User talk:Prime.mover





Archives
For what it's worth I have archived my user talk page in all its offensive embarrassing glory. --prime mover 12:15, 29 April 2012 (EDT)


 * So, what's your affiliation with the RU Nijmegen? --Lord_Farin 17:40, 29 April 2012 (EDT)


 * Participated in a conference on mathematics wikis. Feel free to inform me if I do not have the authorisation to display its crest in conjunction with my name, as it could be construed as presumption. --prime mover 19:38, 29 April 2012 (EDT)


 * I don't know nor bother; I'm with Utrecht anyway - at least until the summer of 2013. --Lord_Farin 04:42, 30 April 2012 (EDT)

Your last contribution to the talk page really was not constructive; I understand this by looking at the clock, but please ensure that you are contributing something in the future. It's not an obligation to respond the same evening (although some would call me a hypocrite for putting this up, I don't really care; feel free to hit back at some point). --Lord_Farin 18:46, 1 June 2012 (EDT)
 * It was constructive enough. I corrected the two points mentioned, but the fact is the last major change to this page IMO detracted from rather than enhanced its meaningfulness, as it failed to keep the notation consistent. What does a man do? It's a crappy page anyway. --prime mover 18:51, 1 June 2012 (EDT)
 * I think the issue was just that it sounded like you were annoyed at Frades rather than at the existing mediocre content. Sometimes it would probably be better to wait rather than responding overly tersely while you're pissed off :) --Alec  (talk) 22:13, 1 June 2012 (EDT)

Perhaps on the book pages, we could put links to theorems that reference that book, for instance, under each chapter, we may list the numbers of the theorem and link them directly to the pages that they correspond to. Is this something that could/should be implemented to any extent? Andrew Salmon 08:55, 24 July 2012 (UTC)


 * If that's something you want to do, then feel free to get under way. --prime mover 09:41, 24 July 2012 (UTC)

I've made an effort to make my style more in line with the proofs on this site, but they still keep getting marked "tidy". What does this one, in particular, need to become "house style"? Transfinite Recursion/Lemma --Andrew Salmon 05:18, 26 July 2012 (UTC)


 * Two points in particular:
 * 1. Spacing, basically. If you notice, every page on ProofWiki (every tidy non-talk page, that is) has a gap between the sections which consists of two blank lines. This forces a noticeable gap between e.g. the Theorem section and the "Proof" heading. Note that when you edit a section separately, the gap vanishes (this is an awkward feature of MediaWiki software) so editing individual sections is not recommended. Funny, but I have a feeling LF has already mentioned this (although I can't find it).
 * 2. Note that every time brackets are used, the "left" and "right" delimiters are used, and braces {} are used to enclose the field being parenthesised. This ensures consistency and provides an immediate way to ensure brackets match.


 * Also worth noting that there are several places where links are not being used. Every concept needs a link to a page explaining it.


 * Also worth noting that whenever you start a new topic on a talk page, do it by pressing the "Add topic" button above, or otherwise add a new heading in the talk page itself.


 * I hate to have to write instructions for this stuff over and above what is in the Help pages (although all this is doc'ed in the House Style page) - I prefer to think that these things can be picked up by following examples. --prime mover 05:36, 26 July 2012 (UTC)


 * That is, as long as the influx of new contributors putting up piles of new information does not exceed a certain bound. --Lord_Farin 10:28, 2 August 2012 (UTC)

What word should we use here
The theory $x < y \implies z+x < z+y$ holds for ordinal arithmetic. Note that the converse does not hold and that ordinal addition is noncommutative. What word should we use to describe this theorem. I'm looking for a term like Ordinal Addition is Associative or Ordinal Addition is Left-Cancellable. Thanks, Andrew Salmon 07:19, 27 July 2012 (UTC)
 * Ordinal Addition Preserves Ordering? --GFauxPas 08:23, 27 July 2012 (UTC)


 * Definition:Relation Compatible with Operation, and we can call it "left-compatible" and "right-compatible" if you need to discriminate. --prime mover 14:05, 27 July 2012 (UTC)

Colons
I think that subpages like Powers of Group Elements/Sum of Indices should be referred to as Powers of Group Elements: Sum of Indices since IMHO the forward slash looks very ugly. --Lord_Farin 10:59, 2 August 2012 (UTC)


 * I agree, and I admit I have been less than diligent at sorting these occurrences out, through sheer laziness. --prime mover 17:19, 2 August 2012 (UTC)

Help
Could you take a look at Lebesgue Pre-Measure is Pre-Measure? I can't seem to identify the issue, it looks like nothing I have seen before in PW. --Lord_Farin 18:11, 4 August 2012 (UTC)


 * The culprits are apparently my $Lord_Farin 18:17, 4 August 2012 (UTC)


 * It looks fine to me. What appears to be the problem? --prime mover 20:52, 4 August 2012 (UTC)


 * When writing consecutive $(($ or $]]$ in the eqn template it apparently breaks the interpreter, probably some issue pertaining to the PHP regexp implementation in MediaWiki. Look back in the history, the first big edit of today, and you can see it for yourself (I can, at least). --Lord_Farin 20:55, 4 August 2012 (UTC)


 * Well, is bound to cause a problem especially when you follow it with a  because that's the delimiters for an internal link. Within a template you might fall foul of more severe restrictions. I have consisently used $\left[\left[{ ...  }\right]\right]$ for Definition:Equivalence Class in the past - recommend you might want to do the same for your contructs: $\left[\left[{ ...  }\right)\right)$ and $\left(\left({ ...  }\right]\right]$. It seems to work. --prime mover 21:01, 4 August 2012 (UTC)

I have adapted it to the latter inside the eqn's indeed; it works. However it is cumbersome and the intuitive form does not lead to problems outside of templates (that I know of). As I see it the dollar signs (ah, that's where it may be from, precedence in parsing delimiters) are parsed before internal links, hence can't be caught by annoying issues with double ['s. On the other hand I may lay off my recalcitrance later, when I'm in a more realistic mood. --Lord_Farin 21:09, 4 August 2012 (UTC)


 * Hah! You invented the notation - you live with it! :-) --prime mover 21:14, 4 August 2012 (UTC)

Style
Hello. I do want to learn this "house style" and the correct formatting for this site. I have been through the house style page several times, but I am confused as to why some of my recent pages have been marked "tidy". I would like to write pages without them getting hit with the "tidy" template, so would it be possible for you to write maybe 3 or 4 words explaining what is wrong with the page the next time you do it? I don't want to impose too much writing or explanation that may be able to be found elsewhere, but maybe you could write something like "more links" or "spacing is wrong" or something to that effect. --Andrew Salmon 04:13, 6 August 2012 (UTC)


 * Will do. Note that some of it is really subtle, like making sure that e.g. there is a colon then a space between the bookreference template and the section it comes from, and using "Also see" not "See also". And note the use of the eqn template. And sentences always being on a new line. --prime mover 05:11, 6 August 2012 (UTC)


 * Some of it's grammatical stuff: "Then" is not followed by a comma. Sometimes it's just that a proof does not flow well as an argument. And so on.


 * As I say, the "tidy" flags are there so they can be attended to later when I'm not working on something else - but as the whole concept of how ordinals and classes are to be treated is to be given a complete rethink so as to be able to accommodate all these different and structurally incompatible approaches, just tidying the style is not such an immediately straightforward task. --prime mover 05:23, 6 August 2012 (UTC)


 * Seeing as you obviously have other plans for the ordinals section, would you recommend that I move onto chapter 9 as that deals with the axiom of regularity instead? --Andrew Salmon 05:40, 6 August 2012 (UTC)


 * Probably. I know nothing about the specific work in question. --prime mover 05:56, 6 August 2012 (UTC)

As requested, I've spent some time adding some explanations to some of the "tidy" tags. --prime mover 06:41, 6 August 2012 (UTC)
 * While at it, is it a good idea to instate one of 'Iff' and 'iff' and one of 'Implies' and 'implies' as standard for page titles? The stuff doesn't matter very much to me as I mostly search through Google, but may be another step towards consistency (among the other naming conventions we have been enforcing lately). --Lord_Farin 13:04, 7 August 2012 (UTC)


 * If we can decide which to use. My money is on lowercase. --prime mover 13:47, 7 August 2012 (UTC)


 * My preference as well. --Lord_Farin 13:53, 7 August 2012 (UTC)


 * I was thinking lowercase because I thought that was what we used for "if", "only if", and "implies". But looking around, that's inconsistent, too.--GFauxPas 14:30, 7 August 2012 (UTC)


 * This is an issue which I am not applying a high priority to, I'm afraid. Perhaps I'm getting fiddle-fatigue. --prime mover 14:46, 7 August 2012 (UTC)

I brought it up mainly to prevent the pile of work from growing further, which would happen if no convention arose (in which case both forms would continue to be added). We'd better stick to our on-the-fly adaptations as such is far more constructive and useful for us and the reader just strolling by. I will amend the appropriate Help section to mention these conventions. --Lord_Farin 14:52, 7 August 2012 (UTC)

Which'
In ongoing annoyance with the lack of a neuter gender counterpart to "whose" in the English language, I have adopted the egologism "which'" (in an attempt to find a close translation to the (archaic) Dutch "welks"); in case I'm being unclear, I mean the correct pronoun in 'The house which' door was open" where "whose" sounds distinctively wrong. This message serves not but to inform you that this use is intentional (and a faint attempt to make it a nostrologism instead of an egologism, but as you're a native speaker I suspect you will have grown used to "whose" or the more pedantic "of which"); please leave it in tact or provide me with the correct one-word alternative. --Lord_Farin 13:55, 6 August 2012 (UTC)

Also, behold the new type of page section I deemed useful: Definition:Convergence in Measure. It was useful mainly because it would be hard to have to come up with the code for $\displaystyle \operatorname{\mu-\!\lim\,} \limits_{n \to \infty} f_n = f$ every time, while I like it a lot better than $f_n \stackrel{\mu}{\longrightarrow} f$. --Lord_Farin 14:40, 6 August 2012 (UTC)


 * "whose" is AFAIK perfectly good grammar. I've never encountered an issue with it. I gather its wrongsoundingness originates from the fact that "who(m)" refers to an animate (or probably, strictly human) object, whereas "whose" is not so restricted, sounds as though it should mean "of whom".
 * I'll respect your suggestion, but I would not be surprised to find someone else "correcting" it. --prime mover 16:52, 6 August 2012 (UTC)


 * And the "Technical Note" looks like a useful innovation to me, go for it. It complements the "Symbol Index" which is shamefully not kept up to date (and was never in date in the first place, come to think of it). One of these days I'm going to go through a mathematical dictionary and extract everything in it to ProofWiki, though, so we have that to look forward to. --prime mover 16:56, 6 August 2012 (UTC)

Definitional Abbreviations
How to denote definitional abbreviations? What is the policy here? --Andrew Salmon 03:20, 7 August 2012 (UTC)


 * Looking around, it looks like the policy is to use $\dashv \vdash$. Is this correct? --Andrew Salmon 03:22, 7 August 2012 (UTC)


 * It's $:=$, see Definition:Definition.

"Start" link
Can the books have a "start" link on their book page that links to the first page that the book references? That is, it should link to the page that you get if you kept clicking prev until you can't anymore. Maybe it could be on the book page? --Andrew Salmon 06:20, 7 August 2012 (UTC)


 * Sounds like an excellent idea. I'll give it some thought - but I have to go to my day job right now. --prime mover 06:43, 7 August 2012 (UTC)

Message
Hello prime.mover. I'm back. I would like to know:

1) How may I upload an image? (my expectation is that my profile may not)

2) How may I upload a .pdf file?

--Jshflynn (talk) 22:00, 17 September 2012 (UTC)


 * I take the liberty to respond as PM is off to bed already.
 * 1) I see an 'Upload file' link under the 'Toolbox' header in the menu.
 * 2) This is currently disallowed.
 * If you explain your intentions, and we approve, site admin Joe may change the permissions to allow PDF uploads. I don't think that we will allow any user to upload files with the current amount of spam accounts; maybe there could be an 'authenticated/privileged users group'. For now, you can send the PDF to my address (lord_farin@proofwiki.org) and I'll look into it (my curiosity is also involved here :) ). LBNL: WB. --Lord_Farin (talk) 22:50, 17 September 2012 (UTC)


 * My view is: no PDFs. Anything therein should be able to be transcribed. If it's a picture, do it as a jpg etc., if it's text then type it up.
 * The reason for no PDFs is that they can not subsequently be edited. --prime mover (talk) 05:17, 18 September 2012 (UTC)

Subsection editing

 * PM, how come you are adding the ability for people to edit subsections? Here's something I was told early on by L_F:


 * "Although convenient, the section-wise editing feature destroys the carefully set up large whitespace separating sections. This then requires a subsequent edit to recover the desired amount of white. It is therefore generally preferable (except on talk/user pages, where house style is not enforced) to edit the page as a whole using the link at the top."


 * I never got around to asking him why the option exists in the first place. Are you fixing this bug or something?


 * It's part of the MediaWiki functionality. Don't know whether it can be turned off. It's not a bug, it's just the way it works. Besides, I'm not the man who controls the software. --prime mover (talk) 23:08, 22 September 2012 (UTC)

Request
Hi PM. This may be rude of me as I'm not entitled to it. Am I allowed to see that 1300 page LaTeX document you mentioned? It sounds fascinating. --Jshflynn (talk) 16:05, 28 September 2012 (UTC)


 * I'm not letting you have the source code but you can have the built DVI file (or PDF if you prefer). Let me know which, and a mailbox to drop it into, and I'll bag it up. I lied, it's more like 1200 pages not 1300. It might have been edited down. The zip is nearly 3 megs. Email me at prime dot mover at proofwiki dot org. --prime mover (talk) 18:53, 28 September 2012 (UTC)

Proofread
I have created an update for "proofread" to allow it to have a clarifying statement in the first template argument (so one can now add comments as well, in place of just the options "grammar" and "both". Showcase is at User:Lord_Farin/SandboxTemplate. If approved, I will place it on Template:Proofread. --Lord_Farin (talk) 15:52, 29 September 2012 (UTC)


 * Looks good. Feel free to deploy it. --prime mover (talk) 16:03, 29 September 2012 (UTC)

Capitals in Titles?
Hey PM. Just out of curiosity. How come in page titles ProofWiki treats keywords as proper nouns. For instance why is Subset Relation is Transitive given that name as opposed to subset relation is transitive or Subset Relation Is Transitive? I have no problem with it as I find it aesthetic. But I would like to know if there is/was a practical reason behind it as well. --Jshflynn (talk) 21:04, 5 October 2012 (UTC)


 * Purely aesthetic. I have distaste for language and presentation that looks kindergarten. I'm a proud fascist. --prime mover (talk) 21:05, 5 October 2012 (UTC)

Second opinion
Can I have your opinion on the stuff described on Talk:Open Sets of Double Pointed Topology? Eventually I want to prove Separation Axioms on Double Pointed Topology/T5 Axiom, but it turned out I need some preliminaries. --Lord_Farin (talk) 12:40, 18 October 2012 (UTC)


 * Well, that turned out to be a lot of work to eliminate just one stub entry. A fresh reminder on why I tend to hate examples when I understand the general definition. --Lord_Farin (talk) 15:14, 20 October 2012 (UTC)


 * The entire contents of is examples. That's its reason for existence. It shows which properties of topological spaces are dependent on which, and sets up examples to prove the various non-dependencies. Fun. --prime mover (talk) 15:23, 20 October 2012 (UTC)


 * While at it, let me explicitly tap my hat to your tireless refactoring duties; impressive how long it takes you before succumbing to the ever-lurking keyboard-smashing frustration it induces. --Lord_Farin (talk) 15:18, 20 October 2012 (UTC)


 * Pff. It's just the direction my OCD takes me. My personal space is a shambolic clutter of open, half-open and closed books, bounded and unbounded ... --prime mover (talk) 15:23, 20 October 2012 (UTC)


 * Luckily, you can always employ the shift operator to clear your mind :). --Lord_Farin (talk) 15:50, 20 October 2012 (UTC)

Topological conventions
Definition:Connected (Topology) has a mishmash of different conventions, and thanks to my changes Definition:Connected (Topology)/Subset is now even worse. I think we need to drop the formality of naming the space, its underlying set, and its topology throughout those articles. Such formality is rarely used in practice because it makes most things both more verbose and harder to understand. --Dfeuer (talk) 19:09, 5 December 2012 (UTC)


 * I don't understand what you mean by "drop the formality of naming the space". Can you explain? --prime mover (talk) 19:53, 5 December 2012 (UTC)


 * Formally, there's a set $S$, a topology $\mathscr T$, and a topological space $X=(S, \mathscr T)$. In practice, the space is identified with its underlying set, and the topology is handled implicitly. So it would be usual to write "Let $X$ be a topological space, let $K = \mathbb R \times X$, Let $U$ be open in $K$, and let $p \in K \setminus U$", rather than the horrible things that would be needed to write out all the formal details. Dfeuer (talk) 20:38, 5 December 2012 (UTC)


 * I don't see there's a problem. We specify it at the start: "Let $T = \left({S, \tau}\right)$ be a topological space" and then we refer to $T$, $\tau$ and $S$ as appropriate. Not horrible at all. --prime mover (talk) 20:56, 5 December 2012 (UTC)


 * If you're dealing with simple theorems involving one or two spaces, it's not too bad. If you're trying to deal with large products and such, it gets messy pretty quickly, and you soon start running out of good variable names, and more importantly working memory (I say, speaking as someone with a limited working memory). A more formal way to look at the informal approach is that it avoids naming the underlying set or the topology, and overloads set notation to allow $x \in X$ to mean "$x$ is a point in $X$" and "$S \subset X$" to mean either "$S$ is a subset of the set of points in $X$" or "The set of points in $S$ is a subset of the set of points in $X$".Dfeuer (talk) 22:53, 5 December 2012 (UTC)


 * We try to move as far away from informal as possible in both our proofs and our definitions. In the context of a linear exposition like a book or a paper, in which the train of thought is more-or-less constrained by the flow of the document, then introducing simplificational notations and short-cuts can be a useful saver of space. But in the multi-dimensional context that is ProofWiki, in which the path through the material is a complicated exercise in graph theory, it is (if not essential), a very good idea to ensure that the notation be kept as uniform, monolithic, consistent, formal and explicit as possible. The aim is for any page to be immediately accessible to any user.


 * Please be aware that we have been through this particular thought process before, several times over (whenever someone makes a similar suggestion to yours). The above philosophy is one of the cornerstones of the entire website. The fact that we have never received a favourable review from anywhere in the world is beside the point. --prime mover (talk) 22:59, 5 December 2012 (UTC)

I have to side with PM here. In the past, I have been frustrated by the complications this philosophy brings notationally; however, I consider this outweighed by the fact that we can make precise various category-theoretical notions that would otherwise only be expressible in colloquial language with appeal to intuition. OTOH, it may be convenient to have a notation for the "underlying set operator" so that we may avoid having to invent triples of variables (of which we then need to remember the definition).

I am very much open to any solution unifying the apparent benefits of both worlds (i.e. retaining rigour with minimal notational clutter); until such is provided, I'd rather stick to formal correctness. It may well be the sole truly distinguishing point PW has to offer in the competition with a comprehensive collection of mathematical books - that, and of course the documentation of all variants and notations around. --Lord_Farin (talk) 23:10, 5 December 2012 (UTC)


 * I have a few thoughts: 1. contrary to a belief common to category theorists, most mathematicians, and the vast majority of mathematics students, are not category theorists. 2. At the very least, components of the triple that are never used in the text shouldn't be named: "Let $X$ be a topological space over $S$" is better than "Let $X = (S, \tau)$" if $\tau$ never actually comes up. 3. When not using set notation, the underlying set needn't be mentioned, so until it gets too awkward, "Let $U$ be a set of points in $X$" is better than "Let $U \subset S$, where $S$ is the set of points in $X$". As for the general distaste for overloading notation, well it might be nice if math didn't do that, but it does, so I think it makes a certain amount of sense to use the notations everyone else does. 4. One option, taken from the world of programming languages, is the module import or implicit variable: let an article incorporate, by reference, the shortcuts of the relevant field. Dfeuer (talk) 23:22, 5 December 2012 (UTC)


 * Points 2. and 3. are certainly valid; another useful sentence may be "Let $\tau$ be a topology on $S$" or simply "Let $\left({S, \tau}\right)$ be a TS". Point 1. I can recognise :). I must admit to not fully understanding 4.. --Lord_Farin (talk) 23:44, 5 December 2012 (UTC)


 * Dfeuer, what do you recommend happen to existing pages? --Jshflynn (talk) 00:10, 6 December 2012 (UTC)


 * Jshflynn, I think they should all be made as clear as possible. Dfeuer (talk) 00:47, 6 December 2012 (UTC)


 * I should mention also that some notation is universally overloaded: $f(x)$ means the function $f$ applied to the argument $x$, while $x(y+z)$ means $x$ times $(y+z)$. Dfeuer (talk) 00:47, 6 December 2012 (UTC)


 * Dfeuer: While your point of view is indeed welcome, your proposed suggestions are in fact not going to happen. Your bold statement that "(such-and-such approach) is better than (thus-and-so approach)" is based on nothing more than your opinion. I happen to disagree and believe that "(thus-and-so approach) is better than (such-and-such approach)". Because, while it is usual for a definition not to explicitly make use of the internal structure of the topological space (as that definition may itself be based upon other definitions rather than on specific properties of the topology), it is likely that proofs that use such a definition do require specific details of the internal structure. The existing approach is therefore better.


 * As for "use the notations everyone else does" that is a fatuous argument: 1. Every piece of notation that is used by everybody else is used on this site. It would be stupid not to. 2. Every piece of notation over which there is dispute is by definition not used by "everybody else" otherwise there wouldn't be a dispute over it.


 * I repeat my earlier suggestion, made more elliptically earlier: if you don't like the structure of ProofWiki then you are more than welcome to start a rival site using a structure and philosophy that you do favour. Maybe perhaps if you were to make some valuable contributions to fill some of the many areas of mathematics which are still undocumented, and demonstrate that you are able to do useful work, your opinions may be held to a higher value. But we have so many editors whose only contribution has been to find fault with relatively trivial aspects of existing well-covered areas that my patience with such editors (never bountiful in the first place) wear thin very easily. Them as can does; them as can't, teach; them as can't teach, criticise. --prime mover (talk) 06:39, 6 December 2012 (UTC)


 * I'm doing my best to add and improve material, which I hope counts as useful. I am getting a bit frustrated by being shown the door at every turn. As for the topological matter, I don't actually understand what you're saying, so if you can give a clarifying example, I would appreciate that. Dfeuer (talk) 07:44, 6 December 2012 (UTC)


 * Point of fact is that you are raising issues on which a consensus has (even if only by default) already been reached. Yes, I concede you have indeed added some pages, a few proofs and alternative definitions. These have been (or are in the process of being) tidied up to suite the house style. You have also made one or two suggestions which have not been taken up, for whatever reasons. That is hardly being "shown the door", although perhaps your rhetorical style of argumentation, for example: "a mishmash of different conventions" (not justified), "even worse" (suggesting it's already badly flawed), "the horrible things that would be needed" (opinion not backed up by example), "general distaste for overloading notation" (whose distaste?), and so on, comes across as argumentum ad passiones and as such is less likely to be approached favourably - particularly on a mathematics website.


 * Contributions which are more-or-less guaranteed to be valued would be the opening up of areas of mathematics which are currently sketchy in nature. Complex analysis (which was started by me then put on hold until I had got some of the topological underpinning established), applied mathematics (very little done beyond Newton's laws of motion), standard results in calculus, probability and statistics beyond the rudiments, and anything much beyond undergraduate level mathematics are all completely wide open. But please be aware of the ever-present issue of house style. Anybody with a maths book in front of them and a rudimentary understanding of $\LaTeX$ can post up pages - what gives ProofWiki its added value is its rigorous design philosophy, whose broad principles are never up for negotiation. --prime mover (talk) 10:46, 6 December 2012 (UTC)


 * In Dfeuer's defence, I think that his point about circumventing parts of the formal constituents of a concept that aren't relevant for/used in the proof of the result is a good one. It can add clarity to pursue this. At the very least, I contend that such an approach shouldn't be eradicated. An other means to obtain more clarity is maybe to more explicitly refer back in the proof to what a certain piece of notation means (e.g. "Recall that $\tau$ is the topology on $X$") if a proof is involved and long. This will make it easier to administrate the backing concepts, allowing the reader to concentrate on the flow of the proof, rather than its presentation. This is however a matter of finesse; in principle, the style PM describes (and incidentally, prefers) is to be taken as the starting point for implementing niceties. --Lord_Farin (talk) 10:58, 6 December 2012 (UTC)


 * Accepted as a working hypothesis. These things will be best judged by the implementation of specific examples, preferably new work rather than amendments to existing pages. It would be instructive to see such an approach implemented and offered up as an instance. Such are more likely to be viewed favourably than discussions on the topic in talk pages. --prime mover (talk) 11:33, 6 December 2012 (UTC)

Style befuddlement
Clearly, it's going to take me quite some time to get a good sense of the style you prefer. In the mean time, I'll try my best to at least get the equations in the right style so it won't take you too long to fix the words around them. I know you like to keep things short and choppy, and I have no objection to that, but it's not something I'm accustomed to or particularly good at as of yet. --Dfeuer (talk) 07:24, 6 December 2012 (UTC)


 * Take your time.
 * You may come to like the style.
 * I find it makes it easier to follow a proof.
 * In the meantime, remember: the return key is your friend. --prime mover (talk) 07:29, 6 December 2012 (UTC)

Nowiki issues
As I have pointed out several times in the past, the nowiki tags are yielding problems (these were most apparent on Help:Editing). I have decided to universally enforce the technique:



in place of the old variants:



as this seemingly repairs the issues (at least for readers; I have seen some quirks while previewing edits). Just a heads up. --Lord_Farin (talk) 13:40, 6 December 2012 (UTC)


 * No worries. We live and learn. --prime mover (talk) 14:14, 6 December 2012 (UTC)


 * ...and Help:Editing has been rendered quirk-free (in passing, I also amended, changed and/or expanded some sections). A second change is that from now on, the use of the nowiki tag should be kept to a minimum, using it only where it is expressly necessary. --Lord_Farin (talk) 14:24, 6 December 2012 (UTC)


 * Already fed-up with wading through the comprehensive list of templates, cf. this special page; there are quite a lot of these that can be deleted (e.g. Template:LaTeX). I suggest we prune. --Lord_Farin (talk) 14:40, 6 December 2012 (UTC)


 * There's not many. LaTeX yes, because it's superseded by MathJax implementation, and the puzzling "!", maybe - but (apart from perhaps some of the semi-experimental "book" templates) I think everything in there has a valid use. --prime mover (talk) 15:02, 6 December 2012 (UTC)

Quick Question
Working with formal languages today I found this algebraic structure. It looks really familiar but I can't place where I've seen it. Any idea what I'm thinking of?:

a b  c  a  a  c  c  b  c  b  c  c  c  c  c

It's not particularly interesting but I just know I've seen it before. --Jshflynn (talk) 22:07, 6 December 2012 (UTC)


 * nope --prime mover (talk) 22:12, 6 December 2012 (UTC)


 * interesting you find it familiar… it seems that it's associative semigroup (by symmetry of its table it appears that it's commutative…) with a zero by this paper (see first table in 5.1.2.ii). questioning here about this grupoid gives index of 80 in the catalog which gives nothing interesting in particular ("minimal non strongly abelian", "minimal non abelian", "non-rigid"—i can't really understand those; it can be that catalog is outdated…). those seem to be little bit incoherent; if it was helpful in any way, please leave a comment on your thoughts about this. thanks in advance! joel talk 16:29, 27 December 2012 (UTC)


 * You might want to discuss this on User talk:Jshflynn as he was the one who raised this. --prime mover (talk) 17:47, 27 December 2012 (UTC)

Authorship reference
I was under the impression that the names of the authors as appearing in the respective work are supposed to be mentioned, rather than how we choose to address them. I have adhered to that impression; is it wrong? --Lord_Farin (talk) 13:48, 13 December 2012 (UTC)
 * Oops you're right - feel free to reverse out any silly changes I've made. Sorry ...--prime mover (talk) 14:02, 13 December 2012 (UTC)

Watchlist bug?
When I try to add Compactness Theorem to my watchlist, I get an error. This doesn't happen when I add other pages. --Dfeuer (talk) 18:04, 13 December 2012 (UTC)


 * Looks like I jumped the gun. It worked the fourth time I tried. Weird. --Dfeuer (talk) 18:05, 13 December 2012 (UTC)


 * If you want to report an error, it's usually a good idea to give an indication of what sort of error. There is something fishy going on at the moment (there's a javascript file that it sporadically can't find) but nothing permanently broken. As I say, though, "an error" is not enough info for us to be able to troubleshoot. --prime mover (talk) 18:14, 13 December 2012 (UTC)


 * It is relevant in this context that Joe intends to spend some of his precious Christmas holiday to fix up the MediaWiki backbone of the site. Maybe - don't get too excited - we'll even push the first version of the transclusion extension. --Lord_Farin (talk) 18:19, 13 December 2012 (UTC)


 * Excellent. --prime mover (talk) 18:21, 13 December 2012 (UTC)

Boolean Algebras/Boolean Rings
I intend to start covering the book I've recently added (as you have noticed). Several issues demand attention:


 * The likely confusion of Category:Boolean Algebra and Category:Boolean Algebras. Suggested resolution: destroying the former and incarnating it in a different manner.
 * Okay, makes sense.


 * Terminology "Join" and "Meet"; Definition:Join needs to be changed (I have indicated to come back to this; now I do so). These concepts really belong in order theory (being respectively Definition:Infimum/Ordered Set and Definition:Supremum/Ordered Set). The operations described on Definition:Boolean Algebra could be named identically, with reference, of course. Maybe it's better to simply include material on Supremum/Infimum on them being treated as binary operations. I also recall some page describing different notations for these, but couldn't locate it.
 * Don't agree with putting them in order theory. They have instantiations in order theory, but they are operations which are themselves abstract, and until they are concretised by applying them to order theory IMO that's how they should be treated.


 * I am tempted to use $\wedge$ and $\vee$ for meet and join, resp. This seems to be the standard convention, as nobody ever seems to care about investigating boolean algebras, lattices or related concepts in logic (where this naturally conflicts with con- and disjunction). If we desire so, we can always decide to pass to $\cap$ and $\cup$ whenever necessary. The $\smile$ and $\frown$ symbols are also an option but MathJax seems to give a suboptimal rendering.
 * $\wedge$ and $\vee$ work for me (as long as I refrain from calling them veg and wee) - again $\cap$ and $\cup$ are concretisations of an abstract concept.


 * In line with the above renaming proposal, the results like Join Distributes over Meet are in general false, and don't belong in Category:Boolean Algebras. They need to be renamed as appropriate (but Join (Boolean Algebra) is Distributive seems awkward).
 * Does join not distribute over meet? I thought that was one of the distinguishing features of a B.A. (or is that Huntingdon algebra?). And at this stage I am out of my immediate depth without reading up on stuff.

Before taking drastic measures (effectively destroying what's currently up - besides some peripheral ripples - is what it's going to come down to), I'd like to hear your thoughts about the matter. --Lord_Farin (talk) 18:36, 14 December 2012 (UTC)
 * If you need to change existing pages which have come from source works that I put up then let me know so I can then go back to those source works to check the context they have come in from and see if I need to amend anything appropriately. --prime mover (talk) 19:28, 14 December 2012 (UTC)
 * As to the second and fourth points, my proposed definition of "join" coincides with a binary Definition:Supremum. Cf. (the always-cursed but occasionally illustrative) WP. This usage is standard in order-theoretical works (particularly lattice theory). As there is a concept of "distributive lattice" it is nontrivial to assume the distributivity laws. I'd like to conform to standard usage of the terms. --Lord_Farin (talk) 19:34, 14 December 2012 (UTC)


 * Okay, if that's what it is. But we still need to retain the group-theory definition of "Join" because it's out there, it's a definition. So a disambig is required. --prime mover (talk) 19:37, 14 December 2012 (UTC)


 * Of course; I think it will return on a place like Definition:Join of Subgroups (incidentally, the join in the lattice of subgroups of a group, as mentioned on the talk). I'll get going then. --Lord_Farin (talk) 19:39, 14 December 2012 (UTC)

The next step in this task involves the rewriting of all results in Category:Boolean Algebras and Category:Huntington Algebras. It turns out the latter definition is called "Boolean algebra" in the literature, while "Huntington algebra" is reserved for an equivalent approach using rather $\vee$ and $\neg$ as primitives rather than also including $\wedge$. There are a lot of other characterisations of a BA/HA, but those can be covered later.

I will be moving the results I don't intend to return (recognisably) to my personal graveyard User:Lord_Farin/Backup and probably there is considerable work in bringing the references to Deskins back in line. This quite massive operation will conclude the refactoring of the lattice theory section and allow me to continue covering Givant/Halmos.

As an aside, there is a growing need, coming with the new approach of multiple definitions on a page, to have theorems which involve proving things that are axiomatically true in one, but not in another definition. For example, $\neg$ in a BA may be defined as a unary operation or by an existence clause. In the former case, Complement in Huntington Algebra is Unique is trivial, while it isn't in the second. Do you have ideas on how to approach this? I have not been able to come up with entirely satisfactory paradigms; either we suffice to add proofs "This is axiom X for Definition Y of Concept Z" or we will have a difficult time aptly naming pages. OTOH these proofs may be sufficiently involved that they deserve their own page (for the arguments are sometimes of more use than only in the proof of equivalence). --Lord_Farin (talk) 18:21, 21 January 2013 (UTC)


 * My own attempts to come up with a usable paradigm are as yet embryonic. As you see I am fragmenting the existing results in PropLog into ever smaller and atomic pieces, with a view to being able to assemble them appropriately into "proof trees" (I'm not sure what to call it when you have axioms at the root and theorems at the nodes, whatever) for any particular axiomatic system. Naming is difficult, as you see I have been reduced to more-or-less arbitrary numbering of "versions" of a particular result.


 * So don't be immediately afraid of tiny results, and don't worry about not finding a good name for them, the names may evolve, and so might the compound structures which they form. --prime mover (talk) 19:20, 21 January 2013 (UTC)


 * The results previously stated for Huntington Algebras have now been reformulated according to Definition:Boolean Algebra. You will want to review the links to Deskins located on the pages about HAs in User:Lord_Farin/Backup and make them reappear on the appropriate page for BAs. --Lord_Farin (talk) 20:32, 22 January 2013 (UTC)


 * Thx - will do once I've sorted out Exponential. --prime mover (talk) 20:34, 22 January 2013 (UTC)


 * I am completely lost. I can see no difference between the definition of Huntington Algebra and both definitions of Boolean Algebra except for the notation used. Also, I have this on the Deskins thread: User:Lord Farin/Backup/Power Set with Union and Intersection forms Huntington Algebra but I'm disinclined to go hunting round for its equivalent in the language of Boolean algebra. --prime mover (talk) 20:53, 22 January 2013 (UTC)


 * I think LF might be intending to change the HA definition to something else to match a traditional definition, but ultimately, these two notions are apparently equivalent, so it's probably more a matter of history than anything else. --Dfeuer (talk) 21:49, 22 January 2013 (UTC)

Firstly, that result now resides on Power Set with Union and Intersection forms Boolean Algebra. You are right to observe that only the notation has changed so as to match current use and compatibility with the lattice theory section. Secondly, I intend to put the definition of a Huntington algebra as follows: A system $(S, \vee, \neg)$ with $\vee$ binary, $\neg$ unary, subject to $\vee$ being comm. and assoc., and the Huntington axiom:


 * $(H): \quad \neg \left({\neg p \vee \neg q}\right) \vee \neg \left({\neg p \vee q}\right) = p$

A Robbins algebra is obtained by interpreting $(H)$ on $\neg p$ for $p$ (and transferring one $\neg$ from right to left). BA, HA and RA are all equivalent (but the last equivalence was only shown in the 90s by computer-aided proving) but they are historically different enough to merit covering them on separate pages. Of course, this introduces the need to appropriately link them; I will get to that in due course. I hope this clarifies stuff. --Lord_Farin (talk) 22:01, 22 January 2013 (UTC)


 * The other results on HAs are to be found approximately identically named in Category:Boolean Algebras, should you look for them. --Lord_Farin (talk) 22:02, 22 January 2013 (UTC)


 * Okay, in due course, I'm up to my ears in refactoring minute results in PropLog at the moment, which is fiddlesome and I don't want to break off from it or I'll get lost. --prime mover (talk) 22:05, 22 January 2013 (UTC)

What I did
Since you mentioned at some point that you lost track of what I did because I did too much at once, I’ve now created a list of all the pages I created on User:Timwi. Besides those, I think I have only done the split of Sine of Sum/Cosine of Sum and a few minor aesthetic or formatting edits. — Timwi (talk) 15:36, 15 December 2012 (UTC)


 * It's not "doing too much at once" that I had a problem with, it was the splitting of pages with book reference citations on them that hadn't been alerted that I was worried about. Terribly sorry, but life's too short at the moment to investigate every single thing. This site can sink or swim for a while till the various real-world intrusions have died down a little. --prime mover (talk) 21:18, 15 December 2012 (UTC)

Well-founded relations and minimal elements
Before we do too much tidying and refactoring, I think we need to see if this proof can be made to work at all. I'm not convinced. Do you have any ideas for how to plug up the hole? --Dfeuer (talk) 22:03, 29 December 2012 (UTC)


 * Sorry. Absolutely none. I can't see its point. A foundational relation is one which allows a minimal element, having defined what a "minimal element" is with respect to that relation. I understand it to be a generalisation of the concept as applied to a poset. But, anyway, having defined a foundational relation to be one in which every non-empty subset of it has a minimal element, what that stupid page purports to do is to prove that the subset of a set on which there is a foundational relation has a minimal element. I can't see the point. The definition of foundational includes the result of the proof in its very definition. So apart from ensuring the style and structure doesn't upset the bottom inspectors, I haven't been paying a great deal of attention to this. --prime mover (talk) 22:25, 29 December 2012 (UTC)


 * What it purports to show is, essentially, that if every subset of a class has a minimal element, then every subclass of that class has one. This is all intended, I believe, to support well-founded induction on proper classes, generalizing both well-founded induction on sets and transfinite induction on ordinals. --Dfeuer (talk) 23:05, 29 December 2012 (UTC)


 * I'm afraid I have no interest in learning the distinction. I disbelieve that class theory has any value whatsoever, so you're like asking a confirmed atheist what colour cloud he wants to play his harp on. --prime mover (talk) 23:10, 29 December 2012 (UTC)

Thought on axiom systems
I know I'm new and ignorant, but I had a thought about something that might make sense for the next big refactoring project: Get rid of the Axiom namespace altogether and instead have an Axiom System namespace for pages collecting axioms of different systems. That would remove the confusing appearance of an intrinsic difference between an axiom and a theorem which I personally find rather annoying, while also removing the need to type extra words to link to something marked as an axiom. Dfeuer (talk) 22:57, 31 December 2012 (UTC)


 * Not really keen. I've been planning on expanding the axiom namespace anyway, to include specifications for objects.


 * After all, it's not like "proving axioms" so much as "demonstrating that a particular object fulfils the axioms". That is, while it can be shown that the Peano axioms can be proved from the ZF axioms (which is what is done in the thread that follows on from the Minimal Infinite Successor Set work), that can also be considered as showing that the Minimal Infinite Successor Set is an object which fulfils those axioms.


 * I think it's valuable to record these various axiom schemata and to indicate the links between them. Completely getting rid of it is a bad move. --prime mover (talk) 23:04, 31 December 2012 (UTC)


 * How do you explain why the Axiom of Choice and the Axiom of Foundation are axioms, while the Compactness Theorem and Well-Founded Induction are not? Aside from the fact that the first two traditionally have the word "axiom" in their names, I'm not seeing the distinction. --Dfeuer (talk) 23:31, 31 December 2012 (UTC)


 * meh --prime mover (talk) 06:09, 1 January 2013 (UTC)


 * We're in the realms of higher philosophy now, which I would hope this website steers clear from, except such questions as can be elucidated and entered into the Category:Philosophical Positions.


 * As far as the development of this site is concerned, we don't actively search out refactoring projects to do. They are tedious. And with the best will in the world, and all the enthusiasm in the cosmos, it would end up being the usual maintenance team who would either be doing all the work or (which usually ends up being more work in the end) clearing up after someone else's half-baked attempt (I'm speaking from experience here), which ultimately means "me". We'd need a better reason to give a complete rethink to the way we document the field of axiomatics just because a contributor finds the treatment "annoying". --prime mover (talk) 07:44, 1 January 2013 (UTC)

Tychonoff refactoring
I took a stab at refactoring Tychonoff's Theorem. I'm sure I did some things wrong, PW-wise, so I'd appreciate a glance that way. I also haven't been able to come up with a clean way to factor out the identical parts of two of the versions, so if you have an idea please go ahead. --Dfeuer (talk) 18:34, 2 January 2013 (UTC)

On Category:Order Theory
I am thinking of reworking the structure surrounding said category. This includes creating e.g. Category:Ordered Semigroup and its siblings. Also, do we want to enforce a strict separation between Category:Order Theory and for example Category:Well-Orderings? Or are there results important enough to be in both?

As an aside, it seems that I am bogging down in making the current state of the site match our expectations and demands. Not that such is a problem; I just thought you'd recognize this. --Lord_Farin (talk) 22:42, 3 January 2013 (UTC)


 * My view is: a result specific to well-orderings would reside solely in the well-orderings category, for example. If a result refers in its title to both, then it goes into both: e.g. "Ordering (in some circumstances) is a well-ordering" or whatever.


 * I'm likewise taking a back seat in enforcing the law. I'll probably wait till it goes quiet (it usually does) or until discipline is maintained under its own momentum (most contributors either fall in line or fall away) and then embark on an effort to tidy up and shuffle it all into shape. --prime mover (talk) 22:47, 3 January 2013 (UTC)

Opposite groups and such
Since you're an expert at logic, do you think you could come up with a general principle to assist with things like the proof I just wrote of $(2)$ in Elements in Coset iff Product with Inverse in Coset? It seems like there should be a way to say that all statements of a certain form are logically equivalent to the form they take when all the group products and subset products are flipped around. --Dfeuer (talk) 20:52, 3 February 2013 (UTC)


 * Nope, don;t understand what you mean. As far as I could see the proof was fine as it is. I don't see that the changes that have been made to it are an improvement (apart from changing the notation). I'm tempted to revert. --prime mover (talk) 21:05, 3 February 2013 (UTC)


 * Don't do that yet. I'm going to work on it tonight. The plan, as stated, is to make the proof of (1) twice as long so as to be clearer. Then this proof of (2) will have a reason to exist. --Dfeuer (talk) 21:16, 3 February 2013 (UTC)


 * I'd rather you didn't - it was fine as it was. If you need to rewrite it, which it appears you are bent on, write a completely different proof. Leave the one there alone. --prime mover (talk) 21:18, 3 February 2013 (UTC)


 * FYI, I'm not the one who added the template saying it needed to be explained more clearly. --Dfeuer (talk) 21:23, 3 February 2013 (UTC)


 * No it didn't say "explained more clearly", it said "in a cleaner fashion". My request stands. Please, if you wish to present a proof which is different from the one posted, write it as a completely separate exercise. --prime mover (talk) 21:59, 3 February 2013 (UTC)

In response to the original comment, there could be proved a principle of duality for groups. It's merely an instance of duality of categories and would build on Definition:Opposite Group. --Lord_Farin (talk) 23:37, 3 February 2013 (UTC)


 * My point stands: it is effectively a different proof and should be worked on as a separate entity. --prime mover (talk) 07:07, 4 February 2013 (UTC)


 * Unfortunately I didn't have the time to finish this up today, but I did rearrange it a bit to support both proof styles so we can have your original proofs of (1) and (2), my as-yet-to-be-written proof of (1), and my current proof of (2) from (1). --Dfeuer (talk) 07:10, 4 February 2013 (UTC)


 * I'm still reverting it because as it stands there is too much wrong with this approach. Save what you want to save somewhere in your sandbox because when you get up it will have gone. --prime mover (talk) 07:12, 4 February 2013 (UTC)

Small Problem In Cantor-Bernstein-Schroeder Theorem/Proof 4
The sequence :$\ldots, a_{-1}, a_0, a_1, \ldots$ is determined by a single starting $a \in S$, since $a_0 = a$.

You then let the $a_i$ with even index be denoted $\left[{a}\right]_S$ and those with odd index be denoted $\left[{a}\right]_T$

Note that both $\left[{a}\right]_S$ and $\left[{a}\right]_T$ depend on a parameter $a \in S$.

Which means the partition
 * $\mathcal A_T = \left\{{\left[{a}\right]_T: a \in T}\right\}$

should be
 * $\mathcal A_T = \left\{{\left[{a}\right]_T: a \in S}\right\}$

(talk)


 * Corrected as suggested. --prime mover (talk) 17:53, 4 February 2013 (UTC)

Extension
I see you've picked up on the extension. Good thing. I have implemented/changed some things in a new version that I'll ask Joe to put online shortly, should I fail to do so myself.

These changes require one to go over the current instances and adapt them as appropriate. I think it will look the same but I'm not sure. In the new set-up the section title will not be automatically transcluded along (which is more common behaviour). Furthermore, the transclude "template" will feature options to include a section title with a link. All is working but it still needs to be published on the main wiki. --Lord_Farin (talk) 21:49, 20 February 2013 (UTC)