User talk:Prime.mover

A Possible Next Direction
I was planning on starting on a project for a website/wiki about proofs, but if I could just incorporate some things into this website that would also work, and probably make things much easier.

Something that I would like to see, which this website does to some extent, is the breaking down of complex mathematical topics all the way down to the simplest axioms(regardless of which they are, and one could use multiple systems) and explicitly stating every step of the way. If one has the time, why not boil down a complex theorem as far down as it can go? Is that not basically the essence of proof anyhow?

One idea is that you could use flowcharts to state every pre-established concept that the proof makes use of. With this someone could also take a famous proof that they might find interesting, and then easily find the exact path(s) of what concepts, theorems, etc. are necessary to understand before they attempt to understand the proof in question. Attached is one 'proof of concept' I was going for with the Pythagorean Theorem from Book I of Euclid's Elements(currently excluding definitions). In this case I didn't flesh out any proposition that already had been fleshed out somewhere else in the image.

Of course, it doesn't have to be in this exact format. With a website one can use hyperlinks, or make the individual branches collapsible, or use other tricks to make things more convenient.

This site already does make use of links in many proofs, which is great. The basic framework is already pretty much here, I just think it could be expanded upon and/or organized further. There wouldn't need to be a flowchart or a similar map for every proof, but wouldn't it make things more accessible/easier to understand?--Alexelam (talk) 04:25, 8 April 2021 (UTC)


 * The philosophy that you have described is exactly what the manifesto states. In theory, every proof can (ultimately) be broken down into a chain of definitions and axioms, all the way back to ZFC and (in the case of geometry) Euclid.


 * There are very likely to be instances of where we have not gone all the way back to axioms, for example, for advanced proofs using basic arithmetic. Reminding the user of the rigorous definition of real addition based on abstract algebraical constructs in field theory backed up by the ZFC construction of the natural numbers is probably overkill -- but the structure to support has already been put in place on (it was one of the first things we did). The philosophy is indeed already there.


 * I see your diagram for Pythagoras's Theorem but it's too small, and when I try to embiggen it, I find that the contents of the nodes have lost their definition. However, I suspect that there are repeated instances of the most basic axioms and definitions. I can totally see where you are coming from, but it might be more profitable to use a directed acyclic graph structure. (Fun fact: by strange coincidence, I was in the process of implementing one of those for a project in my day job while at the same time reading Stephenson's "Anathem". The significance of this would become apparent to a reader of at least the appendices of that literary work.) --prime mover (talk) 05:24, 8 April 2021 (UTC)


 * The file is an SVG so it should retain its definition, if you just click on it and then again at the file page. But you are right that there are redundancies, which is partly why I wasn't sure if links(or color coding) would work better or not. I didn't think of the acyclic graph idea, which is pretty good. I suppose that what I was going for was more of a UI reworking than a philosophical one, at least for proofwiki.
 * For now I'll probably just make a couple of them and try to add them as an image to the theorem's page.


 * I personally would like to see some worked examples of ZFC, for as much discussion as it gets, but I get that most people don't need that much rigor. Of course not every proof needs to go all the way back, if it's simply linking up with what has been established on another page.
 * --Alexelam (talk) 06:19, 8 April 2021 (UTC)


 * For it to be useful, such a diagram should be immediately comprehended by a single glance. I would gather that such a diagram should be designed first and foremost as an aid to understanding rather than an exercise in ingenuity, and so the user should not need to zoom in as though scanning it through a microscope. In my past career as a software engineer, I had great experience with documentation which did little to aid the understanding of a function, consisting of such tree-diagrams, and (beyond bulking out the bumph in order to bamboozle a client into believing we had provided the documentation required) it never actually did the job of explaining how it worked.


 * And, as I said above, if you've got multiple instances of the same node in a given tree, it really is not a tree. A proof is not in general a tree. It is a . IMO this is a vitally important concept which is vanishingly rarely emphasised in the mathematical discipline of proof theory. The latter is almost universally taught informally with a considerable amount of intuitive reliance on the concept of "circularity" without ever once indicating what that actually means.


 * Now none of the above paragraph is actually implemented in, mainly because I have not encountered a reliable primary source which discusses the matter properly -- it is just something that is acquired in the mind of the student by gradual osmosis. We have gone no further down the road of philosophical logic than the basic axioms of natural deduction, and sufficient faltering steps towards establishing some framework of mathematical logic, so the field here is wide open for someone who a) understands sufficient about this field as to be able to communicate it lucidly, and b) has adequately embraced the philosophy of this site as to be able to transfer that understanding to a suite of pages on that present it. --prime mover (talk) 06:41, 8 April 2021 (UTC)

Change of base formula for logarithms
I placed a comment and alternate discussion at Talk:Change_of_Base_of_Logarithm--Guy vandegrift (talk) 21:38, 18 December 2021 (UTC)


 * So I see. If you can find some way of somehow turning this into a formal proof, then feel free to add it as a second proof. --prime mover (talk) 21:45, 18 December 2021 (UTC)


 * I finished the second proof on Change of Base of Logarithm. I hope you like it, but will move it to Wikiversity if you don't.  I greatly enjoyed learning about Proofwiki, and will certainly emulate portions of your style in my future efforts on Wikiversity.  I strongly advocate the development of parallel proofs on the freely available internet.  My vision is for colleges to someday utilize these proofs as part of an open source bank of "undergraduate prelim" exams that are described on the Wikiversity page: Quizbank/Cost-benefit analysis/Undergraduate prelims .--Guy vandegrift (talk) 23:25, 19 December 2021 (UTC) (I am also User:Guy vandegrift on Wikiversity)


 * No doubt you have seen how your proof has been incorporated into our page Change of Base of Logarithm.


 * Note that the extra discussionary material is in general not the way we do things on, unless it's a particularly troublesome, confusing or controversial concept, for example AoC, LEM etc. I think we already have $\log_a b = \dfrac 1 {\log_b a}$ as a page in its own right. If not, then can be added to Change of Base of Logarithm as a simple corollary. I'll get round to looking at it, but I'm not up to anything more intellectually challenging than a Dudeney puzzle-book right now, and even that's hard work. --prime mover (talk) 12:22, 20 December 2021 (UTC)


 * You are definitely sharper than I. My down time is spent checking GoogleNews-facebook-email-GoogleNews-facebook... until I am ready for a nap.


 * I am a bit concerned about the reference to "randomly" selecting from $\{a,b\}$ in the "proof" (it's more of a derivation). Perhaps I can cook up a phrase that explains that other choices yield equivalent results, but not the exact equation.  I think the randomness is essential because I liked to derive all my own formulas whenever possible. My proof is easy to remember only if no effort is made to make the "correct" choices. Perhaps we need a concluding sentence, e.g., "Other choices involving $\{a,b\}$ yield formulas that are equivalent to this result".  If you wish, I would be happy to put a bit more thought into this and make an edit.--Guy vandegrift (talk) 16:25, 20 December 2021 (UTC)

Proposed change to two of your pages
I borrowed and enhanced something I found on and placed on Wikiversity at Speak Math Now!/Week 9: Six rules of Exponents/Logarithms#Easy to remember.  Inclusion of this enhancement into  requires changes to two pages:
 * Definition:Summation/Inequality/Multiple Indices (needs modification to include superscripts/subscripts, as well as the omission of the Sigma symbol.)
 * No it doesn't. That page is a subpage of the page defining a summation by an inequality, and such is that notation that superscripts are not used. And no sigma has been omitted, as far as I can see. --prime mover (talk) 18:53, 16 January 2022 (UTC)


 * Change_of_Base_of_Logarithm (needs comment that includes a link to the aforementioned "Multiple Indices" page.)
 * No, I don't believe it does. --prime mover (talk) 18:53, 16 January 2022 (UTC)

Would you me like to insert the enhancement into by editing those pages? I ask because I am unfamiliar with both the editorial policies and intended scope of ProofWiki and don't want to waste my time on something that will get reverted.--Guy vandegrift (talk) 18:35, 16 January 2022 (UTC)


 * No thank you, as I don't understand what you're talking about.


 * For future reference, put any suggested changes like this on the relevant talk page. --prime mover (talk) 18:53, 16 January 2022 (UTC)

ProofWiki extension
I recall seeing a remark by you somewhere (couldn't find where, that's why I came here) that use of the extension's transclusion would not present a link in the "What links here" section.

However, based on this example with Definition:Language of Predicate Logic and Definition:Language of Predicate Logic/Formal Grammar. I have the strong feeling that as long as a title is included, it should work fine.

Does this address your concern regarding "What links here", or are there cases where we do not want a title?

Btw, I am aware of the TOC and other problems with the extension, but unfortunately they are more complicated to tackle, so one thing at a time. &mdash; Lord_Farin (talk) 10:21, 22 March 2022 (UTC)


 * As long as "what links here" genuinely does show all pages which transclude a given subpage we are golden. Unfortunately, there is a drawback in that the parent page is not listed as a transclusion, which makes it less than perfect. If we can fix that issue it would be a great improvement.


 * We need to investigate what happens when the name of a transcluded page is not in / format. In that latter case, the link at the top to the direct parent page is apparent - in other cases it is not. We may be able to get round this with consistent use of redirects. --prime mover (talk) 11:28, 22 March 2022 (UTC)

Transfinite Induction
Apart from the base Transfinite Induction, I see you made more structured versions First Principle of Transfinite Induction and Second Principle of Transfinite Induction. That's a nice improvement (although we might want to add specifics for common scenarios such as $\On$ with $\in$).

How do you see the connection between these? Or am I just too impatient? &mdash; Lord_Farin (talk) 17:36, 24 May 2022 (UTC)


 * The ordinal versions will probably appear in S&F in due course. They will be included as a specific example of TF on the general well-ordering. bear wioth me, I've been thinking about how to merge all this stuff together with the minimum of complication and the maximum of generality without losing the basic implementation on the natural numbers, which is where we come in when we're still at school. --prime mover (talk) 17:40, 24 May 2022 (UTC)

deleted page Measure is countably subadditive
Hi, my effort vanished. Can I get my proof from the deleted page? I would like to add my proof to the existing page.--Usagiop (talk) 16:14, 8 June 2022 (UTC)


 * It needs a lot of work to bring it up to standard. For a start the links underneath the text don't match the text. The page talks about countably subadditive and the link points to additive. As there is already a page for subadditive function, I suggest you might want to create a subpage for your proof and transclude it as is standard practice on . --prime mover (talk) 17:52, 8 June 2022 (UTC)


 * Sorry that I created that duplicated page, I simply could not find the existing page because I was looking around under wrong categories. Apart from that, is it not possible for me get my proof back from the deleted page? I want to reuse that. But if difficult, then OK, I give it up. Generally I am trying to put a direct proof if possible. I prefer to see a simple direct proof for an elementary result.--Usagiop (talk) 18:15, 8 June 2022 (UTC)


 * I undeleted that page. I can't understand why you can't find it. It's Measure is countably subadditive, exactly as you left it. Both that and Measure is Countably Subadditive are in Category:Measures.


 * For the record, you will no doubt have noticed the general style of page titles, and of course you will have taken note of this when you read the help pages and learned about house style. Significant words are always capitalised.


 * Incidentally, I recommend you take note of where changes are made to pages you write, as although there may appear to be any semantic difference between before and after changes, we take pride in a rigid consistency of style throughout the site. This includes neat spacing and presentation of source code, explicit definition and description of everything, and the wide spacing between sections which, while they may seem stupid and pointless, are elements of our presentational style which serves as the "trademark" style of.


 * We also like to steer clear of having "conversations" in maintenance sections (as presented by use of our standard templates). You will see when such a template exists the invitation to embark on any such discussions in the talk page. There is even a link to that talk page already there in the presentation of the section. You are encouraged to take advantage of that convenience. Then it keeps the page itself tidy and presentable. We have a very bad reputation in the mathematical community for being appallingly and laughably low quality. It would be nice if we were able to remedy that perception. --prime mover (talk) 18:38, 8 June 2022 (UTC)


 * Thanks, now the page can be deleted again. I am seriously trying to learn the style and appreciate your improvements. Currently it is still not easy to find correct template/macro usages and syntax.
 * "I can't understand why you can't find it" I wanted to say that I did not realize yesterday that the page already existed because my search started from Definition:Measure (Measure Theory). For today, I just overlooked your undeletion. --Usagiop (talk) 19:07, 8 June 2022 (UTC)


 * I have added a LinkToCategory template to that page, so you should be able to find it next time. --prime mover (talk) 19:11, 8 June 2022 (UTC)


 * Thanks, may I append a small question here? Do you know how to embedded the math expression $x=a$ in the template below?--Usagiop (talk) 19:22, 8 June 2022 (UTC)


 * Yep, certainly, it's in the FAQs: Help:FAQ/Technical questions/Can't get a maintenance template to register my parameter --prime mover (talk) 19:26, 8 June 2022 (UTC)


 * Thanks--Usagiop (talk) 20:07, 8 June 2022 (UTC)

Why my solution of 100 using four 9s is deleted?
Was it consideres invalid? Is it more proper to pinpoint the reason when deleting?--AuroraAeon (talk) 10:22, 27 August 2022 (UTC)


 * Because the page is intended for solutions of the problem of making $100$ (implicitly in base $10$) with four $9$s, not $100_{81}$ with four $9$s.


 * Your solution was simply a trivial instance of the equally trivial way of making $100$ to the base which is the square of any digit. $2 \times 2 \times 2 \times 2 = 100_4$. $3 \times 3 \times 3 \times 3 = 100_9$.


 * If you want to post up the general case and then instantiate it, then feel free, but it seems a bit pointless, unless we want to start a category of amusingly trivial results for children's parties, or something. --prime mover (talk) 10:33, 27 August 2022 (UTC)

Change of Defof was undone
In the page House Style it wrote "Here, note that a further evolutionary step has been made: to replace the code Definition of Set Intersection with the template construct for further streamlining of the source.".

But my change of Defof was undone. --AuroraAeon (talk) 07:52, 4 September 2022 (UTC)


 * Two points to note here:


 * a) Your change did not replace  with , you replaced   with  . I really hope I don't need to explain why the latter is not a direct replacement for the other.


 * b) In the context of the material on the help page, use of the Defof template was specifically in relation to the formal presentation of proofs using the Eqn template, in particular, the contents of the  parameter. It places an explicit capital letter at the beginning of Definition for a start, and use of it in a discursive sentence in the body of the proof is ugly.


 * Please accept that random stylistic changes of the sort which you are making will probably be rolled back without comment. Those which do improve the page will probably be kept, but then and only then. --prime mover (talk) 08:03, 4 September 2022 (UTC)


 * Also note that I have added a note in the house style rules to make this clear. --prime mover (talk) 08:13, 4 September 2022 (UTC)

Lost page "Definition:Integral Domain Axioms"
In an attempt to rename the page Definition:Integral Domain Axioms to Axiom:Integral Domain Axioms, I've managed to lose the page entirely and both pages are now redirects. Not sure what I did wrong. Hoping that you are able to recover a version of the page from somewhere.

Sorry for the inconvenience. --Leigh.Samphier (talk) 12:35, 16 September 2022 (UTC)


 * Not a clue what happened there. I think it's good now, but I can't remember how I implemented the original rule $\text C$. For the record I copypasted the Ring axioms, amended them, and added the extra axioms manually, with reference to the source work. --prime mover (talk) 13:29, 16 September 2022 (UTC)


 * Thanks much appreciated. I'll finish the rename now. --Leigh.Samphier (talk) 13:36, 16 September 2022 (UTC)

New page "Axiom:Non-Archimedean Norm Axioms (Vector Space)"
I'm looking at creating a new page "Axiom:Non-Archimedean Norm Axioms (Vector Space)" for the non-Archimedean norm axioms on a vector space. See User:Leigh.Samphier/Refactor/Axiom:Non-Archimedean Norm Axioms (Vector Space).

This of course suggested that this new page should be merged with the page Axiom:Non-Archimedean Norm Axioms which are the non-Archimedean norm axioms on a division ring. See User:Leigh.Samphier/Refactor/Axiom:Non-Archimedean Norm Axioms.

This would entail creating a new page "Axiom:Non-Archimedean Norm Axioms (Division Ring)". See User:Leigh.Samphier/Refactor/Axiom:Non-Archimedean Norm Axioms (Division Ring).

Publishing these pages would require current references to Axiom:Non-Archimedean Norm Axioms to be moved to "Axiom:Non-Archimedean Norm Axioms (Division Ring)".

Many references to Axiom:Non-Archimedean Norm Axioms are via the template. Initially, I thought that this might be ok, as the two sets axioms are similar. Unfortunately, the axiom (N2) differs between the two sets and have different names.

On a division ring, (N2) involves multiplication and is called multiplicativity. On a vector space, (N2) involves scalar multiplication and is called positive homogeneity.

Options for moving forward:


 * (1) Not intorduce the new page "Axiom:Non-Archimedean Norm Axioms (Vector Space)" as proposed in User:Leigh.Samphier/Refactor/Axiom:Non-Archimedean Norm Axioms


 * (2) Introduce the new page and change the template to reference "Axiom:Non-Archimedean Norm Axioms (Vector Space)"


 * (3) Create a new template  that reflects the specificness of the axioms and references "Axiom:Non-Archimedean Norm Axioms (Division Ring)" and change all invocation of the template   to the newtemplate.


 * (4) Create two new templates  and   that reflects the specificness of the axioms and references references the appropriate pages. Change all invocation of the template   to the the appropriate newtemplate.

Since changing the templates/creating new templates will involve yourself, how would you like me to proceed? Keep in mind that I'm happy to change any references to one template to another in we go with options (3) or (4) --Leigh.Samphier (talk) 03:00, 18 September 2022 (UTC)


 * Please don't proceed with this at the moment. I will sort it all out in due course. --prime mover (talk) 08:13, 18 September 2022 (UTC)


 * First just create your new Axiom:Non-Archimedean Norm Axioms (Vector Space). Then rename Axiom:Non-Archimedean Norm Axioms to Axiom:Non-Archimedean Norm Axioms (Division Ring). Then edit the pages invoking Axiom:Non-Archimedean Norm Axioms (using What links here) to invoke Axiom:Non-Archimedean Norm Axioms (Division Ring), including Template:NormAxiomNonArch.


 * Then leave it there, I will see what I can do to take it from there. --prime mover (talk) 08:54, 18 September 2022 (UTC)

Renaming page "Definition:Group Action Axioms" to "Axiom:Group Action Axioms"
On a similar note, I started to rename the page "Definition:Group Action Axioms" to "Axiom:Group Action Axioms" but found that many references to the page "Definition:Group Action Axioms" are via the template GroupActionAxiom

Do you want this page renamed? --Leigh.Samphier (talk) 03:12, 18 September 2022 (UTC)


 * I'll sort it. --prime mover (talk) 08:13, 18 September 2022 (UTC)


 * When you move a page, the redirection mechanism does all the work for you of making sure all the pages stay looking sweet. Then, by doing a "what links here" operation on the new page, you see all the places where there is an old link. All that needs to be done then is to edit each page to find those instances of the old page and replace them with the new.


 * Please don't move a page, then change your mind and copy the contents of the new page back into the old page. It is very confusing.


 * If one of those pages needing redirection is in a template, then (assuming it's not admin-locked) all you need to do is edit the template to replace invocations of the old page with the new. This will then have the effect of making a large number of pages automatically invoke the new page. So, all I did was a) remove the subsequent edit to Definition:Group Action Axiom so as to re-enable the redirect, edit Template:GroupActionAxiom to change Definition:Group Action Axiom to Axiom:Group Action Axiom throughout, and then mop up the pages which directly linked to Definition:Group Action Axiom to replace with Axiom:Group Action Axiom. Ten minutes tops. --prime mover (talk) 08:33, 18 September 2022 (UTC)

Definition:Paraboloid
Hi. I created this page because I mainly wanted to add this proof which I discovered myself. (I already added it here).

Unfortunately, I believe I have not got any permission yet to upload any sketches or GIFs here myself.

Can you do me the big favor of adding this proof for me? Simcha Waldman (talk) 08:33, 18 September 2022 (UTC)


 * If you have not got permissions to upload graphics, there's something wrong with your account. Contact Joe. --prime mover (talk) 08:35, 18 September 2022 (UTC)
 * Then what is the process of uploading a photo or GIF? I could not find how to start. Simcha Waldman (talk) 08:38, 18 September 2022 (UTC)


 * Upload file --prime mover (talk) 08:39, 18 September 2022 (UTC)
 * Where does it say that? I cannot find any such page. Simcha Waldman (talk) 08:42, 18 September 2022 (UTC)


 * Side menu. Is it not there? --prime mover (talk) 08:47, 18 September 2022 (UTC)
 * Ah, I see it now. Thanks. But why is it limited only up to 2 MB? Simcha Waldman (talk) 08:50, 18 September 2022 (UTC)