User talk:Lord Farin

Template for Gentzen proofs?
Since we have a template for non-Gentzen tableau proofs, it might be worth constructing one for the new Gentzen ones you're constructing at the moment. It should save some considerable effort and page space. What say? --prime mover (talk) 15:05, 2 April 2014 (UTC)


 * I don't expect many proofs in this style, since even Ben-Ari tries to move on to different proof systems quickly. It is not a proof system that is very common or popular (other Gentzen systems are, however). I deem it wise to not create a template specifically for this proof style.


 * Nonetheless, given that we can expect more and more proof systems in the future, it might be a good idea to generalise Template:BeginTableau to arbitrary proof systems, and provide a generic template which can act as a semantic hull around the MediaWiki syntax, just like Template:Eqn and Template:Axiom do. This will make it easier to adapt to future needs. &mdash; Lord_Farin (talk) 17:36, 2 April 2014 (UTC)


 * More challenging ... I'm not immediately planning on doing all that much more in this area (I only raised it in the first place so as to have something to plant ZFC in back in 2008 and it all got a bit unwieldy) so for the moment I'll leave this until I have another manic episode. --prime mover (talk) 19:28, 2 April 2014 (UTC)

Boolean Algebra
I have been investigating the "Wanted Pages" list and clearing out dead links to superseded pages. One such is Category:Boolean Algebra, where there is still a link from the Definition:Algebra page. Is it appropriate to replace this with Definition:Boolean Algebra in your opinion, or to remove it from that particular list in which it appears? --prime mover (talk) 08:23, 2 May 2014 (UTC)
 * ... or indeed replace with Category:Boolean Algebras? --prime mover (talk) 08:27, 2 May 2014 (UTC)


 * I think it'd be best to remove it. A link to Definition:Boolean Algebra could be added to the "Algebra (Abstract Algebra)" subpage. &mdash; Lord_Farin (talk) 21:11, 2 May 2014 (UTC)

Big refactoring job on Warner thread
I see the good work you're doing on the refactoring the Naturally Ordered Semigroup stuff I did way back when (some of the earliest stuff I posted up). It's going to be a while before I get to reviewing the citation flow (and I don't really want to make a start until I'm fairly sure you're finished) so request the pages flagged up for deletion be retained till after that's been done.

I want to get as much of this tedious Euclid topped off before I go any further with anything else, so bear with me for the moment. In the meantime, good work! --prime mover (talk) 22:38, 19 January 2015 (UTC)


 * Thanks. It's satisfactory to put everything I have prepared into place, and it's going much smoother than I anticipated. I'll give you a note when I think I'm finished. I'll write up new proofs in the process so as to connect with the other axiomatisations, but that shouldn't hurt Warner too much. Don't expect things to be perfect the first time around, but I should be able to put up a correct architecture that we can build upon. &mdash; Lord_Farin (talk) 22:44, 19 January 2015 (UTC)

Templates
I would rather that you hadn't deleted all those templates. I know they were sitting around not doing much, but I had plans for some of them -- particularly "Authorship" and the various "Syllogism" templates. Not sure where I was going with BookRef but I know it started as a good idea. Could we have these back, or do you have good reasons for keeping them deleted? --prime mover (talk) 21:13, 1 March 2015 (UTC)


 * You can have them back, but since some of them had been sitting idle for more than a year, I figured any plan for using them would amount to starting from scratch anyway, so a round of cleaning wouldn't be bad. But sure, restore what you'd like. Perhaps a good idea, though, to keep this kind of early-stage idea in your sandbox &mdash; makes it that much clearer that it's something you plan working on some day, or at least the call to drop it is all yours. &mdash; Lord_Farin (talk) 21:57, 1 March 2015 (UTC)


 * Okay good call, I'll get on with doing that. Be aware though, a year is a short time in ProofWikiLand ... --prime mover (talk) 22:15, 1 March 2015 (UTC)

Lots of source reviews
Yes, as you see I am splitting down composite pages into their simple component parts -- which leaves a considerable amount of redirecting the source flow.

If you find you no longer have the patience for this minute level of detail, then as far as I'm concerned it's no problem to leave the source flow merely landing on the parent page (particularly in the case of De Morgan).

Have fun. --prime mover (talk) 23:10, 24 March 2015 (UTC)


 * I've taken out most, but the last few require me to dig up five sources. This is beyond my patience now. I will get to it eventually. &mdash; Lord_Farin (talk) 18:30, 25 March 2015 (UTC)


 * All is done. &mdash; Lord_Farin (talk) 22:40, 26 March 2015 (UTC)


 * Good job. I am myself working methodically through Warner. I should reach the Natural Numbers in a week or so -- if I don't get sidetracked by something that needs fixing or that got missed and needs elaboration. --prime mover (talk) 22:56, 26 March 2015 (UTC)

Question about Definition:Smallest/Ordered Set
Back in December 2013 you placed an "expand" template onto Definition:Smallest/Ordered Set saying:
 * Some links to this page are actually referring to the smallest element of a subset. This has to be defined, and the links changed to the resulting subpage.

I've looked at this, and raised such a subpage Definition:Smallest/Ordered Set/Subset, but I'm unclear as to how well this serves us.

After all, a subset is a set, and has the same properties as a set, and so the smallest element of a subset is defined in the same as the smallest element of a general set -- whether that set is a superset of it or not.

Hence a page containing something like "the smallest element of $T$ where $T \subseteq S$" is equally well served by Definition:Smallest/Ordered Set as it is to a separate page defining the concept of "smallest" in the specific context where the set in question happens to be the subset of an ordered superset. None of the works I have raise it in a separate definition (however I see you have access to the Munkres and Birkhoff works which I don't, so while I can't check them, maybe you can).

The only circumstance I can think of where the concept may be worth separating out and emphasising is the one where $S$ is partially-ordered while $T$ is totally ordered -- but we have that covered by the page Definition:Chain (Set Theory).

Can you take a look at this and add some thoughts? I should have asked the question at the time, but back in Dec. 2013 I was freezing my nuts off in $-10^\circ \mathrm{C}$ blizzards, and the brain was less well disposed to think about it. :-) --prime mover (talk) 08:34, 5 April 2015 (UTC)


 * The most apparent definition arises in the context of a woset. While it is ultimately the same definition, a reader may fail to recognise that the ordered set one is talking about is actually the subset.


 * One might add that Munkres explicitly defines this on subsets. It is also relevant in the intuitive coupling of largest element and supremum.


 * I'm pretty sure, though, that Munkres triggered me to create the expand template. Does that address your concerns in an adequate manner? &mdash; Lord_Farin (talk) 21:55, 6 April 2015 (UTC)


 * Okay, given that I'm unfamiliar with the Munkres, has the treatment I have offered on the subpage I added consistent with his treatment? --prime mover (talk) 22:01, 6 April 2015 (UTC)


 * Most definitely, although he doesn't bother with the formalism of writing $\preceq \restriction_T$. &mdash; Lord_Farin (talk) 22:39, 6 April 2015 (UTC)

mathbin, mathrel, mathop
Recommend we go through and change "mathop" to "mathbin" and "mathrel" as appropriate, as we progress? I confess it's not a job I fancy doing in one go. :-) I picked up on the differences when I went through the work on TeX codes at the weekend, so I'm fairly well up to speed on it and I appreciate that it "ought" to be done, but it's not something I can nerve myself up to.


 * Gradual seems like just fine to me. Or "as noticed". &mdash; Lord_Farin (talk) 21:56, 7 April 2015 (UTC)

While I'm here, I wonder whether the "mathbin" entries on Inverse of Order Isomorphism is Order Isomorphism should actually be "mathrel" as $\preceq_1$ etc. is technically a relation not an operation. What say? --prime mover (talk) 18:13, 7 April 2015 (UTC)


 * It was a subconscious thought after changing that page (among others) that this was actually wrong that triggered me bringing this up in the first place. I have fixed it.


 * Further investigation ... in places where we have  and so on, we can in fact just remove the mathop altogether, and just have , because it appears that MathJax may have fixed the bug whereby subscripted relations were not being treated as relations.


 * Check out:

So not only is mathop now demonstrably different from and inferior to mathrel, mathrel is not even needed.

IIRC the reason we started using mathop in the first place was because it was the only one of these modifiers that had actually been implemented on MathJax adequately at the time. The new version of MathJax seems to have resolved all of this. --prime mover (talk) 06:44, 8 April 2015 (UTC)


 * Awesomeness (TM). &mdash; Lord_Farin (talk) 14:59, 8 April 2015 (UTC)


 * ... although another reason we started using mathop was to put some spacing between summation limits. Neither mathrel nor mathbin do the job here, only mathop does what we want it to:








 * --prime mover (talk) 14:58, 8 April 2015 (UTC)
 * --prime mover (talk) 14:58, 8 April 2015 (UTC)


 * Hmm... Some cursory search and testing have convinced me that continuing to use \mathop is the way to go, although it is not an elegant solution. There is simply no other option I know of, except manually fiddling around with spacing. &mdash; Lord_Farin (talk) 15:18, 8 April 2015 (UTC)

NOS
I have finally reached the Naturally Ordered Semigroup chapter of Warner (having hurried through the chapters on Ordering without completing all the outstanding work -- I'll return to that later). Note that I am checking the pages off on your User:Lord Farin/Sandbox/NN Refactoring‎ page as I go, particularly when I delete stuff that has a delete mark against it. You may want to follow along behind and check I'm not breaking stuff. --prime mover (talk) 21:00, 10 April 2015 (UTC)


 * Thanks. Looking good. If I now can muster the energy to work through the off-line list I have compiled for MISS, we might actually get somewhere with this project. &mdash; Lord_Farin (talk) 08:37, 11 April 2015 (UTC)

Families
Advice needed on where to go with this one.

Munkres is the only author I've seen who defines the terminology of indexing sets using definitions which are intuitively clear:


 * a) An Definition:Indexing Function is the actual mapping from $x: I \to S$
 * b) A Definition:Indexed Family is the set of elements of $S$, together with the mapping itself.

Every other source I've seen calls the mapping itself the "family", despite giving it the intuitively-suggestive notation $\langle x_i \rangle$ (or whatever notation used).

Consequently I have decided to go with Munkres's definition, despite the fact that he appears to be in a minority.

Or do you see this as: everybody else has failed to define the concept precisely enough, and has made a mistake by failing adequately to distinguish between the mapping itself and its codomain?

It is also interesting that Munkres is the only one who specifies that the mapping itself needs to be a surjection -- a point which I still have yet to address in the definitions.

As a practical matter, however, I have changed the links on Halmos and Givant so as to allow it to point to Definition:Indexing Function instead of Definition:Indexed Family. You may wish to review this in order to make sure the flow accurately reflects the specific treatment of Halmos and Givant here: do they define a "family" as the mapping, or the mapping together with its codomain?

I also need to consider whether to include the "also defined as" on Definition:Indexing Set/Family on a separate page and then transclude it onto other pages in the same way as Notation and Note on Terminology.

Are you able to cast an eye over this area? I just need a second opinion on it. Thanks. --prime mover (talk) 09:09, 25 April 2015 (UTC)


 * There are basically two points of view at work here which are conceptually quite different. The majority of writers takes the indexing set $I$ as the starting point; from this point of view, it is more natural to define the concept in the way they do (e.g. Halmos/Givant do it in this fashion), as simply the function $x: I \to S$.


 * On the other hand, we have Munkres (and it's inconceivable he is alone). The viewpoint now is radically different: We start with a set $S$ (in Munkres' case, a set of sets), which we want to index. In this view, it makes sense to bring $S$ along explicitly, and to require an indexing function to be surjective -- after all, it was not merely a subset of $S$ that was to be indexed.


 * With this in mind, I think it is not warranted to choose between the two. Rather, we should aim for an exposition that somehow manages to unify these treatments. I'm sorry to burden you with this task, but ultimately I think this is the best way to go. &mdash; Lord_Farin (talk) 09:53, 25 April 2015 (UTC)


 * Are you happy with the approach which I have just taken? --prime mover (talk) 21:49, 26 April 2015 (UTC)


 * Except for the note I left on one of the talk pages, the content looks good. Regarding presentation, it is maybe a bit awkward to have Indexing Set as the master page. Perhaps Indexed Family ought to be the parent page, with all related concepts as subpages; in this way, subpages will describe portions of the entire thing, which is the Indexed Family. (But I understand if you don't want to embark on that journey right now.) &mdash; Lord_Farin (talk) 08:08, 27 April 2015 (UTC)


 * You're right, it does appear as thought "indexed family" is the main concept, and all the other parts of it should perhaps be subpages. It's not quite as big a job as it looks on the surface, though, because our redirect strategy is a good one. --prime mover (talk) 15:31, 27 April 2015 (UTC)


 * All instances of Definition:Family have now been reviewed and replaced by a link to the appropriate instance of "indexed family", be it "of sets" or "of subsets" or neither. Time for a break; Definition:Family can now become a disambiguation page as suggested in a conv with Joel on Definition talk:Indexing Set/Function a while back. --prime mover (talk) 20:03, 27 April 2015 (UTC)

Abstract Algebra and all that malarkey
I'm getting terminally bogged down in the Abstract Algebra work from Warner, so I am going to take a break from it and work on something else for a bit. I have a yearning to start something new, or continue from where I left off, as this maintenance and refactoring is starting to give me nightmares.

If you have any inspiration as to how to clean up the mess that is the recursive definition of the general $n$th power of an element that I abandoned so cruelly last week, then please feel free to succour and nurture it back to health. --prime mover (talk) 16:04, 3 May 2015 (UTC)