# User talk:Caliburn

Welcome to ProofWiki! Since you're new, you may want to check out the general help page. It's the best first stop to see how things are done (next to reading proofs, of course!). Please feel free to contribute to whichever area of mathematics interests you, either by adding new proofs, or fixing up existing ones. If you have any questions please feel free to contact one of the administrators, or post your question on the questions page.

Here are some useful pages to help get you started:

- Community Portal - To see what needs to be done, and keep up to date with the community.
- Recent Changes - To keep up with what's new, and what's being added.
- Check out our house style if you are keen on contributing.
- Main Page talk - This is where most of the main discussions regarding the direction of the site take place. If you have any ideas, please share them!

Cheers! prime mover (talk) 15:18, 17 August 2017 (EDT)

## refacoring

I see you're chewing your way through a lot of refactoring and restructuring. Keep up the good work.

One thing that may make your life easier (and also make our pages look prettier) is: if you're building a fraction with a single digit / letter on top and/or bottom, you can leave off the braces, as long as you keep the spaces: that is, `\dfrac 2 a`

rather than `\dfrac{2}{a}`

, as long as you don't write `\dfrac2a`

which makes it less than readable.

We also prefer spaces between entities in the same way we prefer spaces between words when writing English -- the fact that the $\LaTeX$ compiler ignores them is a fact, yes, but it makes the code more readable to put spaces in, and the code lays itself out on the page better around page breaks.

Also -- watch for circularity when crafting proofs. Cheers. --prime mover (talk) 18:38, 30 August 2017 (EDT)

## Point of grammar

I point you to:

and also:

Minor points, but I'm sure you'll be okay with it.

Cheers, --prime mover (talk) 10:45, 3 March 2018 (EST)

## Whittaker and Watson

You will notice I added the source work you are using (info off the internet, Wikipedia mostly) and took the liberty of rationalising the references to it so as to use the edition you are using as a source.

This is how we have traditionally been handling materials from books with multiple editions -- in some cases an extensive rewrite of a source work has made this necessary.

Hope this is okay, and if so, I recommend you might want to use the style as amended on the pages you've written which cite it.

You may also want to populate the book page itself to reflext its contents, but as this is a boring job (I know, I've done a few of them) you might prefer to leave this to someone else who may also have that same edition. (If such a contributor exists on this site, that is.) --prime mover (talk) 07:27, 18 March 2018 (EDT)

- Thanks, understood and much appreciated, so I'll have a look. Whittaker and Watson is actually old enough to be public domain. I'm using the third edition in particular because it was the latest edition I found on archive.org's open library. (I have quite limited access to texts, but this scan is easily quality enough to substitute a physical copy.)
- I'm not sure how different each edition is, I'll have to look. Ideally it's just minor typographical corrections.

- The important thing is that if this is the edition you are using, then that should be the one that is referenced. No need to scour all editions for every difference. --prime mover (talk) 11:30, 18 March 2018 (EDT)

- Yeah, of course. As always I'll look at your changes and take note, no worries.
- You're free to populate the appropriate pages using the online edition if you want to, but I'll probably get to it eventually. (it's not as if my work, or knowledge for that matter, is very broad at the moment) Can you give an example of a complete, or near-complete, Book: page that I can look at so I can get a feel of the formatting? It would be helpful.

- Thanks again, Caliburn (talk) 10:24, 18 March 2018 (EDT)

- One taken at approximate random: Book:Nathan Jacobson/Lectures in Abstract Algebra/Volume I.

- Most are (or should be) done. All that exist on my own library shelf are, for example. Although lately, through lack of a decent enough scanner and conversion package, I've not been filling in all the small details. --prime mover (talk) 11:28, 18 March 2018 (EDT)

## recent work

The quality of your submissions is consistently superb. Just thought I'd say. --prime mover (talk) 12:29, 19 April 2018 (EDT)

In accordance with prime.mover's praise and my own comparable observations, I have added you to the "trusted" users group. This enables you to do whatever you need in the course of normal editing, without needing us.

Enjoy, you've earned it! — Lord_Farin (talk) 13:59, 22 April 2018 (EDT)

## Sources section: prev and next links

Please may I remind you about the Sources section, and the function of the prev and next links?

It was always intended that these links provide a linear ordering on the source work in question. Thus (except at the beginnings and ends of source works) there should be exactly one page for each "next" link, and from that "next" page exactly one corresponding link back to it again. This linear flow becomes compromised when someone copies and pastes an entire page, Sources section and all, to another page for editing, and pays no heed to these Sources links. There are then two pages with matching "prev" and "next" links and the flow is no longer linear, but branches.

Either the new page is in the source work whose links have been copied, in which case the links are to be updated accordingly (into wherever in the flow it fits, with all the complicated work that entails) or it does not, in which case that link should be removed (and if there are no links left, the entire Sources section should be removed with it). If you don't have the work in question, and you don't know whether the new page corresponds to material in that source work, then add the `{{SourceReview}}`

template into the Sources section of both the new page and the one it came from, and someone who does have that source work (and the patience to update the links properly) will attend to it. If you add a comment (the first anonymous parameter to that template) explaining what you did and what needs to be reviewed), this would be a bonus.

As you see in the invocation of the Refactor template, we specifically request that people who are not "experienced editors" do not perform these refactoring tasks, because of the difficult nature of the task that assails us when we find that the source flow has been broken. (Unfortunately we have learned that a number of contributors seldom care to honour this request, as they seem to enjoy refactoring and don't care about the source flow, but we press on regardless.)

If you don't care much for the source flow yourself, then at least please add that invocation of `{{SourceReview}}`

into the Sources section of pages you copy.

Many thanks. --prime mover (talk) 06:35, 15 May 2018 (EDT)

- Added the sources section from the other page as an afterthought while extracting it out. Didn't think to check ordering. Will remember to do so in the future. No point rebelling against reasonable requests in a small community, so I would never be neglectful intentionally. (find it weird you say it's commonplace here) Thanks, I appreciate your feedback as per usual. Caliburn (talk) 11:28, 15 May 2018 (EDT)

- Good job. --prime mover (talk) 16:45, 15 May 2018 (EDT)

## moving without leaving a redirect

Please, when you move pages, try **always** to leave a redirect. There is practically always something that directs to the old page. When you don't leave a redirect, these all get lost.

Also, if you are moving mathematicians into the Mathematicians namespace from Writers, can you also add the mathematician to the appropriate Mathematician date and country page? They are likely to get lost otherwise. --prime mover (talk) 11:42, 16 May 2018 (EDT)

- I agree, but I'm confused. You normally delete the redirect afterwards so I just assumed that's what was done. Suppressed redirects show in the deletion log the same way, so I don't see the difference. If the intent is to direct readers to the right page (which the deletion log does anyway), why not just keep the redirect? Though, I got the impression this site likes to use a minimal number of redirects from discussions. I also got the impression that the Writers subpages were obsoleted, so they were all to be moved to the Mathematician namespace, have I misunderstood? And yeah, I'll do that in future. Caliburn (talk) 12:48, 16 May 2018 (EDT)

- Yes, we delete the redirect.
**But not right away**.

- Yes, we delete the redirect.

- Imagine the following scenario. "Theorem A" has a link in it to "Result B". "Result B" is renamed to "Result C" except that "Result C" now has a completely different name. No redirect is given. So "Theorem A" now has a redlink to a page that no longer exists. Another editor comes along, sees this redlink to the page that does not exist and goes ahead and rewrites "Result B" (not having seen "Result C"). Now there are two results saying the same thing.

- So please, when you rename something,
**keep the redirects**until such time as**all**the pages that have "Result B" in them have been (manually) edited to point to "Result C" instead. Then, and only then, do we delete the page "Result B" which contains a link to "Result C".

- So please, when you rename something,

- Yes, the Writers paces are obsolescent, agreed. So as and when you find enough biographical details of a mathematician to include him/her as a complete Mathematician page, then we need to: a) add that mathematician to the appropriate date range page in the right place, b) add that mathematician the correct country of origin page in the right place, and c) remove the reference to the writer from the Writer page it came from (the one starting with that initial). Then and only then does the redirect get deleted.

- This is exactly why we placed a request on the Refactor page that only experienced editors do refactoring, because they understand all this. Just renaming pages is easy to do, but all the followup work: finding all the links to the old page and changing them to point to the new page; restructuring the pages they are transcluded in; reworking the Sources section -- that's not quite such fun. I have spent many a tedious weekend cleaning up after an editor's well-meaning but ultimately misguided attempt to change things around without thinking of the consequences. --prime mover (talk) 15:42, 16 May 2018 (EDT)

- The third line suffices, I was only confused by your advice to not delete redirects at all, just a straightforward clarification. I completely understand why redirects should be kept as I said previously. Redirect cleanup is something that's easy to do semi (or even fully) automated, (eg. with AWB. Though this should be used with someone familiar with the tool as it can cause quite a mess if misconfigured.) so if an editor moved pages en masse without changing links to them, it'd be quite easy to resolve that with the help of Special:WhatLinksHere. I don't intend on going on a spree suppressing redirects or anything. I'll always correct anything I slip up on if notified, so you don't need to worry about cleaning up after me. Caliburn (talk) 16:45, 16 May 2018 (EDT)

- Don't know what AWB is (it meant Average White Band when I was at school), so I don't know what you mean here. We have tried using automated tools to do automatic replacement of links before, but a) the things are riddled with bugs which render them unusuable, leaving the cleanup task worse than otherwise, and b) we can't guarantee that the links are all in the correct format (for example, some editors leave underscores in their links because it's more convenient for them, and someone else will always go through and clean up). Yes, WhatLinksHere is the primary tool to determine what link here (although you'd be surprised how few editors seem to know about it), and yes, while it's "quite easy" to resolve the redirects, when there are several hundred links to change, you can understand it can get a bit boring. But this is not about the updating of the links, this is about retaining the redirects in the first place so that the WhatLinksHere tool actually throws you the bone to get you started. --prime mover (talk) 17:10, 16 May 2018 (EDT)

## Style of presentation of these probability distribution pages

Hi,

A quick heads up: when you write (or rewrite) one of the pages detailing the properties of one of the probability distributions (Bernoulli, Binomial, etc.) it is important that rather than just present the notation, for example, $\Binomial n p$, that you also write it in words and provide a link back to the definition page.

A case in point: we now have Expectation of Binomial Distribution, which has this on it:

- Let $X \sim \Binomial n p$ for some $n \in \N$ and $0 \le p \le 1$.

... and the reader is left asking the question: what is $\Binomial n p$?

I appreciate that the name of it is given in the title of the page, and that the link to the page appears in the Definition of Binomial Distribution in Proof 1, but the site philosophy "there's no such thing as too many links" rules supreme, and we need to show it as something like the page used to be:

- Let $X$ be a discrete random variable with the binomial distribution with parameters $n$ and $p$:
- $X \sim \Binomial n p$

- Then the expectation of $X$ is given by:
- $\expect X = n p$

Was there a reason for deliberately removing the fact that $X$ is a discrete random variable? In the source work I got this from it explicitly specifies $X$ as being so. --prime mover (talk) 07:55, 30 March 2019 (EDT)

- I saw the specification of "discrete" as redundant (implied by the distribution), but this is fair enough, I see your point. An alternative that I thought about was practically the same as what was there before - so I'll put it back. Caliburn (talk) 08:03, 30 March 2019 (EDT)

- Nice one. Good job taking on this area of work, which has never really got off the ground. --prime mover (talk) 08:06, 30 March 2019 (EDT)

## Naming conventions

A quick heads up, it's something which seems to have evolved:

Names for pages (definitions, results) refer to singular objects, unless the result specifically discusses plural objects.

On the other hand, names for categories refer to plural objects, unless the thing in the category is genuinely a singular concept.

I wonder whether the category for Raw Moment should be "Raw Moments"? My thinking is that there are lots of different instances of "raw moments". Same probably aplies to "central moments" as there seem to be more than one: "first central moment", "second central moment", and so on.

You will probably come back to me and say: What about "Exponential Function", should that also not be "Exponential Functions"? Yeah, I know, I'm conflicted about that one -- but it's big enough to be really unwieldy to change them all now.

Your thoughts? --prime mover (talk) 05:59, 20 June 2019 (EDT)

- I'll go with whatever's standard. Pluralising makes more sense there when read out loud, and would be consistent with the naming of eg. Derivatives, Primitives and so on. I think exponential function is fine, because it's understood to mean $\exp$ specifically. Will go about changing it now. Caliburn (talk) 08:31, 20 June 2019 (EDT)

- Nice one. --prime mover (talk) 08:52, 20 June 2019 (EDT)

## new category

What do you reckon on a new category "Definitions/Statistical Distributions" or whatever the appropriate name is? We have a growing number, and it might be useful for the reader to be able to see all of them at a glance rather than have to hunt for them in Definitions/Probability/ What do you think? --prime mover (talk) 07:15, 23 June 2019 (EDT)

## Spiegel's Handbook

high five --prime mover (talk) 18:37, 10 August 2019 (EDT)

## Definition (mainly) pages with / in them

I was fairly sure I'd raised this before, but maybe not (hoping you'd pick it up by osmosis by following examples) but we avoid using the versions of definition pages which have a forward slash in them, for example, `[[Definition:Region/Complex]]`

. Generally (not completely universally yet, but working on it) such pages with subpages have a "permanent link" which are redirects. The most important reason for this is because as and when refactoring happens (as it often does), and the structure of such multilevel pages is changed, we only have to change the target of the redirect, and not every single page which links to , for example, `[[Definition:Region/Complex]]`

. So we would use `[[Definition:Region (Complex Analysis)]]`

instead.

It is straightforward to work out when such a redirect is available, and what it is: to a "what links here" to any such page. --prime mover (talk) 16:42, 15 March 2021 (UTC)

## Subfields of $\C$?

I notice that you have changed a few pages on Hilbert spaces to specifically restrict their domains to $\R$ and$\C$ from the general subfield of $\C$. Is there a specific reason that these results do not in fact hold for all such subfields? A cursory glance suggests that there should be no reason why they cannot apply to, for example, $\Q$ (for at least one of these results I can't see how metric space completeness is needed). I understand you may have a copy of Conway at your elbow. What does he actually say? --prime mover (talk) 05:50, 29 July 2021 (UTC)

- Originally I was mimicking the setup of an inner product space being over subfields of $\C$, then I got slightly nervous when no other source seemed to talk about Hilbert spaces over subfields. (Conway uses $\mathbb F \in \set {\R, \C}$ and so does Rynne&Youngson which I've looked at) Had a google and it seems to be the case that the only proper complete subfields of $\C$ are isomorphic to $\R$ or $\C$, (though such a result isn't on here yet) so there doesn't seem to be any loss either way, they seem equivalent setups. You're right that a lot of the results over Hilbert spaces apply over general inner product spaces, Conway talks mainly about Hilbert spaces so that's the setup that I'm copying over for now. We could go through after to see which generalise. Caliburn (talk) 11:46, 29 July 2021 (UTC)

## Measure theory

Thank you for working on filling out the pages on measure theory. I keep telling myself I need to start work on it to see what it has to offer, but all I have managed to get out of it so far is the attempt to extend calculus to non-continuous domains. I get the transfinite underpinnings, although don't have the patience to prove them. So big continued thanks and all encouragement for your studies. --prime mover (talk) 12:38, 11 December 2021 (UTC)

- No worries and thanks! Definitely does require a lot of patience, many of the fundamental proofs (that I've done so far at least) are just putting a hundred basic lemmas (that are sometimes so mundane texts don't bother to point them out) together with not too many "tricks". It's still pretty fun and it's nice to see stuff slot together. Caliburn (talk) 14:37, 11 December 2021 (UTC)

## Definition:Jordan Decomposition

Do you think it's worth renaming this a Definition:Hahn-Jordan Decomposition? Grounds for suggestion: concept names which encompass more eponyms have preference on $\mathsf{Pr} \infty \mathsf{fWiki}$, and, being reminded that this is a Jordan refinement of a concept named for Hahn, it actually makes it easier to keep track of which concept relates to which theorem. Knowing the Jordan Decomposition Theorem is about a Hahn-Jordan Decomposition makes it much more apparent to the casual reader that the Hahn Decomposition Theorem and the Jordan Decomposition Theorem are both about the same sort of stuff. Thoughts? --prime mover (talk) 21:47, 14 December 2021 (UTC)

- I don't mind. Wikipedia says that the name "Hahn–Jordan decomposition" is apparently sometimes used (though it gives no examples) so there are some grounds. Found something else that called it a "Jordan-Hahn decomposition" too. For now I'm just using the terminology I'm familiar with/is in Cohn. Feel free to play around with it, particularly when my wording is clunky. Caliburn (talk) 22:28, 14 December 2021 (UTC)

- When I added the source of name, I did get the right Jordan, yeah? --prime mover (talk) 23:13, 14 December 2021 (UTC)

## Redirects and permanent redirects

I may have discussed this before: when you start assembling things up into a structure of pages with transcluded subpages whose names have "/" in them, we try to implement specific descriptional redirects which do not have those "/" characters in them. The idea is that this "permanent redirect" is used **whenever** that page is linked to, so that, in the case where we get some refactoring needing to be done on the main pages for any reason, all we have to do is amend the redirect.

It's also a good idea **always** to leave the redirect in when you rename something. It is **very easy** to miss something in the course of refactoring which results in a broken link. If you rename **with** a redirect, you know you are then certain that everything that linked to it still does.

Many thanks for all the good work in this area. --prime mover (talk) 12:36, 20 December 2021 (UTC)

## Measure theory and notation

Please go ahead and take control of whatever you think needs to be done. Better to beg forgiveness than ask permission. See what it looks like when it's done and then we can take a view on the direction we want to take it.

The philosophy is fine, the accessibility of implementation is something that can be worked on gradually after we have something up there with all links in place on the live page.

As I say, I'm not in a headspace to think about the details myself, it's all a big heap of symbols to me -- but as long as everything is traceable back to a well-specified definition and matching notation we won't go wrong. The only problem is taking a notation for granted that is either not immediately obvious or not universal. --prime mover (talk) 12:22, 28 December 2021 (UTC)

## Coverage of Cohn

I noticed your coverage of Cohn in the context of Measure Theory. In my experience it is easy to lose track of where you are, what has been skipped, etc. So I would advise you to set up some page where you can track the progress and avoid getting lost; check e.g. User:Lord_Farin/Long-Term Projects/Schilling for an example of how I did it. — Lord_Farin (talk) 06:30, 28 April 2022 (UTC)

- $\overbrace \smile^{\odot \ \odot}$ If you
*really*want to go mad, you can check out the technique I use: User:Prime.mover/Source Work Progress --prime mover (talk) 07:46, 28 April 2022 (UTC)

## Recent achievement

Sincere congratulations. Best of luck with your future stuff. --prime mover (talk) 12:29, 7 July 2022 (UTC)

## Linear Functionals etc.

In revisiting Conway, I notice that you introduced on e.g. Definition:Bounded Linear Functional, Definition:Bounded Linear Transformation, two subpages, which differ only in that one is strictly subsumes the other. Would you object to me merging the two back into one (the normed vector space version)? — Lord_Farin (talk) 07:26, 25 October 2022 (UTC)

- I don't like it, it's pretty stupid and would never appear in a book. My thinking was that an inner product space isn't technically a normed vector space, but rather is readily identified with one, in a similar sense that a metric space in an extraordinarily strict sense is not a topological space, but is given a canonical topology based off its metric and identified with a topological space. This ignores the fact that metric spaces usually yield neater presentations or characterisations than topological spaces. I guess this is still the case with this as well, but I'd rather have all those as theorems instead. If we're all good bulldozing it then that's great by me, I didn't really like it even as I was doing it, it was just done under the thought that we should avoid just deleting content. Caliburn (talk) 10:38, 25 October 2022 (UTC)

- Perfect. I'll be cleaning it up then. — Lord_Farin (talk) 12:54, 25 October 2022 (UTC)

- I think it is done. On the way I encountered some discussion regarding this idea but I stood by my point. The relevant links should always be made by referring to the induced norm and then the link, instead of duplicating everything. Since we have a proper page on the induced norm it should be easy to do so. — Lord_Farin (talk) 17:39, 26 October 2022 (UTC)

## Publication date of the Le Gall

Can you check your records for the publication date of Book:Jean-François Le Gall/Brownian Motion, Martingales, and Stochastic Calculus? According to https://link.springer.com/book/10.1007/978-3-319-31089-3 it's 2016. You seem to be citing it as 2012. Cheers. --prime mover (talk) 08:11, 2 January 2023 (UTC)

- 2016 is correct, I had read the wrong date. Thanks for the spot. Caliburn (talk) 12:22, 2 January 2023 (UTC)

- I think I've fixed them all. You may want to check. --prime mover (talk) 13:09, 2 January 2023 (UTC)

## Pazy book

Sorry just need to clarify -- I was under the impression that it was first published in 1974, and that 1983 was the 2nd edition -- can you check / clarify?

- First edition second printing? Front of book says "Softcover reprint of the hardcover I st edition" and then "Preface to Second Printing". Caliburn (talk) 10:24, 17 March 2023 (UTC)

- We don't differentiate between printings. We do differentiate between editions. I really don't want to have to have the hard work of maintaining software for every single printing of every single edition, and even if we do have a separate preface to a different printing, I don't want to have to care. So can we assume that the book referred to is in fact a 1983 reprinting of the 1974 edition, or is the first edition actually from 1983? I don't have a copy myself and I am not planning immediately on getting it, so I'm going to have to rely on you for accuracy. --prime mover (talk) 16:50, 17 March 2023 (UTC)

## Minkowski functionals and all that

I'm feeling a bit out of my depth, but I am trying to use your latest work on Minkoswki functionals and convex absorbing sets etc. to educate myself a bit.

I am having trouble because knowledge of a lot of the concepts seems to be taken for granted, and no links provided to crucial underlying definitions -- some of which, when I link to them, seem flawed.

There is much use of invocation of $t$ such that $t > 0$, but the domain of $t$ does not necessarily support an ordering -- hence I am all at sea as to exactly what *is* meant by "absorbing".

Unfortunately I don't have a copy of Rudin so I can't directly go through and read and see what he actually says, otherwise I'd be on it. --prime mover (talk) 07:46, 15 June 2023 (UTC)

- This is what Rudin says exactly. At the beginning of the book, the scalar field is taken to be either $\R$ or $\C$. Caliburn (talk) 08:00, 15 June 2023 (UTC)

## Rename leaving redirect

A quick note: please, when renaming a page, *always* please leave a redirect.

It is then a trivial matter to go through and change the links.

As it is, with the latest rename, you missed one and we had a redlink to a page that no longer existed.

Many thanks. --prime mover (talk) 06:20, 16 June 2023 (UTC)

- Yep sorry, I will just move without redirect in the future and let someone pick this up as a maintenance task since I've done this before. Caliburn (talk) 07:10, 16 June 2023 (UTC)

## congrats

When does your name get added to the Hall of Fame? Mathematician:Mathematicians/Sorted By Birth/1951 + CE --prime mover (talk) 11:25, 27 June 2023 (UTC)