User talk:Lord Farin/Archive 1


 * This page contains archived discussions, for the contributor Lord_Farin felt they could be historically - to the extent this term applies to ProofWiki - significant. It is not intended, but may be merited, that these discussions are continued.

Well-Ordering Minimal Elements are Unique
Good call. I looked myself, but couldn't find it. Good call. --prime mover 00:23, 11 October 2011 (CDT)

Euler-Binet
Superb job on Euler-Binet Formula (that induction step eluded me for years - I'm a mediocre mathematician). I have a minor worry concerning the Binet Form which I originally got wrong $\Delta = \sqrt{m^2 + 1}$ but I'm now looking at MathWorld and it has $\Delta = \sqrt{m^2 + 4}$. What's your source for $\Delta = \sqrt{4 m^2 + 1}$? --prime mover 12:03, 14 October 2011 (CDT)
 * I will conform to MathWorld. I just attempted to think of a formula that appeared plausible, and came up with this; probably one of my bad habits. Glad the issue is resolved anyway. --Lord Farin 12:09, 14 October 2011 (CDT)

Foldable editor
Hey, that rocks. --prime mover 14:18, 19 October 2011 (CDT)

Extension
If you're interested, maybe we could turn the foldable template into a extension, so we could have something like: some lemma

If it works out well maybe even extend it to a general proofs. This should allow for a more customized environment. Let me know if your're interested / think it's a good idea. --Joe (talk) 06:37, 21 October 2011 (CDT)
 * I'm not quite sure what there is to improve by making this transition. In my opinion, we'd best keep structuring the pages quite simple. But, if you have a mind-blowing improvement in mind, I have a willing ear. At this point however, I am not sure what your point is. --Lord_Farin 09:34, 21 October 2011 (CDT)
 * Yeah, I didn't describe that very well. So what I've been thinking of developing for while, but have been to lazy to do, is a MediaWiki extension for ProofWiki. Basically this would include any features we want to add to ProofWiki that MediaWiki doesn't have. So for instance, your foldable sections could be used in a much broader sense. For instance we could have multiple parser tags such as: proof, lemma, etc. Lemma could have a default setting to automatically be hidden. Say you want to hide a proof (for some reason), you would wrap your proof inside  .... tags. Basically not just an extension for hiding page elements, but to improve functionality beyond what's currently available. Essentially to improve the way we present mathematics. Lets hope this makes sense. --Joe (talk) 10:02, 21 October 2011 (CDT)

I see where you are going. Users could specify that proofs never should be hidden, the frequent onlyinclude tags could be reworked to, when absent, automatically use the part of the page within the theorem tag... The possibilities are limitless. I could aid in developing this; however, I deem myself not such a virtuoso that I could do it on my own. Maybe we could start a discussion about what desired functionality the extension should have; such to prevent ambitious and not really necessary or desired functionality. The core should always be that it makes writing and reading theorems and proofs on PW easier. --Lord_Farin 11:46, 21 October 2011 (CDT)
 * Agreed, lets see what Prime.mover thinks --Joe (talk) 12:21, 21 October 2011 (CDT)
 * (wakes up) ... ooerr, wassup? urrr ...
 * Making reading the theorems easier should be no. 1 priority. To that end, I have tried to create a consistent style (but can't take full credit because there was considerable input from others).
 * Rules of thumb:
 * a) We could aim for a rigorous one-definition-per-file, one-theorem-per-file, one-proof-per-file system. I am working through stuff now (you've probably noticed) re-treading the exercise to plunder the books, and pages where there are multiple definitions have had the sub-defs factored out into separate, but transcluded, pages. Theorems are more variable: sometimes it is the statement of the theorem which is onlyincluded, and sometimes it's the proof. The latter happens when there are multiple proofs for the same theorem, the former when there multiple theorems have somehow accumulated (through similarity of subject matter) in the same page (see Trigonometrical Identities and Subset Equivalences for example). This is not completely universal - stuff still needs to be hauled out and refactoried - but it's in progress.
 * b) One of the awkward aspects of the evolved format is the aesthetic appearance of having two blank lines at the end of each section, so there's a wide white gap in between. Now, when you edit a section on its own, rather than editing the whole page, when you save it, it loses one of those two lines so you need to edit the whole page again to add the second line.
 * That's two things. Now if we could start a template, and a  and a  and a  etc. template, we could formalise the structure of a) and include by default the issue raised as b).
 * I'm not sure where to start with this, in order not to make the entry of proofs more fiddly and less intuitively obvious (we already have some hopeless cases who can't even work out how to put a heading in place, so getting them to follow rather more esoteric technique of entering everything via a less-than-universally understood template will be difficult to say the least. Once most of the pages are in the standardly templated formats, then there will at least be something to follow - but with the thick end of 10000 pages to edit this is going to be a long job - and it's barely 6 months since the last smoking-fingers marathon.
 * Try something out, see where you get to, and we can see what it looks like. The folding lemma template was a triumph. --prime mover 14:18, 21 October 2011 (CDT)
 * Okay, if I get some free time tomorrow I'll set up a development environment to work with and setup a basic extension. Are you familiar with git and ssh? I was thinking another feature would be for it to scan every page when saved and check for several things: a theorem, a proof (or a stub template), as well as at least one category. Then prompt the user to add these if not done already. Just thinking out loud. --Joe (talk) 20:37, 21 October 2011 (CDT)

I have worked with git before. Also have set up some SSH connections in the past, but that was years back. At least I still have git installed. I'll see the details coming. Will we also need something like Subversion or anything of that sort (I haven't worked with that before)? --Lord_Farin 01:46, 22 October 2011 (CDT)
 * Git is like subversion only better! Can you email me your ssh public key. --Joe (talk) 09:24, 22 October 2011 (CDT)
 * Done. --Lord_Farin 09:43, 22 October 2011 (CDT)
 * Awesome, I have some errands to run then I'll git (pun intended) to this. --Joe (talk) 09:55, 22 October 2011 (CDT)
 * ... of course, in Britain, "git" is a term of abuse: http://en.wikipedia.org/wiki/Git_(slang) ... just sayin' --prime mover 03:19, 23 October 2011 (CDT)

Intervals
I see you've picked up on the notation $[a..b]$ for denoting an interval - good call (many don't like it because it's new). I also notice you're adding the microspacing between the dots: $[a\,.\,.\,b]$. I'm not sure whether to bother with it. A lot of existing pages still have the $[a\,.\,.\,b]$ format, but I've been gradually removing them as I find them. It used to be important-ish when we were using the MediaWiki version of $\LaTeX$ up until early this year, when we moved to MathJax. The latter rendering engine does not put any perceptible space in place when you use \, so I have been gradually going through as I find them to remove instances of backslash-comma (if necessary in certain constructs, like before the $\mathrm d x$ in integrals, replacing them with backslash-space, which *does* put a noticeable space in place).

So the discussion would be as to whether to leave intervals as $[a..b]$ or space the dots out more, like $[a \. \ . \ b]$. IMO the latter looks a bit too spaced out, so I've been going with $[a..b]$ (or $[a .. b]$ as I prefer to write it.

In short, fiddling around with $[a\,.\,.\,b]$ is just too tedious with the current rendering engine, and you might like to do it as $[a .. b]$ instead. --prime mover 15:52, 22 October 2011 (CDT)
 * Excellent. Maybe better change the version in MediaWiki:Edittools as well, to promote consistency. I assume that $\left[{a .. b}\right]$ is still preferred over $[a .. b]$ though (as to keep in line with the general guidelines). But then, when copy-pasting it doesn't really matter anyway. Thanks for the heads up... it will save some work. --Lord_Farin 15:57, 22 October 2011 (CDT)
 * Yes, I omitted the left[{}]/right above for simplicity. I have amended the Edittools page (thx for heads up) but it's of limited use anyway because I have not figgered out how to get it to work when there are spaces in the string to be rendered (thus making backslash-space a combination that we can't use in it). --prime mover 16:10, 22 October 2011 (CDT)
 * http://www.mediawiki.org/wiki/Extension:CharInsert says that spaces and templates have to be inside nowiki tags. That probably solves the problem. Also, a + can be used to position the currently selected text, cq. place the cursor. --Lord_Farin 16:22, 22 October 2011 (CDT)
 * Yep, got the {+}, see some of existing templates. Will experiment with spaces in nowiki tags - see what happens. (But not tonight, it's been a long day and I still have domestic chores to do.) --prime mover 17:17, 22 October 2011 (CDT)

Talk pages
I think I've answered all your posts on the talk pages, if I've missed any please let me know. A lot of this stuff is limited in scope to the source works that I've been able to consult (my personal library of works, I've been told, is painfully inadequate but my resources are limited). --prime mover 15:48, 24 October 2011 (CDT)
 * There is one more: Talk:Existence of Local Coordinates‎. --Lord_Farin 16:34, 24 October 2011 (CDT)

Email
Hey, what's your email set to? Email's from other users ("E-mail this user") are being bounced to admin @ pw. --Joe (talk) 16:18, 7 November 2011 (CST)
 * I set it to lord_farin @ pw, and have confirmed it without problem. I have received a notification of you placing this comment on my page through the same account though... Sounds like a look into the 'E-mail user' functionality is justified. --Lord_Farin 16:22, 7 November 2011 (CST)

Comments in proofs using eqn template
I notice you're changing where I've been putting comments in of the form "by such-and-such" to "By such-and-such". Probably doesn't matter too much, but the grammmatical construct I had in mind was along the lines "(some expression) by such-and-such", the "by" being a conjunction to the part of the sentence that gives the reason. I haven't been consistent about this, I admit, and it may in fact be technically "cleaner" to omit the conjunction altogether, just giving the reason. On balance I prefer the conjunction, but (as I say) if it is uppercase I think it makes it look clumsy. Not to bother about changing them back at this stage, but there's no reason to change the first letter to uppercase unless you feel strongly about it. --prime mover 14:00, 9 November 2011 (CST)
 * I think it looks clumsy to put lowercase (although I follow your reasoning), because most references to theorems are put without the 'by' before it (therefore, they start with a capital). I merely tried to enforce consistency by capitalising all first letters. I'm fine with leaving pages as-is, but then, when I was changing them anyway, I deemed it a small effort. Point noted. --Lord_Farin 15:58, 9 November 2011 (CST)

New notational style
"Please tell me what one thinks about the notational style I just thought of for long expressions on my talk page" ...


 * Mixed feelings. I suppose it makes it clearer as to where the equation begins and where it gets split by an operator, which is a good thing (it fixes something I've been vaguely uncomfortable with) ... but in Squares of Linear Combination of Sine and Cosine you lose the obviousness and the pattern of the groupings that lead to the next line. Both have advantages. --prime mover 16:13, 9 November 2011 (CST)

whoops sorry
Yes I know it wasn't your edit that changed the number in bottom-elimination, but yours is the undone comment that accompanies the message ... sorry. --prime mover 13:39, 10 November 2011 (CST)

To all of my followers
I would like to invite you all to comment on the first paragraph of User:Lord_Farin/Sandbox. I have set up the definitions tonight, but am somewhat reluctant to put them on the main site immediately. --Lord_Farin 18:20, 17 November 2011 (CST)
 * Looks okay to me. I'll give them a proper going over in a bit, but the structure is fine. --prime mover 00:29, 18 November 2011 (CST)

Considering the notation
Not sure whether we need $\R_+ \cup \{0\}$ as the way $\R_+$ is defined in Definition:Positive or wherever it's $\{x \in \R: x \ge 0\}$. This will of course always be a bone of confusion. You could always just leave the codomain as $\R$ and take it for granted that the mapping will never be surjective. As it is impossible to generalise to what the precise image set actually is, as it is always just going to be "some subset of $\R_+$ it's impossible to specify the image for the general case anyway. --prime.mover
 * I agree to some part. Ideally I would write $\R_{\ge0}$ but I thought it'd be best to stick with the defined notation. -- LF
 * $\R_{\ge 0}$ totally rocks for all the right reasons. It is utterly obvious and completely straightforward. I suggest we "initiate a project" to change to it. -- p.m
 * Have started it. An entry in the Symbols namespace should be created for $\R_{>0}$ and $\R_{\ge 0}$ (the (strictly) positive reals), and maybe also for $\Q_{>0},\Z_{>0}$ and the like. I put this up mainly to avoid forgetting it. --Lord_Farin 17:45, 2 December 2011 (CST)
 * Done. --prime mover 01:41, 3 December 2011 (CST)

Transclusion - beware
If you work on a page with "onlyinclude" tags in it, be careful - the section inside it is included in another page. The case in point was Definition:Convergent Series which I've put the onlyinclude tags back in and reconfigured the level of headings. Otherwise Definition:Convergence looks odd. --prime mover 15:27, 13 January 2012 (EST)
 * The problem with transclusion and those tags is that upon rigorous restructuring and/or adding a lot of extra information, it is difficult to know what the structure of the page needs to be, cf. what other pages need attention. To all of the (very) active members: Use the 'What links here' feature, and click 'Hide links'. This generally leaves only the transclusions, which can then be investigated to determine the plan of action. --Lord_Farin 18:23, 13 January 2012 (EST)
 * Good call ... never tried the "Hide links" option. Up till now I've worked this thing by scanning down the complete list. --prime mover 01:38, 14 January 2012 (EST)

Had to put this up
Those of you slightly familiar with programming will have fun reading this. --Lord_Farin 17:58, 23 January 2012 (EST)


 * "If a maintenance programmer can't quote entire Monty Python movies from memory, he or she has no business being a programmer." Too true, mate.
 * This entire post depresses the life out of me, it's too close to my mundane existence. --prime mover 16:29, 24 January 2012 (EST)

Thanks
Thanks for helping me set up Tarskis' Geometry, LF :) --GFauxPas 14:02, 24 January 2012 (EST)


 * Welcome. I've noticed that I can grasp and use new definitions and axioms at speeds greatly above average. It would just be selfish to keep that advantage to myself and not put it to good use ;). --Lord_Farin 14:06, 24 January 2012 (EST)


 * LF I'd like your help for the Axiom of Continuity. Though I understand the axiom itself, there are some concepts there that are too delicate for me. Namely,the author gives a presentation of the axiom as a 2nd-order statement or an axiom schema, while the information is (he claims) still expressible as a first order statement. I don't know how that works, and I'd appreciate your illumination of the matter once you get a chance to look at it. --GFauxPas 17:11, 24 January 2012 (EST)


 * As it stands, and if I read correctly, the second-order statement is subtly stronger than the schema (because not all sets can be defined in first-order logic; hence cannot be covered by first-order statements). However, first-order theories are quite important because they have a theorem (the Completeness Theorem) stating that if something is necessarily true in all models of a theory (like Tarski Geometry, or Set Theory), then you can prove it (!). See WikiPedia. This is not true for second-order theories. Lastly, the sets that first-order logic 'misses' can often be circumvented in some way, but at a price: theorems like Peano's Axioms Uniquely Define Natural Numbers fail when P5 is replaced by the corresponding first-order axiom schema. Hopefully, you could follow that. --Lord_Farin 17:37, 24 January 2012 (EST)
 * I didn't get everything in that paragraph but it helped me out, thanks! But what does the author mean that the axiom can be used in first order form, even though it's presented as second order? --GFauxPas 22:16, 24 January 2012 (EST)


 * I think he means that, if you are willing to pay the price I mentioned earlier, you can swap the second-order axiom for the schema to receive all benefits of the extensive theory on first-order logic (as this is the only axiom which is second-order). --Lord_Farin 02:59, 25 January 2012 (EST)

A poset is an upper semilattice if every pair of elements has a supremum
Please see my talk page. Thanks. --KBlott

Done --KBlott 18:21, 27 January 2012 (EST)

Renaming pages
Probably best not to suppress the redirect when renaming pages or existing links will break. There's a case in point on kblott's homepage where he's listing all the proofs he's written. Just a thought - it's always possible to go back and delete any unwnted redirects later, but can be more challenging to replace links to no-longer-existing redirects. --prime mover 14:15, 28 January 2012 (EST)


 * I like to keep the place tidy. However, I'm apparently careless at times; therefore, from now on I will first flag for deletion, then proceed changing links, then delete. --Lord_Farin 17:43, 28 January 2012 (EST)

Thanks
Thanks for helping me set up Tarskis' Geometry, LF :) --GFauxPas 14:02, 24 January 2012 (EST)


 * Welcome. I've noticed that I can grasp and use new definitions and axioms at speeds greatly above average. It would just be selfish to keep that advantage to myself and not put it to good use ;). --Lord_Farin 14:06, 24 January 2012 (EST)


 * LF I'd like your help for the Axiom of Continuity. Though I understand the axiom itself, there are some concepts there that are too delicate for me. Namely,the author gives a presentation of the axiom as a 2nd-order statement or an axiom schema, while the information is (he claims) still expressible as a first order statement. I don't know how that works, and I'd appreciate your illumination of the matter once you get a chance to look at it. --GFauxPas 17:11, 24 January 2012 (EST)


 * As it stands, and if I read correctly, the second-order statement is subtly stronger than the schema (because not all sets can be defined in first-order logic; hence cannot be covered by first-order statements). However, first-order theories are quite important because they have a theorem (the Completeness Theorem) stating that if something is necessarily true in all models of a theory (like Tarski Geometry, or Set Theory), then you can prove it (!). See WikiPedia. This is not true for second-order theories. Lastly, the sets that first-order logic 'misses' can often be circumvented in some way, but at a price: theorems like Peano's Axioms Uniquely Define Natural Numbers fail when P5 is replaced by the corresponding first-order axiom schema. Hopefully, you could follow that. --Lord_Farin 17:37, 24 January 2012 (EST)
 * I didn't get everything in that paragraph but it helped me out, thanks! But what does the author mean that the axiom can be used in first order form, even though it's presented as second order? --GFauxPas 22:16, 24 January 2012 (EST)


 * I think he means that, if you are willing to pay the price I mentioned earlier, you can swap the second-order axiom for the schema to receive all benefits of the extensive theory on first-order logic (as this is the only axiom which is second-order). --Lord_Farin 02:59, 25 January 2012 (EST)

Hi there... anything else I should know
Hey there. I'm a new user, and I noticed you've been following along cleaning up my edits. Any chance you could add anything else that I should watch out for? I should be able to learn from the ones you've corrected, although I couldn't find a good guide on all the nitpicks around. Scshunt 03:20, 17 February 2012 (EST)


 * Sorry to butt in ... I take your point regarding "nitpicks". Some of the structuring does seem arbitrary and overly fussy, but there is method in our madness. One day we ought to make sure that all our nitpicks are gathered together on one page, but this has not happened yet (mea culpa).
 * In the meantime not to worry - tidying up is just something we do (well, me in particular) when nerving up energy for something that will take a considerable amount of hard work. --prime mover 07:20, 18 February 2012 (EST)


 * Sorry, I didn't meant that to come off badly. I consider myself to be a skilled picker of nits, much to the annoyance of those around me, so I'm not in the least annoyed that you want to maintain a consistent style. That's vital for making sure that the project doesn't become a mess. --Scshunt 01:47, 19 February 2012 (EST)


 * Skilled nickers of pits (oh wot-EV-er) are welcome. --prime mover 02:10, 20 February 2012 (EST)


 * You should check out Help:Editing; it contains most of house style. The most important thing is that it is strived for that all definitions get their separate pages, rather than one page containing a load of definitions. For example, you will see that I moved the definition of connectivity back to its own page. Feel free to ask if anything is unclear. Oh, and indeed, I prefer to answer a question on the same page, it's easier then to keep track of the conversation. --Lord_Farin 03:23, 17 February 2012 (EST)


 * Ok, thanks! Scshunt 03:25, 17 February 2012 (EST)

Preimage
I have refactored the Definition:Preimage page which now has the following (nested) transclusions:
 * Definition:Preimage/Relation
 * Definition:Preimage/Relation/Element
 * Definition:Preimage/Relation/Subset
 * Definition:Preimage/Relation/Relation
 * Definition:Preimage/Mapping
 * Definition:Preimage/Mapping/Element
 * Definition:Preimage/Mapping/Subset
 * Definition:Preimage/Mapping/Mapping

The point is: you have a link from Schilling into this page, and that link may (probably will) be relevant to only a subset (perhaps only one) of these pages. I don't have immediate access to this book, so would you be able to reconfigure these links appropriately?

And just so that you are in on my plan:

I have also added redirects to these pages:


 * Definition:Preimage of Element under Relation
 * Definition:Preimage of Subset under Relation
 * Definition:Preimage of Relation


 * Definition:Preimage of Element under Mapping
 * Definition:Preimage of Subset under Mapping
 * Definition:Preimage of Mapping

The plan is that if these redirects are used as the main link into these pages from other pages, if it is decided to refactor again (because the above structuring "doesn't work" for some reason) then minimal changes will need to be done from linking pages.

Also note I haven't addressed Definition:Inverse Image yet because I need a break ...--prime mover 05:33, 18 March 2012 (EDT)


 * Formally, Definition:Inverse Image should have the ref, as that's what Schilling says. From the context I'd say Definition:Preimage of Mapping should have the ref. --Lord_Farin 16:37, 18 March 2012 (EDT)

Could you please help?
Hi Lord Farin, I'm having quite a bit of trouble here. It is a response to your comments regarding the axiom of choice. If you could be of any help there, that would be really great. Thanks a lot. I hope you don't mind me posting this kind of message here. –Abcxyz (talk | contribs) 22:45, 26 March 2012 (EDT)
 * No, I don't mind, rather, I am delighted. What else could talk pages be for? Minor thing: the space in my username is preferably replaced by an underscore, but MediaWiki does not support this. This is because using a space instead of underscore makes my username a bit pretentious. But you are invited to abbreviate to LF ;) --Lord_Farin 03:13, 27 March 2012 (EDT)

Separate def and cat
I'm not sure. If it is a category that is being defined, I see no problem with including its definition on the actual category page. It was a deliberate direction I went in. (Okay, PropCalc probably shouldn't have been done like this, but for example Category:Naive Set Theory and Category:Symbolic Logic IMO should remain the way they are currently being rendered.

Feel free to argue your case ... --prime mover 06:35, 16 June 2012 (EDT)


 * In my opinion, a category is merely a structure, a means to collect similar results under a common denominator. As such, the category should (IMHO) be separated from the field it describes. Description of fields of research appears to me as a bona fide contribution to the Definition namespace. You will probably say that a 'field of research' is nothing more than (de facto) a category; to me, however, a 'field of research' is a collection of mathematical ideas going in the same direction, whilst a category on ProofWiki is nothing more than what we use to differentiate results and easily locate them - a backbone for the particular interpretation we give to mathematics on ProofWiki. But this is a rather abstract and arbitrary reasoning; perhaps the most compelling argument is that one expects definitions (i.e., descriptions) to be in the Definition namespace. In summary, an analogy: I view the research field as a book (say on the same field) while the category is but the index; I would like to keep them separated. --Lord_Farin 06:48, 16 June 2012 (EDT)


 * How about transclusion then? I'm rather fond of the idea of being able to click on a category and seeing its definition included. --prime mover 07:21, 16 June 2012 (EDT)
 * An acceptable (maybe even good) compromise. Feel free to implement. --Lord_Farin 07:24, 16 June 2012 (EDT)

Warning about FULLPAGENAME
Be wary about using the FULLPAGENAME technique in e.g. section titles. When they are transcluded, they automatically expand out into the name of the page you have transcluded that page into. So, for example: /Formal Grammar in the Definition:Language of Propositional Logic page will expand to Definition:Language of Propositional Logic/Formal Grammar but if you then transclude Definition:Language of Propositional Logic into Category:Propositional Logic it expands itself into Category:Propositional Logic/Formal Grammar for which there is no page. So suggest that as a general rule use the explicit page name rather than relying on the Mediawiki software to interpret it. --prime mover 10:11, 16 June 2012 (EDT)


 * That's a good point, better than mine. I use(d) that construct mainly as it is shorter and accommodates for any future moving of the page. But the transclusion hampering (well, technically it's a feature :) ) outweighs this possible benefit. Thanks for bringing it to my attention. --Lord_Farin 10:24, 16 June 2012 (EDT)

Union and Intersection
I have completely refactored these, into a total of 5 separate pages each, and I think I've sorted out the references accurately (nightmare job but now it's done). I draw your attention to Schilling, which may spread over several of these pages but I don't know because I don't have immediate access to it. Feel free to tidy up those refs. --prime mover 22:03, 27 June 2012 (UTC)


 * Though Schilling uses the general notation often, he doesn't introduce it, only the binary cases get special attention. I think the refs are fine as they are now. --Lord_Farin 22:07, 27 June 2012 (UTC)

Language quibble
I'm not certain about the usage of the phrase "very similar result". At school I was taught by a colourful character who told the anecdote of a newspaper editor who, when seeing the word "very" in a piece submitted by a journalist, would read it back to him and replace every occurrence of "very" with "bloody" (substitute the expletive of your choice).

Consequently, I'm not sure whether, in the context given:


 * Fubini's Theorem, a very similar result pertaining to integrable functions.

... the term "very" adds anything. If it is similar, IMO that is all that needs to be said:


 * Fubini's Theorem, a similar result pertaining to integrable functions.

Your thoughts? --prime mover 10:25, 17 July 2012 (UTC)


 * Agreed; it's just so (very :) ) tempting sometimes to use a lot of words... --Lord_Farin 10:53, 17 July 2012 (UTC)

Deletion of talk pages
Probably not a good idea to just delete talk pages - they go some way to explaining the various processes that have gone on while other contributors were (for example) asleep - even if the talk page itself says something like "Damn - I misnamed this. Can it be renamed?" and so on.

No worries now, I've worked out what happened, but it did confuse me for a moment. In this particular case the misnamed page "B Algebra is Right Cancellable" redirecting to "B-Algebra is Left Cancellable" is truly bizarre, so I'm redirecting it to where you would expect it to go. --prime mover 07:45, 20 July 2012 (UTC)


 * In the future I'll preserve talk pages for the sake of documentation. --Lord_Farin 14:36, 20 July 2012 (UTC)

Double redirects
I see your Definition:Composite Morphism redirecting to Definition:Composition of Morphisms and also that the latter in turn redirects to Definition:Metacategory. Such double redirects don't work (click on the first of these links and see what happens).

Recommend that Definition:Composition of Morphisms is instated as a page in its own right, rather than being a redirect to Metacategory, and if necessary be transcluded into that page. Otherwise Composite Morphism will need to be changed to redirect to Metacategory itself, which will cause confusion as and when Composition of Morphisms is eventually made into its own page.

All good fun. --prime mover 08:44, 16 August 2012 (UTC)


 * In the pipeline are: Definition:Object (Category Theory), Definition:Composition of Morphisms, Definition:Identity Morphism. Furthermore, an alternative definition of category (disposing of objects altogether in favour of identity arrows) is to be developed. I'll get there. --Lord_Farin 08:50, 16 August 2012 (UTC)

To not clutter PMs userpage
I am entering the second year of my course at university. Contributing to proofwiki.org and simple.wikipedia.org have taught me to explain myself better. I am currently creating a very clear summary of the material we will be taught in the analysis module of the first term. My intention is to upload the file here then direct the other people on my course to it and introduce them to proofwiki at the same time (to which I will attribute the rigor of the text).

A further (and more general) reason is that should something unspeakable happen anything of use I have produced for the mathematical community will be public domain.

The userpages are excellent but a self contained document is sometimes better.

--Jshflynn (talk) 23:39, 17 September 2012 (UTC)


 * If you want to produce self-contained documents, then the best idea is to put them in an account which you yourself maintain, and then they can be linked to. The whole idea of a wiki is that material on here can be edited.
 * Another point worth making is that ProofWiki is more akin to a dictionary, whereby one page is one definition / proof. It is usually the case that documents as you describe contain a whole series of such, bound together as a train of thought. Such would be better in an encyclopedia. There are plenty such in the internet domain already. ProofWiki is, if not unique, then rather more specialised in its approach. --prime mover (talk) 05:24, 18 September 2012 (UTC)


 * Google docs does not yet allow pdf documents to be shared. Until Google Drive is released I will use Issuu.com. My goal is that if a person were to type in real analysis .pdf onto google that this would be available to them. The content of the document will not be text book like (with prose and questions). It will just be proofwiki like but linearized for someone who wants the to go from A to B on the topic of analysis with the reading style of proofwiki. Here is a demonstration of what it may look like: (though it will be more readable than that hopefully).
 * --Jshflynn (talk) 07:20, 18 September 2012 (UTC)


 * To a certain extent, the backbone of the abstract algebra orginated as a 1300-page LaTeX document that I had written between about 2003 and 2008, so I can completely see where you're coming from.
 * If you see the links at the bottom of many of the long-established pages, you will see under the "Sources" the actual source works which were plundered to generate the bulk of the material in the first place. Note the "previous" and "next" links, which provide an insight into the original linear design of those works.
 * I can envisage something similar here. I'm not generally a fan of linking to external PDFs as source works, on the grounds that they can be ephemeral and subject to link rot, but I'm open to persuasion if this approach really does enhance the value of ProofWiki. --prime mover (talk) 11:55, 18 September 2012 (UTC)


 * I have noticed on a lot of the pages credit is given to Seth Warner's book 'Modern Algebra'. I have recently ordered this on line and am attracted to the work because it proves the constructions of the number systems $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$ and $\mathbb{R}$ are unique up to isomorphism. In seek your opinion on a few matters to help me write this document:


 * 1) Should a good introduction to analysis begin by constructing $\mathbb{R}$ from $\mathbb{N}$? Many books begin by immediately giving axioms for $\mathbb{R}$ but do not provide a proof that complete ordered fields are unique up to isomorphism (is it just not useful in an analysis course?)


 * 2) If it should begin this way. Should it begin with (a) the very algebraic construction of $\mathbb{N}$ as a naturally ordered semigroup or (b) with a Peano structure? (I have already been doing so with (b) but will try and change it to (a) depending on your opinion).
 * And of course, my apologies to L_F for carrying on a conversation here. Feel free to put in your two cents.

--Jshflynn (talk) 12:24, 18 September 2012 (UTC)


 * My primary analysis lecture notes contained a supplementary appendix concerning the construction of $\R$. This is generally sufficient because mostly analysis is taught before the formal foundations of mathematics are addressed. In this way, rigour is not sacrificed but one can get under way immediately with the subject of interest (real analysis) without having to plow through technicalities that a large portion of mathematicians (sadly) isn't interested in. I would suggest a similar approach. Peano structure is more insightful as it does not require the abstraction of a semigroup (which can come in as intimidating to new mathematics initiates). --Lord_Farin (talk) 13:04, 18 September 2012 (UTC)


 * Warner's good for abstract algebra. But if you want a way into Analysis, try an analysis text. The only basic one I have is the Binmore work, which starts with an informal definition of a real number:
 * "It will be adequate for these notes to think of the real numbers as being points along a straight line which extends indefinitely in both directions."
 * This may be adequate for you. Note that apart from some examples and exercises, and the last chapter, Binmore is (on ProofWiki) just about complete, so that may be a good place to start.
 * Note BTW that  \R, \N, \Z, \Q, \C  work on this wiki just as well as  \mathbb{R}  etc., and create far more streamlined code. (Not all letters can be treated like that.) Instances of  \mathbb{R}  etc. will be changed to  \R  etc. in pages. --prime mover (talk) 16:49, 18 September 2012 (UTC)

Properly name mathematicians
In general I agree, but on a talk page it's of less importance, yeah? --prime mover (talk) 08:14, 22 September 2012 (UTC)


 * True, but once one lets it slip for just a bit, it is all too common that such behaviour give rise to a less astute attitude when it actually matters. I understand where you come from, the UK keyboard not natively supporting diaereses, but it was an easy fix on the Dutch (i.e. US International) keyboard. No offense intended. --Lord_Farin (talk) 08:20, 22 September 2012 (UTC)


 * Where "astute" is not really the word I am looking for, but I'm having a (quite rare) struggle with a language barrier here. --Lord_Farin (talk) 08:22, 22 September 2012 (UTC)


 * I know what you mean and am having trouble myself (which I put down to old age): "conscientious"? "meticulous"? "rigorous"?


 * There probably is a quick and convenient technique for adding a diaeresis using this keyboard, but as diacritics are so rarely used in English the knowledge is not something which is widely spread. In fact, there is a suggestion that diacritic-less redirects are put in place on this site in order to facilitate finding pages which include such diacritics. --prime mover (talk) 09:55, 22 September 2012 (UTC)


 * If either of you are interested. This site is particularly good at making one's vocabulary seem inadequate. I can't believe there's such a word as "mathematicaster" :) --Jshflynn (talk) 12:59, 22 September 2012 (UTC)


 * Thanks for that link; most interesting. After some hours I think I want to convey "vigilant" or some other stronger form of "attentive". --Lord_Farin (talk) 15:01, 22 September 2012 (UTC)


 * Argh - timesuck alert! Must resist ... --prime mover (talk) 21:32, 22 September 2012 (UTC)

Multi-proof pages for proplog theorems
I fully note that there are many pages in Propositional Logic which have more than one proof on them. Please don't feel you have to note them all with a Refactor. I will in due course be getting round to them when I reach my books on logic in the nest of paper-based products that forms the "office" in which I work. If you want to add Refactor to them, feel free to - but rest assured I will be on the case. Just not this week, we have a project delivery on Friday and we still have some interfaces as yet unfinalised ... --prime mover (talk) 20:37, 6 November 2012 (UTC)


 * My adding of refactors is (as you have undoubtedly noted) fully characterised by the pseudo-random variable LFMouseClick. I won't be hunting down pages needing attention systematically, only on a per-encounter basis. Good luck with your project deadline. Considering the amount of sources you added to PW, and looking at my own desk, I can only imagine what a mess yours must be :). --Lord_Farin (talk) 20:40, 6 November 2012 (UTC)


 * See my user talk page ... --prime mover (talk) 20:53, 6 November 2012 (UTC)


 * XD lol. Impressive collection by the way. Although I suspect mine will grow too in the course of the coming years, when my bank account facilitates it. I'm sure it'll increase a lot when I leave my parental refuge... --Lord_Farin (talk) 21:03, 6 November 2012 (UTC)

Request
In section 1.17 in the documentation of the xymatrix is something that looks like a finite automaton. I can't seem to get it to work as it says there is an error on this line:

\ar ‘dr_l[l] ‘_ur[l] _a [l]

Could you post the diagram here for me so I have something to build on. Thank you. --Jshflynn (talk) 16:40, 9 November 2012 (UTC)


 * I think the issue is due to the fact that your apostrophe ‘ is different from mine `. The xymatrix sample page at http://sonoisa.github.com/xyjax/xyjax.html (particularly the last one (XymatrixFeature)) provides insight in sonoisa's implementation. I think I discern in the code (which I don't fully understand as I'm not an expert at xypic/xymatrix either) that my apostrophe is to be used. It could be that you have to change your keyboard layout in your OS to be able to type the correct apostrophe. If this doesn't solve the issue then you know where to find me. --Lord_Farin (talk) 17:59, 9 November 2012 (UTC)

Symmetric Difference
The Definition:Symmetric Difference page now has two complementary definition pages, one of which is relevant for : $\S 2$: Problem $2$ - feel free to adjust the citations appropriately. --prime mover (talk) 21:23, 12 December 2012 (UTC)


 * Fixed; thanks for the heads up. I've removed the WIP indications. --Lord_Farin (talk) 21:32, 12 December 2012 (UTC)

I messed up
Hiya, I created Exponential of Sum/Complex Numbers and then I was going to write the proof, but I messed up and it turns I don’t actually have a solid proof that works. Should I leave the skeleton page around? If not, what else do I do? — Timwi (talk) 15:46, 13 December 2012 (UTC)


 * In this case, I think it'd be best to simply put a call to Template:Stub in place of the proof. The result is true, so no need to destroy it. --Lord_Farin (talk) 15:50, 13 December 2012 (UTC)

Done
I finished the changes on Sine of Sum/Proof using Exponential Formulation and Cosine of Sum/Proof using Exponential Formulation. — Timwi (talk) 15:51, 13 December 2012 (UTC)
 * Tidy tags amended accordingly. --Lord_Farin (talk) 15:53, 13 December 2012 (UTC)
 * So what “minor TeX house style” changes are still missing? — Timwi (talk) 16:06, 13 December 2012 (UTC)
 * Some code style; I have fixed the coding of the eqn templates (look at the changes to see what I mean, it's rather involved to explain and immediately apparent). All that remains now is left-right fuss. --Lord_Farin (talk) 16:09, 13 December 2012 (UTC)
 * OK done. — Timwi (talk) 16:16, 13 December 2012 (UTC)
 * You had missed a few instances of brackets, I've fixed them up; otherwise, good work, tidy tags removed. --Lord_Farin (talk) 16:27, 13 December 2012 (UTC)

Out of curiosity, what difference does the extra curly inside \left(...\right) make? It seems to display the same... — Timwi (talk) 16:17, 13 December 2012 (UTC)


 * The curly braces are grouping indications for TeX; they serve to ensure that every \left is paired with the intended \right</tt>. Especially when using an external editor (e.g. via the Firefox plug-in It's all text) that highlights matching braces, such can greatly simplify the frustrating search for an occasional omitted or excess brace. --Lord_Farin (talk) 16:27, 13 December 2012 (UTC)


 * Do you really need \left({ ... }\right) for every parenthesis, even things like $\sin(2x)$ and $(2n)!$?... — Timwi (talk) 17:53, 13 December 2012 (UTC)


 * We enforce it to avoid problems with copy-pasting and subsequent editing of stuff inside parentheses. In this way, the parens will always size appropriate to their content, even if that content vertically grows or shrinks due to changes. Equation references like $(1)$ and $(3')$ are excepted from this admittedly strict style rule. --Lord_Farin (talk) 17:57, 13 December 2012 (UTC)

Fixing the links to Sine and Cosine of Sum
Now that I’ve split this page, I went and fixed all links to it. However, a couple are left: One of them is at the bottom of Sum of Squares of Sine and Cosine in a book reference (the “prev” value); and the other is in a tidy-up tag in Sine and Cosine of Complementary Angles, which I don’t understand what it’s saying. Wanna take a look and fix? Then the split is complete :) — Timwi (talk) 17:25, 13 December 2012 (UTC)


 * Oh, another one: Derivative of Sine Function/Proof 1 — Timwi (talk) 17:29, 13 December 2012 (UTC)


 * I take it that PMs note on your talk settled the matter. Notifying me (or PM, doesn't really matter) is however a good step in general when you're in doubt. --Lord_Farin (talk) 17:42, 13 December 2012 (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) 15:37, 15 December 2012 (UTC)