# User talk:Jochen Burghardt

(Jochen Burghardt's Talk page)

## Subsumption lattice

Hello Jochen, You replied in the correct way. As for the supposedly incorrect review, the page that you mentioned in your message to me does contain similar language, however that does not mean that it is the correct way to write an article. The reviewer of the article may have been mistaken. Good luck for any future articles you propose! Thomas85753 (talk) 12:15, 22 August 2012 (UTC)

Hello again,

Try Mass-energy equivalenceThomas85753 11:06, 23 August 2012 (UTC)

Hi Jochen, I moved your article into the main namespace, after some minor copyediting. Cheers, —Ruud 13:26, 4 May 2013 (UTC)
Many thanks!!! I'm a bloody novice among Wikipedia authors and felt unable to meet Thomas85753's critics. Jochen Burghardt (talk) 19:02, 9 May 2013 (UTC)

## A belated welcome!

Sorry for the belated welcome, but the cookies are still warm!

Here's wishing you a belated welcome to Wikipedia, Jochen Burghardt. I see that you've already been around a while and wanted to thank you for your contributions. Though you seem to have been successful in finding your way around, you may benefit from following some of the links below, which help editors get the most out of Wikipedia:

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I hope you enjoy editing here and being a Wikipedian! If you have any questions, feel free to leave me a message on my talk page, consult Wikipedia:Questions, or place {{helpme}} on your talk page and ask your question there.

Again, welcome! (talk) 08:48, 7 June 2013 (UTC)

## "Size" for cardinality

Hi Jochen, I agree with the point you made. "Number of points" needs to be avoided when talking about infinite cardinalities (even with the quotes). I chose "size" to replace it because that seemed to be the alternative used elsewhere in this article. It is certainly not a perfect choice and not one that I would normally use in my own writing, but for consistency it seems to be the best choice. While it is possible that some readers could confuse size and length, it is unlikely that anyone who does would be sophisticated enough to understand the meaning of a one-to-one correspondence. Thank you for the addition. I didn't check to see if you created the image, but if you did I would suggest that you increase the line width (to 2 or 4 pixels) otherwise the colors are too pale and the point you are making with the colors is weakened because they are hard to discern. Bill Cherowitzo (talk) 04:06, 8 June 2013 (UTC)

## punctuation

Please see my edits to Anti-unification (computer science).

right: pp. 74–83
wrong: pp. 74-83

Ranges of pages, years, or other numbers, or of letters of the alphabet, use an en-dash, not a hyphen. This is codified in WP:MOS. Michael Hardy (talk) 21:02, 30 June 2013 (UTC)

## Table floating layout

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In the articles

I used the "float: left;" style parameter to arrange several tables in a nice way. However, I'd like the text following the tables to be ordinarily left-aligned (as would be usual in the absence of floating tables) rather than floating around the tables. In particular, the 2nd article ("Word_problem ...") looks very ugly now - its "See also" section should begin below the tables rather than right to them.

How can I achieve that? I didn't find any appropriate hint in the Help:Table article. Many thanks in advance. Jochen Burghardt (talk) 17:11, 11 August 2013 (UTC)

What you want is the {{clear}} template. I have added it to those articles. However, Confluence_(term_rewriting)#Motivating_examples still doesn't really look good to me, and I wonder whether it wouldn't be better to put the group axioms and all the small proofs into a large table to neatly arrange them. Huon (talk) 18:34, 11 August 2013 (UTC)

## Disambiguation link notification for September 9

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## Thumbnailing animated GIFs

There's not trick to it, and it's not even intentional that the sieve illustration on Prime number is not animated in the thumbnail. It's a feature of the MediaWiki software: It does usually create animated thumbnails, but if the overall image size exceeds a certain configurable limit, it only generates a still-image thumbnail. The overall image size is calculated from the geometric extents of the image but also the number of frames in the animation; so if you have a relatively large image and a relatively long-running animation (as in this case) there is no way to make Wikipedia create an animated thumbnail. Presumably this is so in order to reduce server load, because creating animated thumbnails can potentially require much computing time on the server—or so I would guess. --SKopp (talk) 10:41, 13 October 2013 (UTC)

## October 2013

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## November 2013

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## Cantor's diagonal argument

Hi Jochen. I'm happy to see that you are editing Cantor's diagonal argument. In the past, I felt that the article could be improved but I only made changes to one section.

However, I think you may have made a common error in your exposition of Cantor's 1891 proof. Here's how Cantor's proof is presented on page 823 of Gray, Robert (1994), "Georg Cantor and Transcendental Numbers", American Mathematical Monthly 101.

3. CANTOR'S DIAGONAL PROOF. We now turn to Cantor's 1891 article [9], which contains his well-known diagonal proof. Cantor begins by discussing his 1874 article. He points out that it contains a proof of the theorem: There are infinite sets that cannot be put into one-to-one correspondence with the set of positive integers. Then he asserts that this theorem has a much simpler proof than the one given in 1874. His new proof uses the set M of elements of the form E = (x1, x2, … , xν, …), where each xν is either m or w. Cantor states that M is uncountable, and notes that this result is implied by the following theorem:
If E1, E2, … , Eν, … is any simply infinite sequence of elements of the set M, then there is always an element E0 of M which corresponds to no Eν.
Cantor proves his theorem by using the diagonal method to construct E0. Note that, once again, Cantor states a theorem that separates the constructive content of his work from the proof-by-contradiction needed to establish uncountability.

Of course, you may want to check Cantor's original article to make sure the above exposition is correct.

The above quotation was not written for Wikipedia readers and assumes the reader can fill in the proof-by-contradiction: Assume that the set M is countable. Then its elements can be written as a sequence Eν. Applying Cantor's theorem to this sequence produces an E0 that does not belong to the sequence. This contradicts our original assumption, so M must be uncountable.

I believe there are several reasons why Cantor's constructive theorem should be mentioned:

• It is historically accurate.
• It is important for the reader to understand that the diagonal method is constructive. After all, Gödel used it to construct an unprovable sentence in number theory. Also, Turing's answer to the Entscheidungsproblem uses the fact that the diagonal argument can construct computable numbers. (Turing constructs a computable real number that does not belong to a sequence of computable real number.)
• It shows readers how Cantor separated the constructive content of his work from his proofs-by-contradiction. Another example of this can be found in Cantor's first uncountability proof.

Once again, thank you for working on Cantor's diagonal argument, and I look forward to your edits on this and other articles. --RJGray (talk) 00:50, 8 December 2013 (UTC)

Hi Robert(?) J. Thank you for your elaborate and convincing explanation. When editing the article for the first time, I just felt its presentation should be improved, but didn't pay attention to the separation of constructive and indirect proof. Following your hint, I (only then) checked Cantor's original article, and found your(?!) 1994 AMM paper in perfect agreement with it. I tried to adapt the wikipedia article accordingly, also using your above text as basis for the indirect proof.
Reasons for some deviations were: "Binary digits" are more common than Cantor's original "m"/"w" symbols (he might have in mind the german "männlich"/"weiblich" = "masculine"/"feminine" - ?), maybe a "0"/"1" version of the picture should be used for consistency. I kept the set name "T" and sequence name "s" found in the article, where Cantor used "M" and "E", maybe I should adapt this. I used "i" as general index to avoid Cantor's Greek "ν" (less easy to understand). I used "enumeration" (of sequences) for a list of members of T and "sequence" (of bits) for a single member of T to ease reference to, say, vertical and horizontal coordinates in the diagonal argument's matrix. I tried to rephrase your indirect argument text in conjunctive form to emphasize the speculative nature.
Maybe each of the two proof parts should have its own subsection, but I couldn't yet find appropriate headings for them.
Best regards - Jochen Burghardt (talk) 11:37, 8 December 2013 (UTC)

Hi Jochen. Your rewrite is excellent−I especially like your clear and concise way of expressing the constructive and indirect aspects of Cantor's work. On the issue of changing T to M and s to E, I see no reason for changing them or for using Cantor's m and w. My MAA article (yes, I did write that article) is an historical article that contains quotations from Cantor's article, so it was best for me to use Cantor's notation. In the article Cantor's first uncountability proof, I used xn rather than Cantor's 1874 ωn notation. However, I suggest that you replace the index i with n since sn and "nth digit" is easier to read than si and "ith digit". Also, the section "Real Numbers" uses n as an index.

As for the picture with m and w, I think they can be changed to 0s and 1s. Also, the E can be changed to s (and renumbered to start at 1). Then you could make the first 7 elements in your proof identical to the first 7 elements of the picture so the picture would be an illustration of your proof.

I think that the two proof parts are fine together in one section. Since the uncountability result is an application of Cantor's constructive theorem, I regard it as belonging to the same section since it shows how Cantor's theorem can be used. As for writing the proof-by-contradiction in subjunctive form, I think this is a matter of taste. In English, the subjunctive is not used very much, so I tend to not use it. The section Square root of 2#Proofs of irrationality does not use the subjunctive, but the article Proof by contradiction does.

I like your addition of graphs to the section "Real Numbers". Since this section is about bisections, I don't think it's a question of whether they distract from the main theme of diagonalization, but a question of whether they enhance the "Real Numbers" section (which they do). However, I think some readers may find the left picture confusing since it does not illustrate a bijection from (0, 1) to (−π/2, π/2). Instead, it illustrates a bijection from (e1, e2) to (s1, s2) where e1, e2, s1, and s2 are positive.

You are doing excellent editing and it's a pleasure to communicate with you.--RJGray (talk) 02:19, 9 December 2013 (UTC)

Hi Robert. Thank you for your compliments. As you suggested, I changed i to n, and adapted the picture (however, I don't know yet how to produce Svg from LaTeX, so the Jpg thumbnail looks somewhat noisy). Concerning the "Real Numbers" section and its pictures, I meanwhile thought about using a rational function (as shown in File:Bijective map from interval (0,1) to R.gif; the function looks like being strictly increasing, but I didn't prove it)) to avoid tan and function composition, hence also to save one image. On the other hand, the current approach, using "components off the shelf" is more typical for mathematicians, so maybe we should keep it (I'd adapt the linear map image to the proper intervals in that case). I'm quite indecisive about that; what do you think? Best Regards - Jochen Burghardt (talk) 12:52, 10 December 2013 (UTC)

Hi Jochen. One small experiment for your illustration of Cantor's argument: Try removing the commas (and perhaps spacing the 0s and 1s closer together?). Then it may be simpler visually, and it's an illustration so you don't need the precision of the commas. I don't know how to produce Svg from LaTeX myself, but I noticed that the original illustration was created on Inkscape, which can be downloaded free from inkscape.org. Also, I noticed that you labeled the resulting sequence as sn rather than s.

As for the pictures in "Real Numbers", I suggest either doing one picture using the composite function tan(πx - π/2) or replacing the current linear one with πx - π/2. I feel that the most important thing about illustrations is that they should agree with the text. By the way, the text uses tan(x) because it's a common way to get a bijection from an open interval to R. Also, most readers should be familiar enough with tan(x) to realize that, restricted to (-π/2, π/2), it is a bijection (your tan picture will help readers here). Keep up the fine work! --RJGray (talk) 02:54, 11 December 2013 (UTC)

## Cantors erster Überabzählbarkeitsbeweis

Hi Jochen. I'm happy to see that you are editing Cantor's first uncountability proof. Have you read the German version de:Cantors erster Überabzählbarkeitsbeweis? It does not follow Cantor's original approach of a constructive theorem followed by a proof-by-contradiction. It also contains a non-constructive proof of the existence of transcendental numbers instead of Cantor's original proof. In fact, the German version seems to have come from the original English version of "Cantor's first uncountability proof".

I am currently working on a French translation of "Cantor's first uncountability proof". Do you have any interest in doing a German translation? I think that you would do a great job, you are a native German speaker with excellent editing abilities. Of course, I understand that the article is a bit long with all its footnotes, but I think it would be great for Cantor's original approach to appear in the German Wikipedia since he was a German mathematician. --RJGray (talk) 02:30, 15 December 2013 (UTC)

I'm not sure I want to get involved with German wikipedia, where a lot of rules, templates, etc. are quite different. I'll think about it. - Jochen Burghardt (talk) 12:45, 16 December 2013 (UTC)

## Sfrac template renders slash and horizontal line in mobile view

 This help request has been answered. If you need more help, place a new {{help me}} request on this page followed by your questions, contact the responding user(s) directly on their user talk page, or consider visiting the Teahouse.

In the article section Hoare logic#Conditional rule, I used the "sfrac" template to create a natural deduction-style rule (consisting of a horizontal line, some formulas above it, and some below it). The rendering looks fine in the desktop view. However, in the mobile view, an additional "/" is shown immediately above the horizontal line. I guess the "/" is shown due to a programming error in the template code, but I don't have a clue how the template code works. Many thanks in advance. - Jochen Burghardt (talk) 20:00, 13 January 2014 (UTC)

This is how sfrac looks like in desktop view (it is ok):

{B ∧ P} S {Q}    ,     {¬B ∧ P } T {Q}
--------------------------------------
{P} if B then S else T endif {Q}


This is how sfrac looks like in mobile view (the "/" should not be there):

{B ∧ P} S {Q}    ,     {¬B ∧ P } T {Q}
/
--------------------------------------
{P} if B then S else T endif {Q}

Thanks for your attention to this detail. For the relevant people to see it, please, ask at the mobile front-end feedback page or file a bug like linked at the top of the page. Thanks. ☺ Gryllida (talk) 20:24, 13 January 2014 (UTC)

## Galois connection reference

I notice that in this edit you added a reference to one of your own papers. Personally I don't have a problem with that, but some editors don't like it. It's probably safest to suggest it at the article talk page first. Deltahedron (talk) 20:51, 1 February 2014 (UTC)

Thanks for your advice; I followed it. - Jochen Burghardt (talk) 21:13, 1 February 2014 (UTC)
I'm sure it will be OK. Deltahedron (talk) 21:17, 1 February 2014 (UTC)

## Converting citation to cite doi

Please do not convert {{citation}} to {{cite doi}}.

• They have different formats: citation uses commas as separators, while cite doi uses periods.
• Citation allows author names to be spelled out, while cite doi requires them to be given using initials (this requirement is enforced by bot editing)
• Citation works with {{harv}} referencing, while cite doi in its default behavior does not.
• Changes to citatations made using citation are visible in watchlists, while changes to the separate pages made by cite doi are not, causing cite doi to be much less resistant to vandalism.
• Citation is much more flexible, while cite doi requires incompatible citation templates to be used for references that do not have dois.
• Per WP:CITEVAR, "Editors should not attempt to change an article's established citation style merely on the grounds of personal preference, to make it match other articles, or without first seeking consensus for the change."

David Eppstein (talk) 19:06, 16 February 2014 (UTC)

Hello David Eppstein. I naivley assumed that having a central site for e.g. an journal article would be valuable in any case. I therefore created a couple of "cite doi" pages, and replaced articles' references by ((cite doi)) templates. After I saw your reverts, I immediately stopped that activity. Please apologize the inconvenience. I guess, ((cite journal)) shouldn't be changed to ((cite doi)) either? Is there any acceptable way to centralize reference data, without causing problems like those you described above? - Jochen Burghardt (talk) 19:25, 16 February 2014 (UTC)
Here is a complete (except for those already reverted by you) list of articles I changed an the above way:
• cite journal-->cite doi (I'll revert them too, if you wish):
• cite book/conference-->cite doi (I'll revert them too, if you wish):
• no template-->cite doi (I'll revert them too, if you wish):

- Jochen Burghardt (talk) 20:14, 16 February 2014 (UTC)

Thanks! I'll let you decide for yourself which of these you want to undo, but I think of cite journal to cite doi as being less of a problematic change — a couple of my objections to cite doi above are still valid (the ones about watchlists and author initials) but their formatting is pretty much interchangeable with each other. I would love to have a centralized database system like BibTeX where one could just refer to a reference by name and have it formatted automatically in whatever variation is appropriate for the article but I don't think we're there yet. —David Eppstein (talk) 20:15, 16 February 2014 (UTC)

## Disambiguation link notification for March 8

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## March 2014

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## Boolean Axiomatics error?

Hi Jochen, I'm not a WP regular, but I think I spotted an error (perhaps a typo or copy/transcription error) in an edit you made to http://en.wikipedia.org/w/index.php?title=Boolean_algebra_%28structure%29&oldid=571924694

In the edit, you very nicely added some proofs of basic laws from axioms. The error I think I spot is in the proof for Huntington's A1 theorem. The code "XIb" does not seem to refer to any previous theorem or axiom, and a quick google search didn't turn up anything to explain what "XIb" might mean. By looking at the step being justified, however, I believe the correct justification reference/code should be "Abs2". I'm going to make that edit now. If I'm wrong, feel free to revert. ~ RH — Preceding unsigned comment added by 24.57.4.82 (talk) 20:00, 1 April 2014 (UTC)

Hi RH, you are perfectly right, "XIb" should be "Abs2" - many thanks for recognizing and correcting this! The "XIb" originated from [Huntington, E. V. (1933), "New sets of independent postulates for the algebra of logic", Transactions of the American Mathematical Society (American Mathematical Society) 35 (1): 274–304, doi:10.2307/1989325, JSTOR 1989325], where Huntington assigns on p.277 the numbers "Xa" and "Xb" to the absorption laws. Additionally to not replacing "Xb" by "Abs2", I had confused "Xb" with "XIb". - Jochen Burghardt (talk) 20:53, 1 April 2014 (UTC)

## April 2014

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I have not "added copyrighted material" to the Aho–Corasick string matching algorithm article. Apart from minor layout edits, I only added a link to a pdf file. As far as I understood, WP:COPYLINK explicitly allows this (else, I certainly wouldn't have added the link):

Since most recently-created works are copyrighted, almost any Wikipedia article which cites its sources will link to copyrighted material. It is not necessary to obtain the permission of a copyright holder before linking to copyrighted material,...

If you still think my addition was illegal, please give a proper reason. If not, please undo your deletion. Thanks in advance. - Jochen Burghardt (talk) 20:17, 21 April 2014 (UTC)
I agree that this message was badly phrased. However, the issue is whether the PDF file that you linked to was itself a copyright violation: if you know or reasonably suspect that an external Web site is carrying a work in violation of the creator's copyright, do not link to that copy of the work. In this case it is certainly not clear that the web site owner was the owner of the copyright in that page. Deltahedron (talk) 21:17, 21 April 2014 (UTC)
You have linked to an apparent copyright violation. Just because you can find the article somewhere on the internet does not mean that copy is legal. There are no problems with citing copyrighted material or linking to authorized copies of the material. But you need to be sure the copy is authorized.
The added link was to a copy of a printed journal article. The article's first page clearly states "Copyright © 1975, Association for Computing Machinery". If you follow the doi link in the reference, you will see that the publisher, ACM, is still selling the article. The link you provided appears to be in the home directory for somebody named Watson and does not appear to be either Aho or Corasick (or even Bell Labs). There is no evidence that the link is an authorized copy. Glrx (talk) 23:12, 21 April 2014 (UTC)

## Disambiguation link notification for April 6

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## Robert Recorde

Hi, just wanted to stop by to apologise for the edit I made on Robert Recorde. I should have given an edit summary explaining that I used another citation to reference the statement you had (quite rightly) highlighted. However, instead of pressing preview, I hit save. So, sorry about that. I shall endeaver to be more careful in future. All the best, Daicaregos (talk) 12:23, 6 May 2014 (UTC)

## A barnstar for you!

 The Original Barnstar Inductive logic programming is amazing to me. I found this page and the related pages a complete revelation. I had just been thinking, "I wonder if this is a way of creating theory's/hypotheses that explain conditions, in a way similar to resolution". Thanks for your explanations. Thepigdog (talk) 08:50, 15 May 2014 (UTC)

## Deductive lambda calculus

Thanks for your requests for clarification in Deductive lambda calculus. I have responded to your requests.

All criticisms and comments always appreciated.

Thepigdog (talk) 05:38, 19 May 2014 (UTC)

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## June 2014

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## August 2014

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## Bach audio edits

Hi Jochen, thanks for your efforts to add audio to lists of Bach's works. However, on the English Wikipedia we're generally quite conservative about when audio is added to a classical music article ... the sound file must be faithful to the original composition, be performed on acoustic instruments (in almost all cases), and must have appropriate licensing. That's why I've undone your additions of the audio files. We have a template specifically designed for music files (among others), {{listen}}. Graham87 15:00, 15 August 2014 (UTC)

Ok, I see. I quite naively thought it would be a good idea to have an overview page where each (available) file can be played in one click. I didn't think much about the subtleties you mention above. I was too bold this time - sorry. - Jochen Burghardt (talk) 15:09, 15 August 2014 (UTC)
And thanks for cleaning up my mess. According to my Contributions page, all my Bach edits are undone now. (I didn't touch other composers' pages.) - Jochen Burghardt (talk) 15:14, 15 August 2014 (UTC)