User talk:Jochen Burghardt

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Subsumption lattice[edit]

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![edit]

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

"Size" for cardinality[edit]

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[edit]

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[edit]

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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)

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Thumbnailing animated GIFs[edit]

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[edit]

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November 2013[edit]

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Cantor's diagonal argument[edit]

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" (PDF), 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[edit]

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[edit]

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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[edit]

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[edit]

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:

- 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)

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March 2014[edit]

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Boolean Axiomatics error?[edit]

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" (PDF), 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[edit]

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Copyright violation?[edit]

(section header added subsequently - JB)

Stop icon Your addition to Aho–Corasick string matching algorithm has been removed, as it appears to have added copyrighted material to Wikipedia without permission from the copyright holder. If you are the copyright holder, please read Wikipedia:Donating copyrighted materials for more information on uploading your material to Wikipedia. For legal reasons, Wikipedia cannot accept copyrighted text, or images borrowed from other websites, or printed material without a verifiable license; such additions will be deleted. You may use external websites or publications as a source of information, but not as a source of content, such as sentences or images—you must write using your own words. Wikipedia takes copyright violations very seriously and persistent violators will be blocked from editing. See WP:COPYLINK. Glrx (talk) 19:34, 21 April 2014 (UTC)

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)

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Robert Recorde[edit]

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![edit]

Original Barnstar Hires.png 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[edit]

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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August 2014[edit]

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  • "Remarks on the mind-body question"], in: I.J. Good, "The Scientist Speculates", London, Heinemann)</ref><ref>Hans Primas, Michael Esfeld (1997) [http://philsci-archive.pitt.edu/1574/1/

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Bach audio edits[edit]

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)

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A barnstar for you![edit]

Original Barnstar Hires.png The Original Barnstar
For work on Conjunctive normal form. Thepigdog (talk) 01:19, 9 November 2014 (UTC)

a small modification to Schröder–Bernstein theorem - update[edit]

You deleted my addition with the Statement that the proof does not use equivalence classes. I was not clear enough in my writing.

here is another go:

two elements in the set (A union B) relate to each other if and only if they belong to the same sequence. The proof called the equivalence classes that are created by this equivalence relation as a "sequence".

I just wanted to note that to complete the proof you don't have to find the bijection explicitly ,only show that for each sequence, the cardinality of elements of A is equal to the cardinality of elements of B. But this is trivial: if the sequence is infinite then the cardinality is countable infinity (for elements of A and of B). if the sequence has a finite number of elements then it must have an even number of elements : and therefore the number of elements of A is equal to that of B.

no need to build the bijection. no need to consider so many special types of sequences.

thank you for your time — Preceding unsigned comment added by 31.210.187.4 (talk) 13:53, 28 January 2015 (UTC)

My reason for deleting was that your text suggested ("Written concisely") to be a summary of the proof immediately before it, which it was actually not. My criticism wouldn't apply if you're going to present an alternative proof.
However, I still don't understand you above text:
  1. If a sequence is infinite, why should "the" (i.e. its?) cardinality be countable infinity? After all, no restriction is made about A and B.
  2. The notion of cardinality is usually defined after the Schröder–Bernstein theorem has been proven. The validity of the theorem is a prerequiite for the notion being sensible. In particular, the theorem is not about A and B having same cardinality in the first place, but about a bijection existing between A and B.
-Jochen Burghardt (talk) 20:25, 28 January 2015 (UTC)

Thanks for the quick response!. I get it now. let me rephrase with consideration of your comments: when you look how each sequence is constructed you can see that I have an element from A then B then A again and so on... . by the construction of the sequence itself it is clear that I can index the elements of the sequence - in otherwords there is a bijection from the sequence to the natural numbers. for "doubly infinite sequences" the simplest bijection is to the integers.

and it is clear that the even(or odd) indexes belong to elements of B and the odd(even) indexes belong to elements from A.

A bijection from even to odd natural numbers(integers) is trivial.

Notice that I did not claim anything about A or B only that the sequences are countably infinite/finite by construction.

If the sequence is finite my original argument (the number of elements in the sequence is even) stays.

About "prerequite for the notion (of cardinality) being sensible" : I just defined sets with equal cardinality with bijections. this "relation" between sets is an equivalence relation. I consider this introduction to infinity as good enough to use the term cardinality for a proof of this theorem. — Preceding unsigned comment added by 132.70.66.14 (talk) 23:18, 28 January 2015 (UTC)

For now, just a counterexample where an uncountably infinite sequence occurs: let A be the first uncountable ordinal in von-Neumann representation, let B=A\{0}, let f:A-->B be the successor function, and g:B-->A be the identity. Then there is exactly one sequence, which is an A-stopper (since 0 has no predecessor), and contains all members of A and of B; it hence is uncountably infinite. - Jochen Burghardt (talk) 23:57, 28 January 2015 (UTC)

Thank you very much. — Preceding unsigned comment added by 132.70.66.14 (talk) 07:58, 29 January 2015 (UTC)

Concerning your introduction of cardinality: The approach I've learned is to define two relations, say ≡ and ≤, on the class of all sets, with the intended intuitive meaning has the same cardinality as, and has cardinality less or equal than. The relation ≡ is defined via the existence of a bijection, and ≤ via that of an injection. It is straight-forward to show that ≡ is an equivalence relation, and that ≤ is reflexive and transitive. The anti-symmetry of ≤ (modulo ≡) is the difficult part, this is just the Schröder–Bernstein theorem. After that, i.e. when ≡ and ≤ has been shown the be an equivalence and a partial ordering, respectively, the notion of the cardinality of a set makes sense.
If I understood you right, your way would be to introduce ≡, prove that it is an equivalence, then introduce a (seemingly) weaker notion of cardinality (e.g. ℕ and ℝ would still have different cardinalities by Cantor's diagonal argument, but you couldn't tell yet which set is "larger"), then use that notion in the Schröder–Bernstein proof, then define ≤, state its ordering property, and establish the usual notion of cardinality. That may be a feasibly way, too. It seems, however, you'd have to establish that in the finite case your notion of cardinality coincides with the "obvious properties of counting" (reasoning about "even number of elements" etc.), and to solve the problem countable vs. uncountable in the infinite case. I don't yet see that his way would turn out more elegant than constructing the bijections directly. - Jochen Burghardt (talk) 11:58, 31 January 2015 (UTC)

I dont think you counter-example works : for the successor function to reach all elements you need a limit step in addition to n+1 step or successor step: the first uncountable ordinal contains the first countable ordinal+1 (omega plus one or second countable ordinal). and the successor can't reach the last elements in omega+1.

Ooops, you are right - sorry. No limit ordinal has a predecessor, so every limit ordinal is the start of an own sequence in my example. I'll have to think about this. - Or can you prove that each sequence has at most countably many elements? - Jochen Burghardt (talk) 17:11, 1 February 2015 (UTC)

I don't think I can present the proof in a better way then what is now. I'll need induction to prove that a sequence is countable infinite. maybe its worthwhile to add a comment to the proof about the "sequences" and call them as they are, if you think it adds a bit more understanding to the proof of this theorem. — Preceding unsigned comment added by 132.70.66.14 (talk) 18:19, 2 February 2015 (UTC)

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Reference errors on 26 March[edit]

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equals sign[edit]

I thought that using the math "equals" sign in the Equation article made it a bit bigger and clearer than the version you used. But what the heck. That's not worth fighting over. However, in the context, the sign should certainly be between quotation marks.DOwenWilliams (talk) 21:10, 1 April 2015 (UTC)

I don't prefer a particular size of the sign; also, the quotation marks are fine. I'd just like to keep the link. Would you accept "\scriptstyle =" ? (Observe that clicking on it links to another article.) - Jochen Burghardt (talk) 05:45, 2 April 2015 (UTC)

Philosophy of mind[edit]

You're very welcome! I'm always curious as to how different values of column width render in various accessibility situations. One guide that helps with this is found in Reflist's template documentation and probably could use some tweaks. There are still a lot of "hard" columnization in articles, so feel free whenever you see a "2" or "3" in a References or Notes section to change it to "20em", which so far seems to be the best. And I've found that from "15em" to "20em" is also good for See also columns, maybe smaller like "10em" if there is a Wiktionary or other template used. Thank you! and Best of everything to you and yours! – Paine 16:58, 17 April 2015 (UTC)

Hi, I don't habe any wikipolicy to quote, but I think that 20em columns are a bit narrow for rendering on desktops. I think the width I've most commonly seen is 30. It still renders well on tablets and it makes the references easier to read. T.Shafee(Evo﹠Evo)talk 08:58, 21 June 2015 (UTC)

I made some screenshots of Point mutation#References on different devices with different settings ("PC": firefox in a 1280x800 window on my PC, "TABLET": on my 8 inch screen diagonal tablet, "desktop": Wikipedia display option "desktop view", "mobile": Wikipedia display option mobile view). I've put a ruler showing centimetres at to bottom to indicate the appearance in the real world. Note that with "35em", the references are unreadable in the tablet in Wikipedia's "desktop" setting (font below my eye's resolution, lower mid image) as well as in "mobile" setting (right column off screen, lower right image). This is the reason why I changed the "35em" to "20em", as recommended by Paine Ellsworth above. Maybe Wikipedia's column rendering algorithms should be improved - on the other hand, I don't really see what problems people have with "20em" on a PC, the upper right screenshot looks fine to me. - Jochen Burghardt (talk) 13:18, 21 June 2015 (UTC)

PC (desktop) TABLET (desktop) TABLET (mobile)
20em Refsize DE de 20.jpg Refsize MO de 20.jpg Refsize MO mo 20.jpg
35em Refsize DE de 35.jpg Refsize MO de 35.jpg Refsize MO mo 35.jpg


I think 20em is awfully narrow for usual full references (full = includes title and date and author etc etc). 30em is the most common width and it looks great to me. It's not really something that I want to edit war over but I remember that I have reverted a few of your edits where you changed the column width to 20em with the explanation that it looks better so on tablets. I'm sorry but I think normal computers, i.e. desktops and laptops, should be prioritized. If you want to keep changing these to 20em then you should gain some sort of a consensus for that first. (Changing 35ems to 30ems though shouldn't be a problem, I think.) — Jeraphine Gryphon (talk) 13:43, 21 June 2015 (UTC)
At first, many moons ago, I began changing "3" (the usual number of columns I found in the Refs sections) to "30em". I don't remember who the editor was, perhaps it was Jochen(?), but I was told that the tablet they used did not render 30em very well at all, and that 20em worked much better for them. So I've been using 20em ever since. As this is an important accessibility issue, I would advise all to be as sensitive as possible to the needs of others. If this means that 30em is better for some but not all, and those some can live with 20em even though it's not quite as good for them as 30em is, then to be accessible to all, the choice should really be 20em, or perhaps slice it down the middle to 25em. Since I abhor edit wars, I would ask that everyone continue to stay on talking terms and not resort to such things. Thank you very much and Best of Everything to You and Yours! – Paine  13:56, 21 June 2015 (UTC)
We can't decide anything final here, this should really be discussed at a more proper venue, like the Village Pump maybe. — Jeraphine Gryphon (talk) 13:58, 21 June 2015 (UTC)
30 em (not 35) has been the standard for columns for quite some time (as far back as I can remember, in fact). If someone wants to change that, the discussion should indeed be centralized and not on one user's talk page. --Randykitty (talk) 14:01, 21 June 2015 (UTC)
I agree with Randykitty - 30em is the standard that I've always seen. 20em is too narrow. GregJackP Boomer! 21:14, 22 June 2015 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── As another piece of relevant information: I've just done some tests with the point mutation page and the see also section with 35em columns renders fine on my tablet (MS surface 3 in both chrome and firefox) and mobile (Samsung galaxy note 3). The columns just re-flow to a single column that fits itself to the width of the screen. What system are the images you posted from? T.Shafee(Evo﹠Evo)talk 04:01, 23 June 2015 (UTC)

My tablet is a TrekStor SurfTab ventos 8.0, running Android 4.1.1; the browser app is just called "Browser version 4.1.1-eng-root.20130502.193714". I couldn't find out more about it. Do you think it is a problem of the browser rather than of the Wikipedia page rendering algorithm? - Jochen Burghardt (talk) 14:03, 28 June 2015 (UTC)
Hmm, I've tried on a couple of other phones (iPhone 5, HTC One) and found that multiple columns are still flowed into a single column of the width of the screen with no obvious errors. You might be right that the TrekStor's browser is rendering the page weirdly. If you happen to come by a different device, could you test it out? T.Shafee(Evo﹠Evo)talk 23:28, 29 June 2015 (UTC)

Need help with a few diagrams[edit]

Hi Jochen,

I'm rewriting Cantor's first uncountability proof, which was nominated for a Good Article but failed because the editors who looked at it found problems with it. The editors did give excellent feedback, which I'm using for my rewrite.

I would greatly appreciate some help from you. Because it will take me at least a couple of months to do the rewrite, I'm in no rush. My problem is that I don't know how to make diagrams, and I'm too busy with the rewrite to learn. I remember the excellent diagrams you did for Cantor's diagonal argument in a proof I had written. Here are my diagrams in ASCII (please ignore the periods—I used them because Wikipedia shrinks all spacing to one space):

——(————|—————|——)———

aN .......... c ............... xn .... bN
Case 1: Last interval (aN, bN)

——|————(———|—————)——

xn .......... an ....... a ............. bn
Case 2: a = b

——(———[——|–——]————)———|—

an ...... a ... c ...... b .......... bn ....... xn
Case 3: a < b

A draft of the rewritten section is at User:RJGray/The proofs. Just look for the 3 cases the proof has. You can experiment with the page; I've set it aside for you. Also, any comments you have on the section will help me. Thanks, RJGray (talk) 20:26, 1 August 2015 (UTC)

Hi Robert, the pictures are no problem; I can provide initial versions of them in the next days. I guess each variable should be exactly below the corresponding v-bar or paranthesis, right? If I have modification suggestions for the page, may I make the changes there? - Jochen Burghardt (talk) 20:56, 1 August 2015 (UTC)