User talk:Lord Farin

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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)