to attempt to learn it. Why?! We're not your personal cleaning company, you know. --Lord_Farin (talk) 08:37, 1 February 2013 (UTC)


 * I was drafting some things with the intention of going back and linking, but then I fell asleep. I'm sorry. --Dfeuer (talk) 13:06, 1 February 2013 (UTC)


 * In that case, I can recommend the use of Template:WIP and Template:Inuse. Also, when you know something is not up to style and you don't know how to fix it, please put a Template:Tidy call so as to display that you at least know something isn't up to standards. --Lord_Farin (talk) 13:23, 1 February 2013 (UTC)


 * If you refer to the one about the order topology on a convex set, style is the least of its current presentational problems. It basically needs to be rewritten from scratch. I'll take a look at how Munkres does it and see if I can find good ideas there. --Dfeuer (talk) 13:27, 1 February 2013 (UTC)


 * For that one, consider Template:Improve. In general, it is advisable to place rough drafts you produce in your sandbox (like you've done with the ordered group stuff) until they've sufficiently crystallised and regularised in order to not detract from the site's aims (rigour, clarity, consistency - you know them) unnecessarily. Regarding Munkres, it'd be awesome if you would start covering it like PM and I do, with prevs and nexts etc. That'd be a really valuable addition to the site. --Lord_Farin (talk) 13:53, 1 February 2013 (UTC)

Glossary of symbols
I haven't seen one. If there isn't one, I think there should be one. If there is one, I think it should be easier to run into in the dark. I'm thinking one table for each mathematical field, with each row showing a symbol, its name(s), and links to definitions of all the things its used for in that field. --Dfeuer (talk) 07:29, 3 February 2013 (UTC)


 * There is one, but it has not been rigorously maintained. Look at "Symbol Index" on the left hand side menu. I'm not sure how much more it can be made to glow.


 * As long as you leave the existing structure in place while you do it, you are welcome to construct the above. --prime mover (talk) 07:51, 3 February 2013 (UTC)


 * More silver polish? Headlights? I don't know how I managed to miss that every time I looked at the sidebar. --Dfeuer (talk) 07:53, 3 February 2013 (UTC)


 * I've just been looking at it, and note that it is seriously incomplete, and has a lot of work to bring it up to the current standard of both presentation and source code.


 * We did experiment briefly with tables in the early stages of ProofWiki but decided that the format did not allow adequate flexibility of what needed to be presented, so we gave up and reverted to the (admittedly not ultimate) form that you see. --prime mover (talk) 07:59, 3 February 2013 (UTC)

Project Gutenberg
To a greater to lesser extent, this wiki is more similar to PGDP than it appears on the surface. Any fool can create a website which posts up random proofs that they like. No attempt at definitions, no attempts to link from one proof to another, no attempt to bind to sources. After all, this is how was started.

What we are trying to do here is create a, well, you know what we're trying to create. However, the aspects of the site which you seem most impatient are more important than you believe they are. No other site pays such attention to presentational, ease of intellectual accessibility, uniformity of style and traceability of sources as this one.

My comments about sticking to what you know are meant exactly as they are said. We do not want a lot of experimental work posted up based on individual working out of stuff, whether by a competent mathematician or no, unless the result itself is referenced (with or without proof) in a published source. If such a proof is presented in a book you have, for example, with something like "The proof of this is omitted", then feel free to go ahead and create a proof. But the statement of the result itself must be sourced'. If it later turns out that the statement is false, we can always add that page to the "Errata" section (see some of the mistakes that have been found in Steen & Seebach, for example).

But individual research is not the way to go. Consider it more as a dictionary than an encyclopedia or fan page. Every entry is rigorously sourced from either a hard-copy or one from a rigid list of web resources. (Yes I know there are already exceptions on this site - they were posted up before it had developed into the site it is - such pages are to be addressed.) So if you want to post up what you think is an interesting result, then make sure you know what you're posting and can source it from hard copy.

If this is not the style of work that you want to do, then my suggestion to you is that maybe ProofWiki is not the place for you. On the other hand, if you disagree with any or all of the above, you are 100% at liberty to block any contributors who do not share your master plan so as to ensure that their incompatible philosophy no longer interferes.


 * I would say that there is also room for auxiliary results that are generally not even stated in sources because they're tedious and obvious. Other than that, I mostly agree with what you wrote. Besides mentioned auxiliary results, I think the only other major category of results one can argue to be admissible is so-called folklore results (which researchers use all the time but aren't actually published anywhere). I think that there is room for a "hull" of unref'd results floating around ref'd results (easy generalisations etc.) but to venture into a research field without any guidance but the internet could turn out inconsistent in some respects, or worse. Lastly, @Dfeuer: let me put in that I think it's better for the site if you stay. I would however like you to take to heart what PM says. --Lord_Farin (talk) 08:35, 15 February 2013 (UTC)

Lattice Theory
Presumably you're about to post up  into the Books namespace? Note that the specific edition you're using (1995) needs to be differentiated from the original 1940 edition using the new amendment to the BookReference template and corresponding work that has been done on the Books namespace by L_F recently (you will have followed the exchange on Friday, I believe it was). --prime mover (talk) 22:12, 16 February 2013 (UTC)


 * I will not have noticed the exchange on Friday. --Dfeuer (talk) 22:14, 16 February 2013 (UTC)


 * In that case I recommend you go back and read it - it is immediately relevant.


 * I also note that 1995 will need to be amended. Editions were 1940, 1948, 1967. 1995 was just the date of another reprint of the 1967 edition. So please replace all instances of that link with  so as to ensure that the sources are accurately linked. --prime mover (talk) 22:31, 16 February 2013 (UTC)


 * The text about printings in this book is most confusing. It appears the copyright may have been renewed last in 1967. The second (revised) edition came out in 1948.  The third edition, seventh printing, came out in 1993. Then the eighth printing (with corrections) came out in 1995.  Whether those corrections are significant or not,  I don't know.  How much difference there was between the second and third editions, I don't know. When I get around to reading the foreword, that may or may not tell me. --Dfeuer (talk) 22:36, 16 February 2013 (UTC)


 * 3rd edition came out in 1967. 7th printing of that 3rd edition 1993. And so on. --prime mover (talk) 22:40, 16 February 2013 (UTC)


 * Anyway, the point is: if you are referencing the edition you are using, then use the link that specifies it is the 3rd edition. Whether it is significantly different from 2nd and 1st editions is neither here nor there. But referencing the 1995 edition is incorrect because there was no 1995 edition. That edition is a later reprint of the 1967 edition. --prime mover (talk) 22:44, 16 February 2013 (UTC)


 * In general I believe it is common to refer to a "revision" when significant changes in set-up and/or content are made. "Corrections" are usually just a parsing of the provided errata to that date. If it were significant, it would invariably result in renewing the copyright for obvious reasons. Or that's my POV - in any case, thanks for using the suggested template form. --Lord_Farin (talk) 13:39, 17 February 2013 (UTC)

On "Intro to Axiomatic Set Theory"
I would like you to inform that I generally consider the pages featuring a link to Takeuti/Zaring's Intro to Ax.Set Thy to be up for a complete rewrite. They are an example of what happens when people disregard the general cohesion and style of PW. They're not worthless, but I'd advise you to spend time on other things.

In due time, when all the basics have been done proper (for which reason I'm covering "Mathematical Logic for Computer Science" &mdash; although side-tracked twice atm) I hope to get back to the work and go over it from scratch. In general I don't feel that PW has enough body to support covering of texts on that (quite advanced) level just yet. &mdash; Lord_Farin (talk) 21:35, 25 February 2013 (UTC)

Don't
Just don't. Behave. You're grown up and should act like it. &mdash; Lord_Farin (talk) 22:53, 28 February 2013 (UTC)

user rights
You see what's happened. I expect you can guess why.

In case you can't:


 * a) Blocking someone without warning is generally considered rude.
 * b) Restructuring is all very well but there is a specific reason for the structuring of subpage names the way they are.
 * c) If you don't understand the thinking behind how something has been done, please consider the possibility that the problem may not necessarily lie with the stupidity of the original contributor. The fact that a particular implementation route differs from the technique that you would have preferred is the result of a choice which may have had a specific reason behind it.

--prime mover (talk) 06:27, 1 March 2013 (UTC)


 * I blocked you for 15 minutes because you were making huge changes to the work I'd done even as those very changes were being discussed. I'm hoping cooler heads will prevail sometime later tonight, because direct confrontation between me and you obviously is not going to get me anywhere. Know ye that explaining the reason behind something will likely be more effective than telling me there is one. I explained myself to you. --Dfeuer (talk) 06:35, 1 March 2013 (UTC)


 * For the record, you did *NOT* block me for fifteen minutes, you blocked me for a whole day. (From memory it was from 22:30 on 28-Feb-2013 to 22:45 on 1-Mar 2013.) I won't comment further on what such action comes across like for fear of falling foul of Godwin's law. --prime mover (talk) 07:06, 1 March 2013 (UTC)


 * Original block was 2 hours (because I was fumbling with the interface), reduced a couple minutes later to 12 minutes. If I'm wrong, it was purely a miscalculation, and I apologize. --Dfeuer (talk) 07:11, 1 March 2013 (UTC)


 * Apology (grudgingly) accepted. I would say in my best Monty Python voice "don't do it again" but the occasion will no longer arise for that to be possible. --prime mover (talk) 07:22, 1 March 2013 (UTC)


 * We'll see. --Dfeuer (talk) 07:35, 1 March 2013 (UTC)

Renaming
Your efforts in processing renaming requests are valued. Two things:
 * When the original title is not plainly wrong/inaccurate, it needs to get appropriate categories to make it more visible (also as an entry point for the site).
 * When renaming, please ensure that the links to the page are updated. This is important and one of the main reasons why renaming requests aren't processed immediately.

In particular, could you please take care of Relation Contains Diagonal Relation iff Reflexive? Thanks in advance. &mdash; Lord_Farin (talk) 18:30, 2 March 2013 (UTC)


 * Thank you for your prompt adherence. Much appreciated! &mdash; Lord_Farin (talk) 19:46, 2 March 2013 (UTC)

Is this in the database?
Hey Dfeuer, I'm looking for a proof that tackles this expression in the database. Can you help?


 * $(B \cup A) \setminus (B \setminus A)$

--Jshflynn (talk) 23:35, 3 March 2013 (UTC)


 * Yes it is, it's in the Set Difference category, can't remember what it's called, family crisis prevent much time spent here. --prime mover (talk) 03:29, 4 March 2013 (UTC)


 * Hmmm.... That's a pretty tough one to name. You could try asking PM or LF, but it's also possible that it's just not there, especially since it's so hard to name.  What do you need it for?


 * As for the actual expression, let me see...

--Dfeuer (talk) 23:42, 3 March 2013 (UTC)


 * Thanks for that :)


 * Upon doing this: Relation Intersection Inverse is Greatest Symmetric Subset of Relation. I came up with this (which is just a hunch):


 * $\mathcal R \cap \mathcal R^{-1} = \mathcal R^\leftrightarrow \setminus \left( {\mathcal R^\leftrightarrow \setminus \mathcal R} \right)^\leftrightarrow$


 * It was a challenge to use symmetric closure and set difference only to come up with something meaningful. I am not sure if it is really worth posting but that expression appeared when I was trying to get from the right hand side to the left. Thanks again. --Jshflynn (talk) 23:51, 3 March 2013 (UTC)


 * Huh. Prove it if you can, or try to disprove it.  While you're at it, there's a classic topological puzzle, the Kuratowski closure-complement problem, you might want to take a crack at.  The solution's probably on PW somewhere.  The problem: prove that if $X$ is a subset of a topological space, then there are at most $14$ different sets you can get by applying the closure and complement operations to $X$. Prove that there is a set of real numbers from  which 14 sets can be so constructed.  --Dfeuer (talk) 23:58, 3 March 2013 (UTC)


 * It's in the plan. Needs a healthy long run-up. It's in Steen and Seebach (the second part of what you put anyway). --prime mover (talk) 08:51, 4 March 2013 (UTC)