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)