User talk:Lord Farin

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:Propositional Calculus page will expand to Definition:Propositional Calculus/Formal Grammar but if you then transclude Definition:Propositional Calculus into Category:Propositional Calculus it expands itself into Category:Propositional Calculus/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 Exponent 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. 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)

Orderings on products
I'd like to merge the current Definition:Ordered Product and Definition:Lexicographic Order, extend them to well-ordered index sets, and rename them Definition:Lexicographic Ordering. What's the right way to do such while preserving history, avoiding confusion, etc.? I think Definition:Ordered Product should probably become something of a disambiguation page, pointing to Product Order and Lexicographic Order. --Dfeuer (talk) 21:58, 18 December 2012 (UTC)


 * These will be edits that hit a substantial amount of PW. Therefore, it's probably best to first set up the stuff in e.g. your sandbox area. That way, we can tweak and adjust all we want without affecting the main wiki with immature or incomplete material. I've done this in the past, can't remember what section of the site it was, but it worked quite well. --Lord_Farin (talk) 22:13, 18 December 2012 (UTC)


 * Found something thornier: the site already has a somewhat different notion of lexicographic ordering, which is not on products at all but essentially on strings whose letters are drawn from a single totally ordered set. So I guess we need two different kinds of lexicographic orderings? The kind on strings appears to be isomorphic to a special case of the one on products, since all that's needed is a product using the naturals as the index set, where the totally ordered underlying set is augmented with a new least element, or so I figure. Dfeuer (talk) 01:09, 19 December 2012 (UTC)


 * The one on strings indeed appears to be a special case (similar to $\R^n$ being a special case of Cartesian product). The two are conceptually sufficiently distinct that I'd advise for them to be separate sections (a set-up like Definition:Continuous Mapping, where the real and topological versions are both mentioned). --Lord_Farin (talk) 08:52, 19 December 2012 (UTC)

Can you take a look at User:Dfeuer/Definition:Lexicographic Ordering on Product and the pages it links to? I think they're a decent start on the lexicographic side of things. --Dfeuer (talk) 07:47, 21 December 2012 (UTC)


 * Definition appears to be correct information-wise, and is nice, very general :). However, it's not up to house style (yet). Do you want me to fix that? --Lord_Farin (talk) 15:27, 21 December 2012 (UTC)


 * You're more than welcome to. Small annoyance: there's a page stating (and beginning to prove) the theorem that the lexicographic ordering of the set of all finite sequences on a well-ordered set with at least two elements is not a well-ordering. A similar result holds for lexicographic orderings on products of infinitely many well-ordered sets, each containing at least two elements, and the proof is essentially identical.
 * However, because encoding the finite sequence set as a subset of the product expands each well-ordered set to
 * at least three elements, neither theorem seems to imply the other. Can you think of any nice way to hit both at once, or do we need to keep them separate? --Dfeuer (talk) 16:18, 21 December 2012 (UTC)


 * I think they'd best remain separate. It would be a good idea (and probably not too hard) to try and give a proof of the finite-sequence version with the more general version. --Lord_Farin (talk) 17:37, 21 December 2012 (UTC)


 * I'm not convinced the product version really is strictly more general. I suspect that generalizing "finite sequence" to "set of ordinals less than $n$" may offer a generalization in which the product version can be embedded. --Dfeuer (talk) 22:31, 21 December 2012 (UTC)

Deterministic Time Hierarchy Theorem
Hiya Lord Farin Lord_Farin, I’ve finished reworking Deterministic Time Hierarchy Theorem to conform to the house style and everything. Would you like to take a look and tell me how I did? Thanks :) If this is good, then I think I got the hang of it, so I think I can stop pestering you :) — Timwi (talk) 02:41, 19 December 2012 (UTC)


 * As far as house style goes, it appears to be up to standard now. However the proof itself still lacks rigour and links. This may be due to the field in which the result resides not being covered in enough detail yet. I'll try to keep looking through your edits, but what errors/mistakes you still make appear to be more due to overlooking than a structural flaw in your approach. Of note is that the  command is to be used only when there are operators needing subscripts or appropriate sizing (see Help:Editing for more details); fractions can be covered by  . Cheers! --Lord_Farin (talk) 15:27, 21 December 2012 (UTC)

Product of Ring Negatives: citations
I draw your attention to the fact that Product with Ring Negative has been renamed from Negative Product and split into two. The references from : $\S 1$: Exercise $6$ will therefore need to be adjusted - presumably (as with every other presentation of this material I've seen) Product with Ring Negative directly precedes Product of Ring Negatives. All yours. --prime mover (talk) 09:52, 23 December 2012 (UTC)
 * Amended; thanks for the note. Product of Ring Negatives isn't covered. --Lord_Farin (talk) 22:00, 23 December 2012 (UTC)

Help merging
Hey, could you help me out a bit with the merges I requested for Set Contained in Smallest Transitive Set (where I goofed up and created a second page because I didn't find the first one) and Induction on Well-Ordered Set (where there are two unrelated pages for the result for sets and for classes)? Or should that second one be just an extra rename and some linking? --Dfeuer (talk) 00:16, 30 December 2012 (UTC)


 * I'll look at it tomorrow. Bed's calling. --Lord_Farin (talk) 22:36, 30 December 2012 (UTC)


 * I have ideas for the former, hopefully Asalmon agrees; after that I'll merge the pages. The second one indeed comprises two results that are in different realms. Not sure how to approach that at this point. Again, there is a lot of substandard work in the area and I feel it's a bit pre-emptive to start refactoring parts of it when it's up for a thorough passing over altogether. So I'm inclined to let that rest at the moment. --Lord_Farin (talk) 11:39, 31 December 2012 (UTC)

Integer Addition properties: citations
The pages Integer Addition is Commutative and Integer Addition is Associative have been refactored into separate proofs. I note a citation for Halmos and Givant on both of those - you might want to check they are on the appropriate pages. --prime mover (talk) 13:31, 31 December 2012 (UTC)
 * Done; the stuff serves merely as motivation for introducing rings and is deemed known, not proven. --Lord_Farin (talk) 13:35, 31 December 2012 (UTC)