User talk:Prime.mover/Archive 5
This is an article of past discussions, from 7 March 2013 to 21 October 2014. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Contents
- 1 New template
- 2 A friendly thought
- 3 History Question
- 4 Is it possible to delete spambot accounts?
- 5 Logic
- 6 Edit in Geometric Distribution
- 7 Please help me to complete this proof
- 8 Where to tidy
- 9 Does it make sense to...?
- 10 What can I do?
- 11 If you do not mind (since I asked a lot of questions)
- 12 How do I know
- 13 About new proofs
- 14 About new page
- 15 Proofreading of new Definition:Formal Language
- 16 My sandbox
- 17 Definition:Trivial
- 18 Logic refactoring
- 19 AI Mashup Challenge
- 20 How to do this?
- 21 Definitions and constructions of the number sets
- 22 Millman/Parker: Geometry: A Metric Approach with Models
- 23 Oliver Heaviside
- 24 General thanks
- 25 Top Stubs
- 26 Restriction continuous
New template
The merit of Template:SourceReview is immediately apparent. Good call. — Lord_Farin (talk) 22:44, 7 March 2013 (UTC)
A friendly thought
I know we're not on the best of terms, but here's a purely friendly suggestion anyway. Since you enjoy logic, you may also enjoy reading about programming language type systems if you haven't already. Type checking and type inference for type systems with parametric polymorphism are particularly interesting. The Glasgow dialect of the Haskell programming language manages to do almost magical things with its type system extensions, and Chris Okasaki (best known for his book Purely Functional Data Structures) and Ralf Hinze are two of the masters at exploiting these features to enforce complex invariants at the type level. See for example Okasaki's paper "From Fast Exponentiation to Square Matrices: An Adventure in Types". --Dfeuer (talk) 18:46, 13 March 2013 (UTC)
- I'm not a fan of Haskell. Having been programming professionally in the software industry for the last 30 years I find I have less and less patience with the effort to takes to learn a new language. I understand that academics may be able to learn all sorts of exciting things by building a language specifically designed to examine this or that, but when you have a customer who won't pay the bill this "this precise effect" is achieved, your emphasis is more on getting the job done than "let's see what fun I can have learning this stuff".
- Hence my intolerance of sloppy coding and lack of adherence to house styles. There is a reason for imposing a style - it's to ensure consistency of approach which minimises the time taken to get up to speed with another person's code.
- I don't actually enjoy logic - but in order to establish the minimal requirements to be able to create the axioms from which the number systems could be established foundationally, I had to put the logic pages together. Dirty job but someone had to do it. --prime mover (talk) 19:15, 13 March 2013 (UTC)
History Question
I have recently noticed that you have been enforcing the standard that $\mathsf{Pr} \infty \mathsf{fWiki}$ is to be an almost entirely source based work. An archive of mathematics as opposed to an experimental ground for research.
I have no favourability towards either as both have their place in the world.
But I wonder as looking on waybackmachine.org it seems that PW was not always like this. On Jan 2010 for instance there were only 10 books in the database.
I would like to know what the primary motivating factors behind this shift towards such high standards were:
- Were people posting poor proofs, invented definitions?
- Was there a high level of internal inconsistency that necessitated it?
- Or was it something more?
--Jshflynn (talk) 11:35, 14 March 2013 (UTC)
- It just seems to make sense. Any mathematical result worth a damn has been published somewhere in some form. With the exception of making explicit some trivial results which are glossed over in the literature, that's about how it is.
- Recently there has been a trend towards posting up a considerable number of often trivial generalisations of useful working results for no real reason but that the result could be proved. My argument is: unless you're specifically trying to get to something profound, and need it as a stepping-stone, there's limited reason to do so. It was instantly countered that I was spending all my time on propositional logic which is by definition trivial, pointless and a completely solved sytem so who am I to lay down the law?
- As regards the argument about definitions, well yes, any statement which is equivalent to an existing definition can be used as a definition, but (in many cases) why would you want to? What would be the point in listing a large number of equivalent definitions of an ever more tortuous nature, merely citing the letter of law of some ad-hoc ruling that "equivalent statements are treated as definitions"?
- Therefore, unless it can be found in the literature as a definition, such equivalences are not taken to be definitions. I don't care how clever a contributor thinks he is - unless responsible for a considerable body of published material, appropriately peer-reviewed and corrected for both accuracy and usability, one's own made-up maths is not going to be treated with the respect that published works are. Because odds-on bet you will find something in a published work that duplicates your own work.
- Unless, of course, you have genuinely invented a result which is a) profound and b) you really cannot find it published anywhere. --prime mover (talk) 11:59, 14 March 2013 (UTC)
Is it possible to delete spambot accounts?
Some of these spambots take perfectly sensible names that a legitimate human might potentially want to use some day. Is there a mechanism for deleting the junk accounts to free up their names? --Dfeuer (talk) 06:34, 27 March 2013 (UTC)
- dunno --prime mover (talk) 06:38, 27 March 2013 (UTC)
- It's possible, but it's not simple. --Joe (talk) 11:00, 27 March 2013 (UTC)
Logic
In your big logic refactoring project, have you determined how you want to deal with Boolean-valued models, predicate logic, or modal logic? --Dfeuer (talk) 07:11, 3 April 2013 (UTC)
- In due course. --prime mover (talk) 07:41, 3 April 2013 (UTC)
Edit in Geometric Distribution
Hello there, I noticed an edit you had made on Definition: Geometric Distribution. You changed $Im(X)$ to $\Omega (X)$, which is incorrect, since $\Omega$ is the set of outcomes in the probability space, and the discrete random variable $X$ is a function from $ \Omega \mapsto A $, or some subset of the real numbers. I think what you had intended is $X(\Omega)$, which denotes the range of $X$. Fs (talk) 04:45, 13 May 2013 (UTC)
- The usual way we call attention to such things is with the mistake template. Just write something like {{mistake|So-and-so is wrong because blah blah blah and it should probably be thus-and-such instead.}} Watch out for math inside said template—it will not take kindly to curly braces or vertical bars. --Dfeuer (talk) 04:18, 13 May 2013 (UTC)
- Good call. If you find any more like that, feel free to change them to $\operatorname{Im} \left({X}\right)$ or $X \left({\Omega}\right)$ or $\Omega_X$ (which might have been what I wanted to put). Long time ago. --prime mover (talk) 05:08, 13 May 2013 (UTC)
Please help me to complete this proof
I cannot figure out how the sixth step evolved to the seventh step in here, and please help me to complete this proof. Many thanks. Kc kennylau (talk) 12:43, 3 July 2013 (UTC)
- It is safe to assume that we administrators keep an eye on one another's talk page. If you do feel the need to address everyone at once, please consider using Help:Questions (or if that doesn't work, Talk:Main Page). — Lord_Farin (talk) 13:59, 3 July 2013 (UTC)
Where to tidy
Could you please tell me what should I tidy instead of just give me the tidy template? Many thanks. Kc kennylau (talk) 06:14, 4 July 2013 (UTC)
- The template is an indication for experienced users that the page is not up to house style (which undoubtedly has some exponents not documented in Help:Contents and its subpages). You shouldn't worry; we're not expecting you to tidy, but rather someone else, when they get to it. The fact that no specifics have been given (usually) means that the whole page should be reviewed (but not necessarily changed). — Lord_Farin (talk) 07:15, 4 July 2013 (UTC)
Does it make sense to...?
Do you think it will be better to transclude 1+1 = 2#Theorem to 1+1 = 2/Proof 1 and 1+1 = 2/Proof 2 so that we do not need to change three page each time? (Don't worry, I'm not going to do any more maintenance job before asking) --Kc kennylau (talk) 11:19, 8 July 2013 (UTC)
What can I do?
Forgive me if you think I have asked too many questions these days (coz imma newbie). Well, obviously, I ain't gonna create tons of new proof (coz I hardly have any new idea except 1+1 = 2). In CP, I am suggested to do maintenance job on {{stub}}
, {{proofread}}
, {{tidy}}
and {{explain}}
. Therefore, I would like to ask for your suggestions, whether newbies like me are capable of doing these jobs (coz I dun wanna be scolded again, just sayin'). --Kc kennylau (talk)
- The recommended approach, as I may have said on another occasion in a different thread, is to pick either a) an area of mathematics with which you are familiar, and/or b) a particular textbook on a topic again with which you are familiar, and work through from fundamentals up till you lose the thread. Even in an area of mathematics which has been well-covered, it is usual that there will be a nugget of information in every text which cannot be found elsewhere.
- As has been stated before, maintenance work is best left to experienced editors. We are part way through an exercise to restructure the entire site, so that all pages will be in a consistent form.
- If you can complete proofs which are in "stub" status, or you have the appropriate skill to address the pages at "proofread" status, or you can fill in details for pages that have "explain" tags in them, then feel free. Please don't attempt to do "tidy" tasks as your writing style is very far indeed from approaching the standard we require for house style (hint: use the space bar and return key a little more frequently - source code with no breaks in it is difficult to read and maintain). --prime mover (talk) 14:30, 8 July 2013 (UTC)
- Thank you for your suggestions :D--Kc kennylau (talk) 14:32, 8 July 2013 (UTC)
If you do not mind (since I asked a lot of questions)
I would like to ask you to stop reverting my edits without any reasons, since this act is very discouraging. --Kc kennylau (talk) 14:52, 8 July 2013 (UTC)
- If an edit has no merit, and does not improve the content of a page, it will be reverted. --prime mover (talk) 18:54, 8 July 2013 (UTC)
How do I know
How do I know when I become an experienced editor and when I do not fail to follow the house styles and when I am able to do maintenance job? --kc_kennylau (talk) 09:36, 12 July 2013 (UTC)
- When a page to which you have contributed is subsequently edited, take note of the changes that have been made to the work you have done.
- Some people seem to pick up this site philosophy seemingly by instinct, as they are immmediately able to produce pages which are completely conformant to house style.
- Others never ever seem to get the idea, and still others do not accept the style rules, thereby making it necessary continually to clean up after them.
- It all depends on which category you fall into. Unfortunately, skills and experience in contributing to other wikis are not always transferable; standard practice on e.g. Wikipedia is frequently not standard practice on $\mathsf{Pr} \infty \mathsf{fWiki}$. Equally unfortunately, we have found that in some cases, the contributors who consider themselves "experienced" Wikipedia editors often seem consider themselves experienced contributors to $\mathsf{Pr} \infty \mathsf{fWiki}$ as well, whereas in fact they are usually not. On such misunderstandings hinge many conflicts of personality, particularly with younger contributors, in whom the Dunning-Kruger effect can be seen to operate. --prime mover (talk) 10:55, 12 July 2013 (UTC)
- You will know you are competent when the work that is needed to bring your pages up to style is less than the work needed to write the page in the first place. --prime mover (talk) 10:55, 12 July 2013 (UTC)
- Thank you for writing to me. I hope that you will not get annoyed by the amount of questions I have asked. I look forward to cooperating with you and contributing more and more in $\mathsf{Pr} \infty \mathsf{fWiki}$. --kc_kennylau (talk) 11:00, 12 July 2013 (UTC)
About new proofs
I am not trying to be sarcastic. I say what I mean and I mean what I say. I would like to ask about what I should do when I am creating new pages, since I would be misunderstood to be refactoring when I actually am trying to merge my proof into the existing single-proof page. According to the house style, I must move the proof to a new subpage and add my proof to another subpage. Should I follow this rule, or should I put my proof directly on the page, and leave all the works for others to do instead? Once again, I am not trying to be sarcastic. I say what I mean and I mean what I say. Sorry for any misunderstanding made due to English being my second language. And please do not be angry, since I have set my heart on contributing $\mathsf{Pr} \infty \mathsf{fWiki}$ and I will never troll. --kc_kennylau (talk) 16:09, 14 July 2013 (UTC)
- If you need to add a proof to a theorem which already has a proof in place, and the theorem and proof is on the same page, then add the second proof on the same page as "Proof 2" and invoke the "refactor" template on that same page. Then the refactoring task can be done by the experienced editors who do a lot of the maintenance work.
- As has been pointed out, there are several aspects to a refactoring task. As yet we have not gathered all this information into one page, because we do not expect new editors to undertake refactoring. The reason for this is precisely because there is a considerable amount to take into consideration.
- Because for simple tasks it does not take a lot of experience to do, it may appear, on the basis of that simplicity, that refactoring is always that simple. But it is not.
- Therefore, as I say, please do not do any refactoring because you do not know the full extent of what needs to be done. --prime mover (talk) 16:25, 14 July 2013 (UTC)
- OK, I will follow your instructions. --kc_kennylau (talk) 16:27, 14 July 2013 (UTC)
About new page
Previously, I have asked about inserting my proof into an existing page with only one proof. Now, I would like to ask about what I should do while creating new pages/definitions, for example Definition:Binomial (Euclidean). Was it appropriate for me to create subpages in that circumstance? I know it is annoying to keep asking questions about the same topic many times, but since I am a newbie and I want to get into $\mathsf{Pr} \infty \mathsf{fWiki}$ more quickly, I feel obligated to ask about things I do not understand. Sorry for any misunderstand made due to English being my second language. --kc_kennylau (talk) 16:31, 14 July 2013 (UTC)
- "I know it is annoying to keep asking questions about the same topic many times," yes it is.
- It is hoped that contributors to $\mathsf{Pr} \infty \mathsf{fWiki}$ may be able to learn by experience. I am temperamentally unsuited to provide ad-hoc one-to-one tuition. --prime mover (talk) 17:54, 14 July 2013 (UTC)
Proofreading of new Definition:Formal Language
It seems that most of the Category:Definitions/Formal Systems can do without restructuring (I have made improvements as necessary by editing), except for Definition:Formal Language. The five new associated pages are listed here; once again, I would like your opinion before pushing this one to main.
Note that I have refrained from implementing the newly suggested definitions regarding alphabets; I deemed it better to take a staged approach, and am not fully decided on the new names yet. More literature research is to be conducted.
This proposed replacement is not but the newest tiny step in re-grounding, generalising and modularising the logic sections, which ought to be testament of the $\mathsf{Pr} \infty \mathsf{fWiki}$ approach. As this process continues I hope that the edits will become of a similarly modular form, not requiring as much headspace and coordination as the changes do now. — Lord_Farin (talk) 22:01, 6 September 2013 (UTC)
- I've been following it as it's been developed. It's definitely a step in the right direction.
- I will take the time to follow through with inspecting the new pages in due course - when my mind is fresher. I was put through the mill today. --prime mover (talk) 22:57, 6 September 2013 (UTC)
- I don't think I can add much to all this. Good to go live, in my opinion. --prime mover (talk) 14:22, 7 September 2013 (UTC)
- Done in principle. I'll be reviewing links now. — Lord_Farin (talk) 14:50, 7 September 2013 (UTC)
- Job's a good 'un. --prime mover (talk) 15:08, 7 September 2013 (UTC)
My sandbox
A look and some responses to the applicable parts of my sandbox are appreciated; the proposals there would go a long way to clear some of the long-time problems we've had in our founding departments. — Lord_Farin (talk) 18:11, 9 September 2013 (UTC)
- If you approve of Proposal #3 in my sandbox, I'm ready to start pushing that part to main. Some pages are listed on User:Lord_Farin/Sandbox/PropLog (the last group under the "rewritten/newly written" heading). An upside of this scheme is that it allows us to leave most of the connectives pages untouched (save minor things like updating links etc.). — Lord_Farin (talk) 10:46, 17 September 2013 (UTC)
Definition:Trivial
I see you're adding Template:Disambiguate calls for Definition:Trivial, even to pages where it is quite obvious that the intended sense of the word is not presently covered among any of the disambiguating pages. There are some options:
- Deleting the links, perhaps placing Template:Handwaving calls;
- Creating a page defining the proper sense of "trivial" intended.
But maybe I'm just saying what you had already thought up. — Lord_Farin (talk) 07:25, 12 September 2013 (UTC)
- The idea was to implement the second option. I put the template in place so it didn't get forgotten. I'm trying to work through the backlog of (now) 174 links to disambiguation pages and process them appropriately - this is just one such.
- The reason for a link is because those who are not completely fluent in English are able to get the sense of what is meant without the need to link to outside this website. GFauxPas has done some similar work in his work on logic, from the semantic perspective (e.g. "ambiguous" etc.). --prime mover (talk) 07:34, 12 September 2013 (UTC)
Logic refactoring
I would like to ask you to read User:Lord_Farin/Sandbox/PropLog/Principle of Structural Induction, and determine if it passes the "not-handwaving" criterion. It could possibly be necessary/justified to take this principle as an axiom. Even Keisler and Robbin say that it "can be proved using induction on $\Bbb N$" -- but in doing so, they need to employ inductive definition (on the length of the formula or s.t. like that). But inductive definition can only be employed after proving the Principle of Inductive Definition / Principle of Structural Recursion, which in my reading needs Structural Induction to be proved. So to use induction on $\Bbb N$ would introduce circularity.
Fundamentally, this seems to be one of the last places where handwavery could be needed. Having this principle, I think it's possible to be entirely formal. So hopefully you'll agree that the current form is good enough. — Lord_Farin (talk) 10:20, 14 September 2013 (UTC)
- Is it possible to use the Principle of Least Counterexample? On the other hand I've looked at that, and (underneath its current state of imprecision) it appears to need the well-ordering property of the integers, which in turn etc. etc.
- Otherwise, yes, it seems adequate to me. We may receive questions from those whose attitude may be more rigorous, in which case we can invite them to have a go at proving it themselves.
- From my distant memory of this level of set theory (but I may be getting it confused with something else), I vaguely remember Montague having proved that any adequately powerful framework of mathematics needs an infinite axiom schema to define it, and that schema basically includes a principle of induction in it somewhere, even if not deliberately stated as such. Hence Peano's 5th axiom, the Axiom of Infinity of ZFC - and now it appears this one of PropLog.
- Might be an idea to link these axioms (at a high level) all together in a page that provides this overview, linked to that theorem of Montague's (which appears not to be Montague's Theorem, which is more an alternative restatement of Goedel). --prime mover (talk) 12:31, 14 September 2013 (UTC)
- I don't know about any of that. For now, we'll just keep in mind that this possibly needs to be an axiom. I'll continue. — Lord_Farin (talk) 13:13, 14 September 2013 (UTC)
The PropLog/PropCalc merge has been set up, and is ready to commence. I expect it to take several days to carry out properly.
I'll be migrating things into the familiar archive/graveyard User:Lord_Farin/Backup. If you have any comments, or know of things that should be taken care of beforehand, this is a good time to say so. — Lord_Farin (talk) 13:03, 26 September 2013 (UTC)
(NB. This operation will not conclude my work on PropLog. It is merely a first step, amalgamating what is known into the PropLog directory. After this, I will proceed to contemplate the finer structure. So anything not directly related to the merge of PropCalc can wait.)
- I think the best technique here would be for you to do what you think is needed, then in due course I can go through it all carefully. There are no big obvious issues that I can see, so sa you know what you're doing, it's all yours. --prime mover (talk) 13:14, 26 September 2013 (UTC)
- It's more or less done. I have created a number of Template:SourceReview calls to verify the integrity of source work flow. I'd appreciate it if you could attend to them in the coming days.
- There are also some redirects which I scheduled for deletion. See my sandbox for a list (under "deletion"). Due to glitches in the "What links here" functionality (I've asked Joe to call the script that fixes this) I can't finish it off just yet.
- After that, we're up for the next step, which is to actually organise what has been thrown together into Category:Propositional Logic and the like. But a major bottleneck has now been tackled. I expect things to be more modular from here on (until the trick has to be repeated for PredLog). — Lord_Farin (talk) 19:00, 28 September 2013 (UTC)
- Good job.
- As for me, I'm reaching the end of the DeleteRedirects I've found in Category:Delete. During the process of this, I have done a little renaming myself of stuff which hadn't been picked up yet. Work still in progress, then I will attend to SourceReviews. There may of course be some in there which you might be able to attend to, so feel free to explore. --prime mover (talk) 19:09, 28 September 2013 (UTC)
- Maybe I owe you an explanation for not joining in very enthusiastically on the DeleteRedirects ("letting you do the dirty job"). Main argument for this was that it allowed for an extra pair of eyes to look at every (possibly non-obvious) delete request. Thanks for your efforts. — Lord_Farin (talk) 18:41, 29 September 2013 (UTC)
- No worries. It gave me the opportunity to do some further tidying up of stuff that I might otherwise not have approached. While I have your attention, what's the planned future for Definition:Propositional Calculus? It seems to duplicate Definition:Language of Propositional Logic but the links are going to need to be addressed.
- While I'm on the subject, SourceReview alerts: rather than just insert the template just above the thread in question, better to lift the questionable source and put it below the others, thus segregating it from the rest, otherwise the confusion is that all sources following the template are in question.
- And further, there are several SourceReview alerts on Ben-Ari 3ed. on various pages, which I believe is yours. Can't place them at the moment, but you can find them by following the thread.
- Best, --prime mover (talk) 18:47, 29 September 2013 (UTC)
- Plan is to "archive" PC (I don't blame you for missing that on my sandbox page), i.e. move it to LF/Backup territory. I'll look at the Ben-Ari 3rd ed. ones. Partly I suspect they are due to the labeled tree formulae not being covered in the new paradigm (I'm on it). This is also the main reason for not archiving PC yet.
- Other thing: Backup territory (AFAIC) does not have to be maintained. It's just an archive in case something goes horribly wrong (and two moves is easier than meticulous overwriting. I might be deleting stuff from there. So if you find some page in Backup links to something, it's fine to just let the link die. — Lord_Farin (talk) 18:52, 29 September 2013 (UTC)
- Having changed the last relevant page linking to Definition:Propositional Calculus, it can in principle be moved to Backup. The last uncovered subpage (labeled trees) has been covered at Definition:Language of Propositional Logic/Labeled Tree. I'll do it; do you think it's reasonable to instantly delete all redirects (we're going to repopulate PC at some point, with an overview of formal systems built on LoPL)? — Lord_Farin (talk) 19:56, 29 September 2013 (UTC)
- Please go ahead. I will attend to source reviews in due course.
- I had a thought about source review flags for Takeuti and Zaring -- since they don't have prev/next it doesn't matter so much, so I may well dispose of such flags and declare that it does not matter much. Similar with other works in a similar position. As for the recent stuff added by Josh Flynn I will notify him.
I have expressed multiple times that I consider the current coverage of T/Z suboptimal and not worthy of my attention. This policy carries through to the Source Reviews.
Josh has sadly decided to sever all links with us; his e-mail address (which the mail account registered for PW forwarded to) has been deleted. I expect him to be back some day in the future, though. But that's more backed by hope than any concrete evidence.
- I wonder whether there's cause to add an optional username parameter to the SourceReview template which can be filled with the username of the user who posted the source citation. This will then be put into a subcategory named for that user, who will then be able to go through his list with greater ease. --prime mover (talk) 20:33, 29 September 2013 (UTC)
Idk. Seems not worth the hassle for the very small amount of users that (regularly) contribute sources. Even fewer use prev/next. There's also the issue of multiple source works being posted by multiple users. OTOH, if we do this now, it will be easier to keep track of in the future. Can I leave implementation to you? — Lord_Farin (talk) 20:52, 29 September 2013 (UTC)
- Under way and done. --prime mover (talk) 20:54, 29 September 2013 (UTC)
I've started splitting up PropLog into nice little bits, for each semantics and proof system. Truth tables could fit under Category:Boolean Interpretations. There are undoubtedly some strange decisions I made, so a glance over the operation would be appreciated. — Lord_Farin (talk) 17:39, 30 September 2013 (UTC)
- It will be piecemeal as and when I find something that look incongruous. --prime mover (talk) 18:36, 30 September 2013 (UTC)
- As you've noticed, I've entered the connectives territory. I note the following:
- The "Boolean Interpretation" section is horribly outdated and needs to go.
- Why? Okay, so it says the same thing as the "Truth Function" section, but in a different language / notation / terminology. I contend that keeping each of the various techniques of representation for these operations is useful. And keeping them in their separate subpages allows for a cleaner / more modular treatment, as well as making it easy to see which content is attributable to which sources. --prime mover (talk) 22:11, 1 October 2013 (UTC)
- First of all, they link to Definition:Model (Logic), which is built in a fundamentally different way than the current revision of Definition:Boolean Interpretation. If we were to update this, it'd come down to parroting the "Truth Function" exactly. So I cannot mentally fit this piece in the new framework. But perhaps it is Definition:Boolean Interpretation that needs to be (re-)revisited -- a defensible route in any case.
- The "Truth Function" and "Truth Table" sections have practically the same content. I suggest merging these -- basically appending the "Truth Table" part to the "Truth Function" part. Redirects can be amended as necessary; transclusion for Definition:Truth Table can be managed through the extension's functionality.
- Same argument. Maybe it's just because I wrote them in the first place, but I see merit in the current structure. If you like, there can be words added to explicitly state that all representations "say the same thing", but I still think they all need to stay. And further nesting of transclusion will add to complexity unnecessarily. --prime mover (talk) 22:11, 1 October 2013 (UTC)
- On second thought, I'm going to go with your point of view on this one. (It is precisely this kind of turns that makes me ask you about things ad nauseam.)
- As to the categorisation of truth table-related results, would it be better to put them under Category:Truth Functions or is a separate Category:Truth Tables (about truth tables, as opposed to Category:Truth Table Proofs using truth tables) in order?
- We can of course put pages like Definition:Disjunction/Truth Table in a new Category:Truth Tables, and Definition:Disjunction/Truth Function in a new Category:Truth Functions section, but I would be unwilling to see them merged. --prime mover (talk) 22:11, 1 October 2013 (UTC)
- Separate it is. Thanks for your replies. — Lord_Farin (talk) 22:22, 1 October 2013 (UTC)
Above, I already alluded to the conflict between Definition:Model (Logic)/Propositional Calculus and Definition:Boolean Interpretation. I'm getting ready to address this, but there are some source works involved.
What does this mean? Well, I've got ebooks for some of them, but e.g. the wrong edition of Hamilton, and no version of Lemmon.
Now, the size of this operation will make it convenient to concentrate the work in my sandbox and push it live in one sweep (like I already did several times recently).
This note is an invitation to contribute, amend, and at the very least, keep an eye on the source works, of what is located on User:Lord_Farin/Sandbox/PropLog. Its goal is to prevent flooding the site with source review templates.
Looking forward to your input: words and actions. — Lord_Farin (talk) 22:17, 3 October 2013 (UTC)
- Flooding the site with source review templates is not a problem for me - especially if you put my username to them. Will respond at greater length in due course - time is limited at present. --prime mover (talk) 05:34, 4 October 2013 (UTC)
- Suggested approach: do a bunch of work, then let me know when you need me to attend to source work citations. Then I can get on with that, while you take a rest (or start working on another area). And so on. Mind, I still like the approach where you just add a SourceCitation template (with my username attached). It's completely less work all round, as all I have to do is go into that folder and start work, rather than have to go hunting for things. --prime mover (talk) 07:30, 4 October 2013 (UTC)
- When you regain access to the relevant source works, a round of work on the recently added source reviews would be appreciated. — Lord_Farin (talk) 00:26, 7 December 2013 (UTC)
As you have noticed, I have more or less switched to a steamroller/lava flow approach to deal with the entanglement of generic and specific terms in the models and boolean interpretations departments, starting from the completely generic and formal Definition:Proof System and Definition:Formal Semantics and gradually moving forward, gradually updating the existing material.
The advantages of these general definitions are immediately apparent: most prominently, their malleability to any language, logic, proof system, and semantics. This gives a unification I haven't found anywhere in the literature (whence, these definitions are at best hinted/handwaved at in source works).
Before taking on the coverage of natural deduction as a "proof system" in this sense, I'd like to have a go at the Keisler-Robbin proof method of tableaus.
This branch of PW documentation is currently a bit awkward in terminology and notation compared to the complete framework of (symbolic) logic. It therefore seems easiest to start from scratch. However, my copy of Keisler-Robbin is different form yours, so it will generate some source flow problems. What are your thoughts on this? — Lord_Farin (talk) 00:26, 7 December 2013 (UTC)
- Do what your own copy says. What is your copy? Different edition? Scusi, drunk in foreign places. --prime mover (talk) 05:22, 7 December 2013 (UTC)
- It looks like it's some PDF from a preprint edition from 1987. It has a lot less paragraphs, and most of the computer stuff seems not to be present yet. I'll see how it goes, and will add source reviews when it seems appropriate (we can't be documenting unofficial preprint versions now, can we?). — Lord_Farin (talk) 07:59, 7 December 2013 (UTC)
To deal with the Definition:Tautology page, I have thought up the following scheme (bullets indicate header levels):
- Definition
- Informal treatment
- Symbolic logic (content will be what is at User:Lord Farin/Sandbox/Definition:Tautology)
- BI
- First Order (in due course)
Similar stuff could be employed to deal with Definition:Contradiction, although that one is slightly more involved due to the term being used in both proof and model theory (vs. Theorem resp. Tautology). How does this sound to you? — Lord_Farin (talk) 18:02, 9 January 2014 (UTC)
- I'd be happier if the informal treatment came first -- it's more likely that a casual browser will make better sense of the page if it starts easy. --prime mover (talk) 23:02, 9 January 2014 (UTC)
- Happy with the new User:Lord Farin/Sandbox/Definition:Tautology? If so, I'll push it live. — Lord_Farin (talk) 13:54, 10 January 2014 (UTC)
- Looks good to me. --prime mover (talk) 22:41, 10 January 2014 (UTC)
AI Mashup Challenge
Now located at ProofWiki:Current events/AI Mashup Challenge. — Lord_Farin (talk) 20:31, 18 September 2013 (UTC)
- Many thanks. --prime mover (talk) 20:33, 18 September 2013 (UTC)
How to do this?
I'm sure you've encountered your share of the type of reference occurring on Equivalence of Definitions of Semantic Equivalence for Boolean Interpretations.
Which is the suggested course of action in cases like this one? Pointers to similar pages would be appreciated. — Lord_Farin (talk) 15:46, 25 February 2014 (UTC)
- The trouble with trying to document multiple paths through an equivalence proof is that because we're trying to do *everything* that means we will end up with a network of proofs like: 1 --> 2, 2 --> 3, 3 --> 2, 3 --> 1 (twice), 1 --> 3 ... while all a particular author is trying to do is an elegant demo that 1 --> 2 --> 3 --> 1.
- What I have done in the past is, if a particular implication has a number of proofs, and they're involved, is set up a separate page to prove, say 3 --> 1, which can then have the Proof 1 / Proof 2 treatment. Then on the "Equivalence of definitions of ..." page, say Definition 2 --> Definition 3 by "(name of proof page you've written)" thus disposing of it in a line. Then it puts all the heavy lifting into its own page (or set of pages) thus leaving the actual equivalence proof page as a streamlined list of links to the appropriate results.
- At least, that's how I envisage it -- although I may not have actually done it like this very often. There are some monster equivalence proof pages (Normal Subgroup, for example) which are approaching this idea, but not many yet.
- Then, once the separate proofs have themselves been teased out of the tangle, assigning the citation to each is easy. --prime mover (talk) 20:34, 25 February 2014 (UTC)
- Seems like a good general approach. I've been looking for an equivalence proof with "redundancy", i.e. with more implications than necessary, but I couldn't find it. I'm still trying to come up with a nice way of presenting those, for there will be many more of them in the long term. Any ideas/examples for that one? — Lord_Farin (talk) 12:26, 26 February 2014 (UTC)
- For "redundancy" we have Definition:Group Axioms which has two non-redundant versions Definition:Left Group Axioms and Definition:Right Group Axioms invoked on the same page ... is that what you were looking for?
- Alternatively, there's ZFC which (in the standard presentation of it) has some axioms which can be derived from others (Axiom of Existence, for example) but we still haven't properly shaken down that section yet (too many different approaches, too many contributors who disagree with the specific presentations of the existing material, etc.). --prime mover (talk) 12:35, 26 February 2014 (UTC)
- I was rather asking about redundant implications in equivalence proofs. E.g. 1 -> 2 -> 3 -> 1, but also 3 -> 2. — Lord_Farin (talk) 12:40, 26 February 2014 (UTC)
- I see what you mean. How about: prove the individual implications in their own pages, then in the equivalence proof do "1 -> 2 -> 3 -> 1 proves equivalence" but then "Also see 3 --> 2" perhaps. I don't really know, the situation hasn't really come up before.
Definitions and constructions of the number sets
We have accumulated a number of definitions for particularly $\N$ and $\R$, and to a lesser extent $\Z, \Q$ and $\C$.
As it happens, my newest project Munkres takes pleasure in starting from the axiomatic definition of $\R$ that I posted earlier today, and define the other number sets from that basis.
This convoluted realm provides to us the opportunity of making rigorous the relative consistency of all these approaches. An ambitious long-standing goal, into which a lot of work has gone already.
One of the things I realised while pondering all this today, is that we need to distinguish between axiomatisations and constructions.
In the most pressing case $\N$ we have:
- the axiomatic treatments of Peano and the naturally ordered semigroup for $\Z_{\ge 0}$, and the Axiomatization of 1-Based Natural Numbers for $\Z_{>0}$;
- the constructive treatments Natural Numbers as Successor Sets, Natural Numbers as Cardinals (lacking proper coverage at the moment) for $\Z_{\ge 0}$, and Natural Numbers in Real Numbers for $\Z_{>0}$.
with heaps of other idiosyncratic definitions to follow.
With this distinction made, there are then a number of theorems that connect these approaches, of the following kinds:
- equivalence of axiomatisations;
- uniqueness (up to some appropriate kind of isomorphism) of structures satisfying an axiomatisation;
- construction fits axiomatisation.
This scheme should provide optimal modularity to one of the areas where such is currently largely absent (seeing how difficult it is to fit in a new definition compared to less fundamental concepts like connectedness or complex inverse hyperbolic functions).
Barring misjudgement of the ramifications of these changes by orders of magnitude, I'd say this could be implemented before the end of the week. What say you? — Lord_Farin (talk) 16:38, 15 April 2014 (UTC)
- Sounds brilliant! Although on the basis of the quantity of work that the above seems to be, my reaction would be: which week? (which year?) :-) --prime mover (talk) 18:00, 15 April 2014 (UTC)
- Oh, and while I think about it, I may have to leave "Source Review" pages for a while, a) I'm having trouble locating crucial books, and b) I'm having trouble locating crucial hours. But please keep on invoking the template as needs be, I'll get to them in due course. I'm out of the country again tomorrow for some days, and the same next week, and in between is more than normally busy ... --prime mover (talk) 18:03, 15 April 2014 (UTC)
- Will do. After all, one of the purposes of the template is to create a persistent reminder that work needs to be done, much like stub and its friends.
- I'll probably draft some stuff today and tomorrow, I'll link you to it once it's in a presentable state. — Lord_Farin (talk) 18:14, 15 April 2014 (UTC)
- I will look at it with great interest, but will probably not get deeply involved at this stage -- I want to finish getting the inverse trig / hyper functions hammered out first. And that, I am finding, is not documented in the format I am aiming for anywhere that I can find -- which is strange. --prime mover (talk) 18:18, 15 April 2014 (UTC)
- Steadily progressing, but I clearly underestimated the work involved. Approaching Induction for the Naturally Ordered Semigroup. How's it looking for you so far? Feel free to comment on page name choices as well. — Lord_Farin (talk) 17:06, 23 April 2014 (UTC)
- 2 days a week spent abroad this last few weeks, which means 1 night in a hotel room away from my library. Corrupting my continuity. Apart from that ...
- As I expected. There's a lot of work involved in the job you've taken on ... looks good so far though. I got distracted (as usual) by deciding to finish off the "Binmore" source work which I abandoned back when I first worked on it but we now have the background in place for me to finish it off. --prime mover (talk) 21:57, 23 April 2014 (UTC)
Millman/Parker: Geometry: A Metric Approach with Models
As you suspected, I have a digital copy of this book, namely the second edition, as it appears in the sources sections now. — Lord_Farin (talk) 17:15, 5 May 2014 (UTC)
- Okay -- then you might want to check out the fact that "back" from Poincaré Plane is Abstract Geometry leads to Definition:Euclidean Plane, but "next" from Definition:Euclidean Plane leads to the not-yet-existing Hyperbolic Plane is Abstract Geometry. Clearly something got overlooked. Either Hyperbolic Plane is Abstract Geometry needs to be written, or (if there's too much groundwork needed at present) "next" from Definition:Euclidean Plane needs to go to Poincaré Plane is Abstract Geometry.
- Done. It turns out that "hyperbolic plane" and "Poincaré plane" are the same thing. — Lord_Farin (talk) 21:16, 5 May 2014 (UTC)
- In other news, I have almost completed the exercise to add stub entries (at least) for missing book entries. Only a few more to go. --prime mover (talk) 17:29, 5 May 2014 (UTC)
- Good job. Also on clearing some of the long-standing renaming exercises. — Lord_Farin (talk) 21:16, 5 May 2014 (UTC)
- Plenty more to do ... and I keep finding more books cited. :-( --prime mover (talk) 21:18, 5 May 2014 (UTC)
Oliver Heaviside
PM, I don't have a biographical source. Can you please make a page for Oliver Heaviside? Thanks much.
--GFauxPas (talk) 10:59, 6 May 2014 (UTC)
- Don't you have a sufficient level of access? --prime mover (talk) 11:56, 6 May 2014 (UTC)
- It's what I do. I primarily use the MacTutor archive, to which there is a templated link on many (but not all) of the existing mathematician pages. --prime mover (talk) 12:22, 6 May 2014 (UTC)
- I have a few, but mainly my library consists of conventional textbooks. --prime mover (talk) 20:09, 6 May 2014 (UTC)
- Heaviside added as requested. --prime mover (talk) 20:09, 6 May 2014 (UTC)
General thanks
It's so nice to have all the integral formulas in one website. Thanks for your effort! --GFauxPas (talk) 11:53, 13 May 2014 (UTC)
- Hardly started yet. The source work I'm using has hundreds.
- Hope you're alright with adapting the good work you have already done on this so far by (a) adapting the names (in particular changing "Integral" to "Primitive" in order to provide an easy way to distinguish between definite and indefinite integrals), (b) tweaking the structure of the existing ones, and (c) replacing a lot of the first-principles use of Integration by Substitution with (where appropriate) Primitive of Function under its Derivative. --prime mover (talk) 12:27, 13 May 2014 (UTC)
Top Stubs
Very neat change, in line with what we discussed. Definitely a change for the better! — Lord_Farin (talk) 20:34, 2 July 2014 (UTC)
Restriction continuous
Dear prime.mover,
I would suggest that the (less general) versions of the continuity of the restriction for metric spaces shall be proven as corollaries from the respective theorems for topological spaces. Note that also sequential continuity at a point is carried to the restriction in the setting of topological spaces. --Mathmensch (talk) 20:45, 13 October 2014 (UTC)
- Dear prime.mover,
- since I am currently working on two theorems involving this issue, a swift answer would be appreciated. By the way: Have you noticed, that in the summary line of my edit of the entry in question I already mentioned that there is a local version of this theorem which holds in topological spaces? --Mathmensch (talk) 20:56, 13 October 2014 (UTC)
- A few basic rules, some better documented than others ...
- a) You do not remove existing material and add your own in its place. If you have developed a different proof, then add it as a further proof. Hence my reinstatement of the original.
- b) I did notice that you promised a version for sequential continuity. I have not yet seen that promised version, however. Neither have I seen any summary line that refers to a "local version" of this theorem.
- c) The supposedly forthcoming transcluded version for sequentially continuous mappings is a different proof and needs to be on a different page, so excuse me while I remove it.
- d) Please respect house style, at least with reference to page naming.
- e) Requests for a swift answer will not in general be viewed with equanimity. --prime mover (talk) 22:24, 13 October 2014 (UTC)
- Dear prime.mover,
- a) I have not developed a different proof for the same result, but instead a different proof for
a more general resultresult in a more general setting. Hence, the rule you quoted cannot be applied here.
- a) I have not developed a different proof for the same result, but instead a different proof for
- b) Yes, as you may have noticed, I have today proven two more results, and the fact that the promised version is not there yet has to do with me being able to get only a finite amount of work done in a finite time.
- c) The supposedly forthcoming transcluded version for sequentially continuous mappings is a generalisation of the theorem for metric spaces, which will follow from it. Another way to deduce the theorem for metric spaces will be another forthcoming local version, which will show the local continuity of the restriction of a locally continuous function.
- d) Yes, I will learn more house style, possibly improve it.
- e) Ignoring requests for a swift answer and instead answering almost two hours later may stress your relations to your fellow editors, as well as destroying the structures they try to build up.
- f) The structural outline as I currently see it is as follows:
-Restriction of Continuous Mapping is Continuous
--Restriction of Continuous Mapping is Continuous(Continuity)
---Global version
---local version
--Restriction of Continuous Mapping is Continuous(Sequential continuity)
---Global version
---local version
- --Mathmensch (talk) 22:45, 13 October 2014 (UTC)
- I will answer immediately to e) above.
- The maintenance of $\mathsf{Pr} \infty \mathsf{fWiki}$ is a labour of love. I drop in as and when I like, and I attend to requests if and when I feel like it. It is neither my responsibility nor my duty to answer any questions posed to me, and it is most certainly not your position to instruct me as to the timescale under which I am to do so.
- The other questions I will attend to exactly as and when the mood hits me. For now I have absolutely no desire to at all, because I have far more important and interesting things to do. --prime mover (talk) 05:14, 14 October 2014 (UTC)
- Your behaviour seems to me not as friendly as it should be. For me it is also a labour of love (as well as a labour of exercise) and I don't wish my work to be undermined. I think the structure I proposed in f) is reasonable, and superior to the categorizing into metric or topological spaces. In fact, the theorem in metric spaces is strictly less general than two of the upcoming ones, as I already pointed out. Therefore, it, in my opinion, is not on the same level as the theorems about topological spaces.
- I do not wish to obstruct you from your work. I hope, however, that the same is the case for you. And please mind the difference between a request and a instruction, and please also mind the events which triggered this request. Labours of love I practice usually with great regularity and not irregularity. And refering to your position does not free you from the obligations of politeness. --Mathmensch (talk) 07:36, 14 October 2014 (UTC)
I will not involve myself in your mild animosity, but let me remark that I do not want to see the subtle differences between (Local) (Sequential) Continuity obscured in page titles. If you want to address Local Sequential Continuity, write it as it is. 't May feel tedious to do so, but the gain in clarity is more than worth it. — Lord_Farin (talk) 08:29, 14 October 2014 (UTC)