User talk:Jochen Burghardt/2015-2019

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a small modification to Schröder–Bernstein theorem - update

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)

equals sign

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 "${\displaystyle \scriptstyle =}$" ? (Observe that clicking on it links to another article.) - Jochen Burghardt (talk) 05:45, 2 April 2015 (UTC)

Philosophy of mind

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! – User:Paine Ellsworth 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	File:Refsize DE de 20.jpg	File:Refsize MO de 20.jpg	File:Refsize MO mo 20.jpg
35em	File:Refsize DE de 35.jpg	File:Refsize MO de 35.jpg	File: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! – User:Paine Ellsworth  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

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):

——(————|—————|——)———

a_N .......... c ............... x_n .... b_N

Case 1: Last interval (a_N, b_N)

——|————(———|—————)——

x_n .......... a_n ....... a_∞ ............. b_n

Case 2: a_∞ = b_∞

——(———[——|–——]————)———|—

a_n ...... a_∞ ... c ...... b_∞ .......... b_n ....... x_n

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)

Hi Jochen, Glad to hear that you can do the pictures. Yes, each variable should be exactly below the corresponding parenthesis, or v-bar. I've played around with the ASCII pictures a bit more trying to make them more similar to each other. It seems that if the (a_n, b_n) intervals were in the same position on each picture, it would be easier for a reader to see the differences between them, especially if we stacked them on the right of the page. I came up with this idea when I was converting my ASCII drawings into tables as an experiment to see how they would look to the user. I have added them to User:RJGray/The proofs for you to see. Also, any suggested modifications you have, just make them to the page. You and I will be the only ones working on this page. Thanks for your help. RJGray (talk) 13:51, 5 August 2015 (UTC)

Hi Jochen. Since you may be making suggestions to the rewrite I'm working on, I added the new lead and "The article" sections that I have also rewritten to User:RJGray/The proofs to give you the context. Feel free to make changes anywhere you want. Thanks - RJGray (talk) 17:43, 5 August 2015 (UTC)

Engaging in argument on talk pages

Hi Jochen,

I'm sure this edit was well-meant, but in my opinion it's not a good idea. I'm not perfect myself and occasionally yield to temptation, but I try to keep it on extremely technical pages where there's a reasonable chance that someone could actually benefit from some little-known exposition.

On problematic pages like the one on the diagonal argument, the halting problem, the incompleteness theorems, etc, we really need to hold the line and direct the querents to the refdesk. If you give them an opening, it can open up a thread that's very difficult to shut off, and the talk page becomes less useful for its intended purpose. --Trovatore (talk) 19:32, 13 September 2015 (UTC)

ArbCom elections are now open!

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Evalution on employees performance listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Evalution on employees performance. Since you had some involvement with the Evalution on employees performance redirect, you might want to participate in the redirect discussion if you have not already done so. Legacypac (talk) 09:03, 4 December 2015 (UTC)

Columns

In response to this edit summary, the fact that there is a bug in page rendering in some circumstances (which is what the screenshots clearly show) should not stop editors from applying the preferred formatting. Rather, the fact that such layouts are used should provide impetus to the developers (either of the website or the browser) to fix the problem. One could certainly file a bug report if the issue is not already known, but we should not be pre-emptively removing column formatting because of a side-effect in a subset of browsers. --Stemonitis (talk) 13:27, 3 February 2016 (UTC)

Thank you for your help on "Georg Cantor's first set theory article"

Hi Jochen, The article Georg Cantor's first set theory article is now up! Thank you again for all your help. To read my public thank you, go to Talk:Georg Cantor's first set theory article#The article rewrite and thanks to all those who helped me. Thanks, RJGray (talk) 01:16, 15 February 2016 (UTC)

Minor edits in equivalence relations

Hi Jochen,

The minor edits I made were converting the mathematics part in Equivalence Relations to proper math notation so that it will render more correctly (and beautifully). I have made no alterations in content.

I don't understand your point of reverting those edits. Would you like to explain?

Rushikeshjogdand1 (talk) 19:11, 15 March 2016 (UTC)

I left an answer on Talk:Equivalence relation#Math style. - Jochen Burghardt (talk) 22:04, 15 March 2016 (UTC)

Congratulations on being updated to extended confirmed user

Hi Jochen, Congratulations and what a coincidence! I was updated to extended confirmed user ‎just 28 minutes before you. The article Georg Cantor's first set theory article is doing fine. Editors have just started to make changes (only 2 so far and the first was reverted by the editor who did it). One of my lead sentences was deleted--it was flawed so I'm rewriting it. I'm happy that people are reading it, and when they edit, they are supplying informative comments. Thanks again for your help on the article, RJGray (talk) 18:23, 6 April 2016 (UTC)

AfC notification: Draft:Lottie Louise Riekehof has a new comment

I've left a comment on your Articles for Creation submission, which can be viewed at Draft:Lottie Louise Riekehof. Thanks! Robert McClenon (talk) 03:30, 2 July 2016 (UTC)

Books move done. - Jochen Burghardt (talk) 16:08, 2 July 2016 (UTC)

Your submission at Articles for creation: Lottie Louise Riekehof has been accepted

Lottie Louise Riekehof, which you submitted to Articles for creation, has been created.
The article has been assessed as Start-Class, which is recorded on the article's talk page. You may like to take a look at the grading scheme to see how you can improve the article.

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SwisterTwister talk 05:28, 7 July 2016 (UTC)

Tree diagram placement help

Hi! I made this (subsequently reverted) edit on Tree (data structure) mainly because all the thumbnail figures are bunched together on the right, making the text on the left very narrow and difficult to read. Perhaps these could be arranged in a different way, like in a gallery? Thanks! J. Finkelstein (talk) 21:56, 7 July 2016 (UTC)

Hi! My reasons for reverting were: you didn't keep the node label sequences from the captions (like "undirected cycle 1-2-4-3") which help an unexperienced reader to identify what is meant; and you didn't make too clear which sentence refers to which image (i.e. above or below the text), this could be fixed by ending sentences with ":". Concerning the image arrangement, I'm impassionate; your inlining may be fine, or a gallery may be fine as well. - Jochen Burghardt (talk) 07:41, 8 July 2016 (UTC)

Might be worth a look

Made these I noticed you did some excellent polishing work on another article of mine:- Heinrich Scholz, Gisbert Hasenjaeger, Hans Rohrbach, Wilhelm Fenner, Wilhelm Tranow. Any editing would be apreciated. Scope creep (talk) 16:19, 15 August 2016 (UTC)

Heinrich Scholz

@Jochen Burghardt, thanks for the edits to Heinrich Scholz. Excellent work finding that reference. I Can you please take a look at my other German articles and determine if you can squeeze some extra quality into them. Thanks Scope creep (talk) 10:22, 26 August 2016 (UTC)

Nondeterministic PDA

Hey, seems like the PDA article is large enough that the content related to nondeterministic PDAs could be split into its own article. Just sayin'. 75.139.254.117 (talk) 17:37, 29 December 2016 (UTC)

There is no nontrivial common superclass of nondeterministic and deterministic pushdown automata (PDA). The formal definition of "deterministic PDA" is a special case of that of "nondeterministic PDA". Hence, every pushdown automaton is a nondeterministic one; some of them are even deterministic (and at the same time nondeterministic) ones. This naming is somewhat confusing, but has widespread use. It can best be understood as "nondet. PDA" meaning "PDA that is allowed (but not forced) to be nondet.", and "det. PDA" as "PDA that is restricted to be det.".

The article doesn't make these relations sufficiently clear. For these reasons, an own article "PDA" wouldn't have much to say beyond the "nondeterministic PDA" article. - Jochen Burghardt (talk) 19:19, 29 December 2016 (UTC)

Today, I tried to improve the article along the above line. - Jochen Burghardt (talk) 18:42, 30 December 2016 (UTC)

Image of Lady Masham?

Dear JB, The image you added to the article on Damaris Cudworth Masham is undoubtedly that of a very beautiful woman and makes the page look lovely, but it doesn't look much like a painting of c.1700 to me. The difficulty is that the source (Find a grave) doesn't give any provenance or reason to think it is a picture of her, beyond the fact that someone has uploaded it there. Whatever the copyright questions attached to it might be (and the source doesn't help with that problem) it really does need some kind of authentication as being really her, such as artist, date, whether contemporary or a sort of retrospective imagination of her, etc etc, otherwise it is just an unsupported image which may have nothing to do with her, and ought to be removed. Can you supply any further information about it? It would be so nice if you could! Regards, Eebahgum (talk) 01:11, 21 February 2017 (UTC)

Dear Eebahgum, I found the image just by chance while trying to re-categorize the images in commons:Category:Philosophers by country. I suggested it in Damaris Cudworth Masham hoping some experts would check if it is appropriate there.

Unfortunately, I have no information beyond the data of its commons description page. I agree with your doubts about the Find a grave page. Some confidence may be gained from the image's appearance in pt:Damaris Cudworth Masham, sl:Damaris Cudworth Masham, and wikidata:Q2332520. However, they all may be wrong, too. - Jochen Burghardt (talk) 06:08, 21 February 2017 (UTC)

Apparently, the image was uploaded on 13 Dec 2016 by Commons and Pt editor ILuna10 (talk · contribs), and used half an hour later in the Portuguese article by an anonymous editor. Magnus Manske (talk · contribs) added it to Wikidata on 24 Jan 2017, from where it got automatically to the Slovene article. Maybe some of these people have additional information? - Jochen Burghardt (talk) 06:29, 21 February 2017 (UTC)

In the Hebrew article, the image was added on 15 ((can't translate month)) 2017 by Matanya (talk · contribs). However, I'm even unable to copy-and-paste the article title to here. There are more links shown on the commons description page, but most if them seem to be automatically generated lists of philosophers without local article. - Jochen Burghardt (talk) 06:41, 21 February 2017 (UTC)

Dear JB, Following doubts expressed by another user on the article talk page, and nothing more substantial forthcoming in the way of provenance, I have suppressed this image in the article, though it remains in Images in case of some future revelation. I hope you think that is reasonable? Eebahgum (talk) 11:32, 19 October 2018 (UTC)

Unambiguous grammar?

Hi, Can you give an example of an unambiguous grammar in which there are more than one derivation for a given string. 112.196.179.176 (talk) 08:44, 22 February 2017 (UTC)

I gave one yesterday at unambiguous grammar#Counter-example, in response of a (your?) recent edit of that page. - Jochen Burghardt (talk) 14:27, 22 February 2017 (UTC)

Usage of \mid

Hello there! On the mathematical induction page, you replaced the \mid LaTeX symbol with '.' Can I ask the reason why? The vertical bar is commonly used as an equivalent to 'such that', and '|' is reserved for absolute value usage, so \mid was instead. Aredaera (talk) 15:07, 31 March 2017 (UTC)

Hi! I often saw \mid in a set, but never in a formula after quantifier. For example, quantifier (logic) lists a lot of notations, but none using \mid. Set builder notation does use \mid. - Jochen Burghardt (talk) 16:54, 31 March 2017 (UTC)

Ah, I see. Then perhaps instead of the '.', a 's.t.' would be better instead? Also, is there by chance any LaTeX stylistic guidelines? (i.e., using \Rightarrow instead of \implies for implication)Aredaera (talk) 22:23, 31 March 2017 (UTC)

My personal opinion would be that one of the notations from quantifier (logic) should be used. I'd use "s.t." in an English sentence, but not within a formula. Concerning \Rightarrow: I guess you are right, and \implies is better, since it indicates the logic relation rather than the typographic symbol. As far as I know, any guidelines concerning mathematics are contained in (or linked from) MOS:MATH.

MfD nomination of User:Jochen Burghardt/sandbox/Quantifier (logic)

User:Jochen Burghardt/sandbox/Quantifier (logic), a page which you created or substantially contributed to (or which is in your userspace), has been nominated for deletion. Your opinions on the matter are welcome; you may participate in the discussion by adding your comments at Wikipedia:Miscellany for deletion/User:Jochen Burghardt/sandbox/Quantifier (logic) and please be sure to sign your comments with four tildes (~~~~). You are free to edit the content of User:Jochen Burghardt/sandbox/Quantifier (logic) during the discussion but should not remove the miscellany for deletion template from the top of the page; such a removal will not end the deletion discussion. Thank you. —Keφr 13:34, 24 May 2017 (UTC)

Deutsche Mathematik

Hello, I saw that you re-added propaganda to the discipline section of Deutsche Mathematik. I removed it as it is not really an "academic discipline" or "field of study" (although maybe some people retroactively study it), but the references are good. I just wanted to explain. Thanks. — Preceding unsigned comment added by Hrodvarsson (talk • contribs) 15:02, 28 May 2017 (UTC)

Cantor's diagonal argument

In regards to your edit of 'Cantors diagonal argument' technically you people claim the one set is (base 2, which is the same as any finite 2 or greater) exponentially 'larger' than the other set, so much larger. You should have corrected rather than deleted. Further all presented versions of diagonal arguments are incomplete. Completed they produce ALL sets of bits not in the considered proposed count. For example all 'diagonals' as all one-to-one mappings of rows to columns not just one. Exponentially many verses one, a very important difference thus the previous version. If you had known this you could have made an addition and also changed 'many' to 'exponentially'. However diagonal arguments are wrong and easily disproved, the table width and height are forced the same whereas the width and height of any counting would be height exponentially larger than width AS THE PROBLEM IS STATED 'all possible sequences of bits' presumably the same length as the width of the table 'infinitly long'. The proof is uncountability due to size rather than uncountability. — Preceding unsigned comment added by Victor Kosko (talk • contribs) 04:53, 14 June 2017 (UTC)

Hi Victor Kosko! (I moved your note down to here, and added a section heading, to keep the chronological order of my talk page. If you answer, please append your text after my signature below.)

I wonder where you found the word "exponential(ly)" in the 'Cantor's diagonal argument' article? It doesn't appear there, and this notion doesn't make sense when dealing with infinite sets. Neither does the notion "many" make sense then, as I stated in recent my edit summary.

The Wikipedia article properly reflects the state of the art about the issue, as presented in mathematical textbooks. If you wish to challenge Cantor's proof, you should submit an article to a mathematical journal, presenting your counter-arguments. Wikipedia is not the place to do this, according to the policy Wikipedia:No original research.

Apart from that, I think that you are wrong: 'width' and 'height' is fixed by the problem statement, so you cannot change any of them in the proof. Best regards - Jochen Burghardt (talk) 12:56, 14 June 2017 (UTC)

The reference for ∞ly larger is the Wikipedia article:

Cardinality of the continuum

In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers ${\displaystyle \mathbb {R} }$, sometimes called the continuum. It is an infinite cardinal number and is denoted by ${\displaystyle |\mathbb {R} |}$ or ${\displaystyle {\mathfrak {c}}}$ (a lowercase fraktur script "c").

The real numbers ${\displaystyle \mathbb {R} }$ are more numerous than the natural numbers ${\displaystyle \mathbb {N} }$. Moreover, ${\displaystyle \mathbb {R} }$ has the same number of elements as the power set of ${\displaystyle \mathbb {N} }$. Symbolically, if the cardinality of ${\displaystyle \mathbb {N} }$ is denoted as ${\displaystyle \aleph _{0}}$, the cardinality of the continuum is

${\displaystyle {\mathfrak {c}}=2^{\aleph _{0}}>\aleph _{0}\,.}$

This was proven by Georg Cantor in his 1874 uncountability proof, part of his groundbreaking study of different infinities, and later more simply in his diagonal argument.

And also many other places in Wikipedia.

The phrase “as presented” in my previous .message and below refers to:

   Uncountable set

In his 1891 article, Cantor considered the set T of ALL infinite sequences of binary digits

From the article, for example.

A clearer version of the disproof:

The diagonal argument, as presented, (for reals, sets of bits, or sets of naturals) cannot work even if its conclusion is true because

For proof A to prove B to be FALSE it must allow B room to be true.

Consider someone asking you to count all 1000 three digit numbers, on 3 lines so only 3 numbers fit! Or they ask you to count all 1 digit numbers and after you count 1 number they say count all 2 digit numbers and after you count a second number they say count all 3 digit numbers …!

The height of the list HAS TO BE the exponential of the width to make room for all the sets to be counted per the statement of the proof 'count all the...' for it to be a PROOF. Saying that doesn't count with ∞ because with ∞ one can do magic has to be PROVEN for the rest to be a proof!

Example of proper counting: In set theory (Cardinal) ∞ is ∞te increase without end. Set the rate of increase of the height of the sets, the real numbers, to normal, have the digits of each real number produced by separate algorithms for each line, small to large algorithms, they can produce true random bits. Force the first digits to be a count sequence so each line is different. Set rate of increase of number of digits of non-random reals to normal, random reals to the (same base) logarithm of normal, this will force the diagonal to the same rate. The sort is by algorithm, like a program but programing language very complex so will always produce infinite list of digits, and in reasonable time as function of the number of digits yet produced by the algorithm. The width of the random numbers relative to the number of numbers counted is the same as natural numbers. The height keeps pace with the increase of possible numbers per the size of the algorithms and number of bits of randomness used to make any random real. Thus π is not ∞ly far thru the list. The height counts as Aleph0 not Aleph1 per analogy to the height : width relation of the set of natural numbers. π , for example, would be as precise in digits as the number of reals counted. Victor Kosko (talk) 21:40, 14 June 2017 (UTC)

A page you started (Maycock (surname)) has been reviewed!

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Ordered pair: Cantor-Frege definition

Dear Jochen,

Cantor-Frege definition would indeed work in NBG "size-wise", but NBG defines relations in terms of ordered pairs!

(Sorry, if this page is a wrong place to discuss this, I have never done this before.)--nikita (talk) 19:29, 14 September 2017 (UTC)

Confluence (abstract rewriting)

Hi Jochen,

You reverted an edit I had made to this article as redundant, but my intention was to change the meaning of the sentence in question - since, as it stood, it was incorrect! I have edited the article again, this time changing the sentence structure more in the hope of making the intended meaning clearer. Please let me know if you disagree with the change I have made.

Thanks, Robin S (talk) 01:49, 3 October 2017 (UTC)

Hi Robin, your new version appears better understandable to me. In the previous version, b,c could just have been chosen luckily to deem a confluent; this is ruled out now. Thanks for noticing and fixing that! - Jochen Burghardt (talk) 05:14, 3 October 2017 (UTC)

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Sources

Hello, can you please add sources to Akadémiai Kiadó? I'm afraid German Wikipedia wouldn't count as WP:Wikipedia is not a reliable source. Thanks, Boleyn (talk) 13:55, 28 December 2017 (UTC)

Sorry, the German article doesn't cite sources, and I'm unable to read the Hungarian article. Maybe, we could wait if some Hungary expert provides reliable sources? Best regards - Jochen Burghardt (talk) 14:19, 28 December 2017 (UTC)

Trovatore's comments on "Cantor's diagonal argument"

Hi Jochen, I was just reading some of the Talk on Cantor's diagonal argument and came across Trovatore's comments in the section: "Cantor" as agent in the argument. It's very important to mention that the proofs are Cantor's, but I think that Trovatore makes a valid point when he says that Cantor is mentioned too much. (I think it's just a little too much.) So I've done a small amount of rewriting (see User:RJGray/Sandboxcantor1#Uncountable set) that just mentions Cantor at the start but not in the proofs themselves. I'd like to know your opinion. I also realized that in the second proof, the initial assumption is not directly contradicted. Instead, the statement "s being an element of T and therefore belonging to the enumeration" is being directly contradicted. I suspect that more often a proof by contradiction doesn't directly contradict the initial assumption. Anyway, tell me what you think of my changes and send me any improvements you come up with. Thank you, --RJGray (talk) 18:45, 10 January 2018 (UTC)

Hi Robert, sorry for the delay. I compared both versions and found you new one slightly better. Cantor's name needn't appear that often, and your new indirect proof is a little bit more clear. By the way: if Bois-Reymond used the diagonal argument before Cantor, this should be stated; so I don't quite understand Estill-math's deletion of 9 Jan 2018. However, when I recently glanced at the Math Ann paper, I didn't find the argument. - Jochen Burghardt (talk) 18:10, 13 January 2018 (UTC)

Hi Jochen, Thanks for looking over my proposed change. I've updated the article. Concerning du Bois-Reymond and his diagonal argument: It's mentioned on the Talk page: du_Bois-Raymond and Cantor's diagonal argument. Of particular interest is note 1 page 187 in Simmons, Keith (1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. {{cite book}}: Cite has empty unknown parameter: |1= (help) This note claims that Bois-Reymond's diagonal argument is a different type than Cantor's.

I agree with the Talk page that something should be mentioned, but some research is needed beforehand. Ultimately, it would be nice to have a section covering both sides of this issue, which would include a comparison between the two proofs and what various mathematicians and historians say about the two proofs.

Here's some interesting material from Stackexchange (of course, we can't use this in a Wikipedia article, but it does say that the diagonal argument is in a footnote on page 365):

He [du Bois-Reymond] refers to [an] 1873 paper where only a particular case was considered. This time he gives a more general version, which Borel highly praised and termed du Bois-Reymond's theorem. A consequence of it, and the motivation, is the non-existence of the "ideal boundary" that can be specified by a sequence of converging/diverging series, as Bertrand earlier proposed (he was thinking of reciprocals to products of powers and powers of iterated logarithms as terms). The du Bois-Reymond's theorem would be the "diagonal argument":

"...if an unlimited family of more and more slowly increasing functions λ1(x), λ2(x), λ3(x) ... is given which for each r satisfies the condition lim λr(X)/λr+1(X) = ∞, one can always specify a function ψ(x) which becomes infinite with x, but more slowly than any function of that family".

The construction of ψ(x) is in a footnote on p. 365, and does show some "diagonality" if one looks hard. There is however no cardinality involved in du Bois-Reymond's setting (Hausdorff will relate gaps to cardinalities only later), so making it into the diagonal argument takes some reading in. In his 1882 book Die allgemeine Functionentheorie (The General Theory of Functions) du Bois-Reymond touches base with Cantorian set theory, and mentions that Cantor showed "continuum of the idealists" to be uncountable. He does not however point out any affinity between the diagonal argument by which it was shown and his earlier construction, let alone lay any claim to it. So whatever the relation between the two it was not apparent to du Bois-Reymond.

NOTE: There is an error in the next to last sentence: du Bois-Reymond book is dated 1882 and Cantor didn't give his diagonal argument until 1891, so du Bois-Reymond couldn't compare his argument with Cantor's diagonal argument. I came across this book years ago and du Bois-Reymond just gives Cantor's 1874 argument. Of course, it can still be argued that if du Bois-Reymond did have a diagonal argument similar to Cantor's later argument, then du Bois-Reymond could have used it to give a new proof of the uncountability of the reals rather than repeating Cantor's 1874 argument.

I'm interested in hearing your opinion of du Bois-Reymond's argument on p. 365 of his 1873 paper and how it compares to Cantor's diagonal proof. --RJGray (talk) 21:48, 14 January 2018 (UTC)

Thanks for the informations! I downloaded the article from GDZ; the diagonal argument is indeed somewhat hard to detect. In User:Jochen Burghardt/sandbox8, I gave a download URL and a viewer URL, and started a translation of the argument. I intend to complete it in the next days. - Jochen Burghardt (talk) 20:09, 15 January 2018 (UTC)

Finished a (sloppy) translation. However, I didn't understand some phrases about convexity which are essential for the proof. Also I'm not sure whether the λ functions are required to be monotonically increasing; the examples he mentioned on the previous page happen to have that property. - Jochen Burghardt (talk) 19:38, 17 January 2018 (UTC)

Found the paper cited on p.364; see User:Jochen Burghardt/sandbox8. Apparently, the appendix (starting on p.29-->88) of this paper establishes the context in which to understand the 1875 paper. - Jochen Burghardt (talk) 20:03, 17 January 2018 (UTC)

Math induction clarification

Hi, Jochen Burghardt! I′ve seen your recent edit at Mathematical induction. Please detail on the associated talk page opened sections what do you consider to be confused phrasing in order to improve clarity of the content to be inserted in article! Thanks--5.2.200.163 (talk) 14:51, 17 January 2018 (UTC)

Galois connections

Hallo Herr Burghardt,

danke für die "citation needed" - Tags im Artikel über Galois connections. Ich bin ein alter, aber kein allzu erfahrener WP-Autor und kenne die Etikette nicht gut genug. In diesem Falle müsste ich eigene Publikationen nennen, und ich zögere, mich in Wikipedia selbst zu zitieren. Deshalb habe ich nur zur WP-Seite über Formal concept analysis verlinkt, dort gibt es Zitationen (die allerdings noch aufgeräumt werden müssen, das haben wir demnächst vor).

Zur Formalen Begriffsanalyse, die ja als angewandte Theorie der Galoisverbindungen verstanden werden kann, gibt es mehrere tausend Publikationen. Da ist es angebracht, nicht einzelne Papers zu zitieren, sondern systematische Darstellungen. Dass alle Galoisverbindungen "bis auf Isomorphie" aus Relationen stammen, kann man als Teilaussage des Hauptsatzes der Begriffsanalyse ansehen. Dieser ist im Buch B. Ganter, R. Wille : "Formal Concept Analysis -- Mathematical Foundations", Springer gut nachzulesen. Außerdem gibt es ein Paper von mir ("Relational Galois connections", Proceedings ICFCA 2007, Springer), in dem der Begriff der Galoisverbindung so weit wie möglich verallgemeinert wurde, bis hin zu Galoisverbindungen zwischen beliebigen Relationen, und in dem dann gezeigt wurde, dass man all das auf Galoisverbindungen zwischen Potenzmengen zurückführen kann.

Es gibt in der Formalen Begriffsanalyse viele Papers zu Algorithmen, zu deren Komplexität etc., und es gibt auch einiges an frei verfügbarer Software. Ich habe vor einiger Zeit aus dem WP-Artikel über Formal concept analysis eine nach meinem Urteil viel zu langatmige Passage, in der allerlei Algorithmen (für ein einziges Problem) verglichen wurden, rüde gekürzt. Ich würde das Buch von Sergei Obiedkov und mir mit dem Titel "Conceptual Exploration" (Springer 2016) zitieren, das enthält immerhin 33 verschiedene Algorithmen mit sorgfältigem Pseudocode. Das sind Algorithmen zu einem Wissensakquisitionsverfahren (der "Merkmalexploration"), das aber wiederum mit Galoisverbindungen arbeitet.

Grüße, --Bernhard Ganter (talk) 20:09, 20 January 2018 (UTC) Ich hab' mal drei Zitate eingefügt. --Bernhard Ganter (talk) 14:56, 21 January 2018 (UTC)

@Bernhard Ganter: Hallo Herr Ganter, danke für die Erklärungen und für die eingefügten Zitate. Selbstzitate sind in WP:SELFCITE "geregelt"; ich finde, Ihre Zitate sind danach ok. (Um solche policy-Seiten zu suchen, ist m.E. Wikipedia:Editor's index to Wikipedia sehr hilfreich.) Ich persönlich würde es sogar begrüßen, wenn Sie noch einen Link auf einen öffentlich zugänglichen Text (PDF) einfügen würden (vielleicht Ihr ICFCA'07-Papier?). —

Mit der neuen Einschränkung "antitone Galois connections between power sets" fällt es mir intuitiv leichter, die Darstellbarkeit über zweistellige Relationen zu glauben. —

In "Birkhoff, Ch. IV, §5" habe ich auf die Schnelle nichts über Galoisverbindungen finden können, sie werden in meinem Exemplar (3. Aufl., 1967) erst in Ch.V, §8 (vor Thm.20) eingeführt. Dort in Exercise 2 kommt immerhin eine zweistellige Relation vor und ein Rückbezug auf §5 (allerdings wohl von Ch.V), aber jedenfalls auf Anhieb konnte ich keine Verbindung zum Wikipedia-Abschnitt Galois connection#Connections on power sets arising from binary relations sehen. Könnten Sie die Stelle noch etwas genauer angeben?

Beste Grüße zurück - Jochen Burghardt (talk) 13:08, 23 January 2018 (UTC)

Danke für Ihre sehr konstruktiven Bemerkungen.

Tatsächlich ist die Einschränkung "between power sets" unnötig. Ich habe sie nur eingefügt, weil ich auf die Schnelle kein passendes Zitat zur Hand hatte. Das kann ja noch kommen. Die Argumentation geht so: 1) Die vollständigen Verbände, die aus Galoisverbindungen zwischen Potenzmengen entstehen, nennen wir Begriffsverbände. 2) Es ist einfach nachzuweisen, dass Galoisverbindungen zwischen Begriffsverbänden durch Galoisverbindungen zwischen Potenzmengen dargestellt werden können. 3) Jeder vollständige Verband ist isomorph zu einem Begriffsverband ("basic theorem on concept lattices"). Das zusammen ergibt die Behauptung. Ich werde mal stöbern, ob's irgendwo gut lesbar steht. Eigentlich steht es auch in dem genannten "ICFCA07-Paper".

Beim "Birkhoff" habe ich den Fehler gemacht, mich auf die zweite Auflage zu beziehen. In der dritten Auflage (die heute aktuell ist), ist das Ganze in der Tat in das Kapitel V ("Complete Lattices") gerutscht. Dort beschreibt der Abschnitt 7 ("Polarities") die Galoisverbindungen zwischen Potenzmengen, die aus Relationen entstehen. Der darauffolgende Abschnitt 8 ist dann den "Galois Connections" gewidmet. In einer Fußnote verweist Birkhoff darauf, dass dies auch schon in der ersten Auflage stand und dort offenbar als Erstveröffentlichung verstanden werden kann. Ein kleines Zuordnungsproblem besteht nun darin, dass der WP-Artikel auf die erste Auflage verweist ("Birkhoff 1940"), die aber heute kaum noch zu finden ist. Ich versuche mal, das zu bereinigen.

--Bernhard Ganter (talk) 15:09, 23 January 2018 (UTC)

Turing machine

Regarding a recent revert:

1. if a Turing machine is NOT a thought experiment, how about updating Computational complexity theory#Turing machine which introduces TMs as such? Perhaps this indicates a problem between distinguishing what something is, vs. how it is used or thought about.
2. I don't see TM under Category:Mathematical objects, although they are under Category:Mathematical modeling (of a hypothetical never realized) computing abstraction
3. Perhaps all mathematical objects (or even abstractions) should be categorized under thought experiments (but I wouldn't go so far).

Dpleibovitz (talk) 20:30, 13 February 2018 (UTC)

My line of thought was this: Formally, a Turing machine (TM) is defined (in Turing machine#Formal definition) as a particular kind of 7-tuple, with the latter clearly being a mathematical object, see Tuple#Definitions. In this sense, a TM is (can be encoded as) a set of sets, like e.g. a natural number (cf. Ordinal number#Von Neumann definition of ordinals).

I guess, since a TM is rather complicated and unfamiliar, and to distinguish it from a real computer, it has been called a thought experiment in the article. However, I think a thought experiment, in a narrow sense, describes some hypothetical situation, often including human acting (the article mentions "causes" and "effects", which is hardly applicable to mathematical models).

In a wide sense, I'd agree with your point 3 (for example, imaginary numbers can be thought of as originating from a thought experiment "what if we had something with its square being -1 ?"), but I wouldn't go that far either.

Best regards - Jochen Burghardt (talk) 20:55, 13 February 2018 (UTC)

Semiorder

My thoughts on a recent edit of yours: I don't think I've ever had an edit survive for 6 years and still be revertable with the "undo" button before! Anyhow, I don't know if the article asymmetric relation was ambiguous back in 2012, but (contra what that article says) I do think the adjective is ambiguous. That is, I do not think it is universally agreed that "asymmetric" means "irreflexive and antisymmetric," whereas I think the definitions of the latter two terms are unambiguous. I was thinking of adding "(that is, it is irreflexive and antisymmetric)" to semiorder, but since the sentence is already a "that is" sentence, that would be ridiculous. So, I guess this is all just a "here is my opinion but I'm not going to change anything" type comment. Best, --JBL (talk) 15:52, 15 April 2018 (UTC)

I was surprised that "undo" still worked, too. I agree that "asymmetric relation" can be misunderstood e.g. as "a relation that is not symmetric" by non-mathematicians. On the other hand, it is a common notions with a fixed meaning for mathematicians. Since the article appears to be of interest not only to mathematicians but also to economists, restoring your edit may have a point. So, if you like to revert again, I won't complain. But maybe we'd wait for another 6 years? ;-) - Best regards Jochen Burghardt (talk) 17:41, 15 April 2018 (UTC)

Ha! I think it is fine for now, but I will put a note in my calendar to revisit the question in 2024. Best, JBL (talk) 21:46, 15 April 2018 (UTC)

Non-trivial article

Hi, I looked at the history of learning automata, and your contributions, and guessed that perhaps you might be a good choice as co-pilot on an article. I stumbled across Tsetlin engine in a Norwegian newspaper a few weeks back, and now wrote a few sentences in a tiny stub article. This is about a new type of learning automata that could be very interesting, at least for rule based knowledge systems. Granmos article is the first I know of, but it could be other sources later this year. This is pretty heavy stuff! I guess there should be a proper article about Tsetlin automata before too much stuff goes into the Tsetlin engine article.

Any ideas? The field of reinforcement learning in this area is pretty new to me. Jeblad (talk) 20:26, 3 May 2018 (UTC)

Just a quick grammar note here: Automata is plural. The singular is automaton. I made a couple of corrections. --Trovatore (talk) 20:34, 3 May 2018 (UTC)

Thanks! Jeblad (talk) 21:20, 3 May 2018 (UTC)

@Jeblad: Sorry, but I'm not an expert in reinforcement learning either; in particular, I never heared about Tsetlin automata or engines before. When you look at the source code of learning automata, you'll see that I added comments about what I guessed from my background knowledge (which is mainly in formal language theory). — This said, I can have a look at the Arxiv paper and possibly add some stuff from it to your stub. — Concerning your distinction of "Tsetlin engine" vs. "Tsetlin automaton", I wonder whether it is supported by the Arxiv paper, since I couldn't find the string "engine" in it. If that word occured only in a newspaper I'd think some non-expert journalist just might have used it as a synonym for "automaton". Best regards - Jochen Burghardt (talk) 10:44, 4 May 2018 (UTC)

It might very well be that the correct name should be "Tsetlin automata" and not "Tsetlin engine". The few notions I found with the phrase "Tsetlin engine" has referred to Granmos learning algorithm. It seems to me that the algorithm is more or less an artificial neural network with alternate primitives, ie. just an implementation of a slighly more general form of an ANN. Jeblad (talk) 12:20, 4 May 2018 (UTC)

Seems like I got the "Tsetlin engine" from another source. Granmo uses "Tsetlin Machine". A quick search in the paper gives me 150 hits. Jeblad (talk) 12:28, 4 May 2018 (UTC)

There are a few references on the net to people that can't get quite the same error bounds as Granmo. I'm tempted to say there might be an error in the paper, but that would be OR! :D Some fun, and some rather harsh remarks at Reddit.[1] Jeblad (talk) 13:03, 4 May 2018 (UTC)

Anarchism

Hi Jochen Burghardt,

I saw your work on articles related to anarchism and wanted to say hello, as I work in the topic area too. If you haven't already, you might want to watch our noticeboard for Wikipedia's coverage of anarchism, which is a great place to ask questions, collaborate, discuss style/structure precedent, and stay informed about content related to anarchism. Take a look for yourself!

And if you're looking for other juicy places to edit, consider adopting a cleanup category or participating in one of our current formal discussions.

Feel free to say hi on my talk page and let me know if these links were helpful (or at least interesting). Hope to see you around. czar 11:39, 13 May 2018 (UTC)

Pure Function

Please use Talk rather than relying on reversion to enforce your view of what "Pure Function" should be about. See https://www.schoolofhaskell.com/school/starting-with-haskell/basics-of-haskell/3-pure-functions-laziness-io to get started. Cerberus (talk) 19:54, 5 July 2018 (UTC)

I followed the policy WP:BRD. I don't intend to enforce a particular naming, but the article should be consistent. I'll continue the discussion at Talk:Pure function#alternate usage of the term: as soon as I find the time. - Jochen Burghardt (talk) 06:25, 6 July 2018 (UTC)

Please see the computer-science resources I cited. Please do not force and article titled "Pure Functions" to deviate from the standard usage in computer science. Cerberus (talk) 13:00, 10 July 2018 (UTC)

Let's continue the discussion at Talk:Pure function, not here. - Jochen Burghardt (talk) 15:26, 10 July 2018 (UTC)

I am hoping you will reply to my comment of 23 July. Thanks. Cerberus (talk) 02:39, 28 July 2018 (UTC)

Thank you

Thank you for contacting Michael Hardy after Georg Cantor's first set theory article was nominated for Good Article. I was on a vacation that started just a few days before Bilorv gave his assessment of the article. It all worked out fine. Michael informed Bilorv that I was away and started making some improvements to the article. As soon as I got back, I started making improvements. Yesterday, I finished the necessary improvements and Bilorv certified that it's a Good Article. So your excellent case diagrams now reside in a Good Article. In fact, they are an excellent contribution to the key proof in the article. —RJGray (talk) 18:36, 18 August 2018 (UTC)

Merger discussion for Terminal and nonterminal functions

An article that you have been involved in editing—Terminal and nonterminal functions—has been proposed for merging with Terminal and nonterminal symbols. If you are interested, please participate in the merger discussion. I noticed you participated in the last merge discussion we had on this topic. Thank you. Enterprisey (talk!) 05:33, 12 September 2018 (UTC)

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Need a translation checked

Hi Jochen, It's been a while since we corresponded, probably because we've been busy with non-overlapping work. As I mentioned to you awhile ago, Georg Cantor's first set theory article became a Good Article. Next, it was nominated for DYK (Did you know?). The subsection Georg Cantor's first set theory article#Dense sequences ran into trouble because the DYK editor felt it should have a reference. I then remembered that Cantor published an improved version of his proof in 1879 that uses denseness. So I'm going to replace "Dense sequences" with "Cantor's second uncountability proof" (which will come after the "Example of Cantor's construction" section and which I will use to give a more modern edition of his proof). By the way, this will make the Wikipedia article even more comprehensive and give his second proof more visibility.

However, since his 1879 article has never been translated into English, Wikipedia rules require that I supply his original proof in German along with a translation. I have done this, but I need someone to check over my translation. I would greatly appreciated it if you would look over my translation. By the way, is it possible to put a Wikitable into a Notes section? Right now, I'm planning to have it as a section at the end of the article titled "Appendix: Cantor's second uncountability proof with translation" but I would prefer to put it in a long note. My translation can be found at User:RJGray/Translate; feel free to make your comments and changes on this page. Thank you, RJGray (talk) 18:11, 19 October 2018 (UTC)

I checked p.5-6 today, and intend to continue tomorrrow with p.7 and your Wikitable question. Concerning my remarks, please keep in mind that I'm a native German speaker, but not a native English speaker; so my English suggestions should be taken with a grain of salt, or sometimes with many grains of it. Best regards - Jochen Burghardt (talk) 20:53, 19 October 2018 (UTC)

I checked the remainder just now. I'll continue with your Wikitable question etc. not before tomorrow, due to an unexpected invitation. - Jochen Burghardt (talk) 16:03, 20 October 2018 (UTC)

I tried to put (an abbreviated version of) your table into a footnote at User:Jochen_Burghardt/sandbox#Table_in_footnote_ref. This worked fine, but in user space the popup doesn't appear on mouse-over (it doesn't ever, the table is not the reason). So I made two tests edits at Georg_Cantor's_first_set_theory_article#Dense_sequences. It seems that a collapsed table in a footnote is rendered fine in the "References" section, but in the popup, the "[show]" button doesn't work. An uncollapsed table is also rendered as expected in the "References" section, but in the popup, the "[hide]" button doesn't work. You can see this behavior via the "View history" page. Probably we can't expect "[show]"/"[hide]" flaw to be fixed in the next future, so you should decide if you can live with it. - One alternative could be to put a collapsible table with the English translation in the text (e.g. "Cantor's original version of the proof"), and referring there in a footnote to the German text I guess it is available at gdz). - Another alternative could be to publish a LaTeX version of the English/German synopsis at commons, and referring to is from a footnote. - Jochen Burghardt (talk) 15:01, 22 October 2018 (UTC)

Thanks for investigating this so thoroughly. I plan to give the editor that requested my modifications the choices and let him decide. —RJGray (talk) 18:56, 26 October 2018 (UTC)

E. Mark Gold

Jochen...

I am not a mathematician but a former friend of Gold. I knew him during his days at Berkeley.

What is the significance of: "Language identification in the limit" today?

I place this question in memory of a talented mind.

Thanks,

Daniel Kucera — Preceding unsigned comment added by Dtkucera (talk • contribs) 03:42, 20 October 2018 (UTC)

Hi Daniel, sorry for the delay. I don't overlook the complete field of machine learning. That said, I'd consider E. Mark Gold a pioneer in that field. It appears that whenever he is cited in Wikipedia (a search for "E. Mark Gold", including the double quotes, returned Computational learning theory, Language identification in the limit, Hypercomputation, Learnability, List of important publications in computer science), his 1967 paper "Language identification in the limit" is cited. - If you knew him personally, could you write a biographical article on him? I think he is one of the most famous computer scientists who still don't have a Wikipedia biography. - Best regards - Jochen Burghardt (talk) 21:46, 26 October 2018 (UTC)

Your revert on Invariant (computer science)

Your rationale for undoing my edits is wrong, as the merge has actually been done. See history of Invariant (computer science) Nowak Kowalski (talk) 10:30, 26 October 2018 (UTC)

Ok, I see now. Yesterday I only checked Loop invariant and didn't find anything merged. - Apart from that, I think Invariants in computer science deserve an own article, and the MU puzzle doesn't look suitable among the other examples at Invariant (mathematics), as e.g. none of them is disrecte. - Jochen Burghardt (talk) 14:09, 26 October 2018 (UTC)

That's precisely why i merged these two articles: the Invariant (mathematics) article paid insufficient attention to discrete examples (all of the discrete ones were in "basic examples" section). Surely the concept of "an invariant under a finite set of transformations" is a special case of the concept of "an invariant under some set of transformations".Nowak Kowalski (talk) 14:39, 26 October 2018 (UTC)

New version of Georg Cantor's first set theory article is done

Hi Jochen, Thanks for all your help with the new version of Cantor's first set theory article. I am finally finished with it. Here are the changes:
Added a sentence to the lead about "Cantor's 1879 proof".
In the "Second theorem" subsection: Changed the proof discussed in the collapsed wikitable in case 2.
Deleted "Dense sequences" subsection.
Added new section "Cantor's second uncountability proof".
I used the example you gave me on using <ref> with collapsed wikitables. It was just what I needed. The editor who is evaluating my changes prefers that I put the translation table in a Notes section, which I have done. The advantage is I can now reference the translation table with the usual referencing. Unfortunately, I can no longer use <ref> within my note. Wikipedia supports a very limited amount of <ref> within refn and efn (which is based on refn). I suspect that the problem is the same as using a <ref> within a <ref>. Instead of handling a <ref> within a <ref>, refn, or efn (which is based on refn) via a procedure call that is placed on a call stack, they allow the refn or efn to keep reading the symbols and when it sees a "{{" or "}}", it gives up. It's an old problem that dates back to at least 2009, see Nested refs fail inside references block. You'll find that a patch was done temporarily, but seems to have been reverted. Thank you, —RJGray (talk) 22:40, 10 November 2018 (UTC)

Hi Robert, I once found the #tag:ref template for references within references. I stored two examples at User:Jochen_Burghardt/sandbox#Markup / template examples ("Reference within note", "Reference within reference"). Maybe one of them can be used as a workaround for your problem (I have no experience with refn and efn). To understand them it is best to look at their source code. Best regards - Jochen Burghardt (talk) 20:40, 11 November 2018 (UTC)

Wikipedia bug affecting lastest copy of Cantor article

Jochen

I have found a bug that is affecting my latest version of Cantor's first set theory article, which could be an annoyance to some readers. I put my updated version into Wikipedia on Monday because the Did You Know reviewers were getting impatient, which wasn't surprising since it's taken me 6 weeks or so to do my updates. Since then, I found a Wikipedia bug and shrunk it.

The bug only appears in Wikipedia space, not in User space. Here's how to get a small example of it. The file is in User:RJGray/Sandbox101. Go to Cantor's first set theory article, go to edit the file, and copy over the file from User:RJGray/Sandbox101. Then:

1. Select "Show preview".
2. Go down to wikitable. You will see that that the header says "show".
3. Go back up and hover over [proof 1] superscript. Popup appears with header that says "show".
4. In popup, click "show", popup now says "hide".
5. Go down to wikitable. Header is larger, still says "show" (it should say "hide"). Text now shows.
6. In popup, click "hide", popup now says "show".
7. Wikitable disappears! This is the worst bug in terms of being bothersome to readers since they probably won't realize that they can get it back.
8. In popup, click "show", popup now says "hide".
9. Wikitable reappears!

I've never worked with the Wikipedia programmers. I have no idea if they are volunteers like the Wikipedia contributors and I don't know who to contact with this bug. Also, I used to program a lot so I'm willing to help on the bug. Any help you can give me would be greatly appreciated. Thanks, RJGray (talk) 17:14, 15 November 2018 (UTC)

Hi Robert, I followed your description and can confirm the strange behavior in my browser (firefox 59.0.2), too. I experimented with adding text after the table: it is rendered fine in all cases, just the table in between dis- and then re-appears.

I once tried to report a bug (at User_talk:Jochen_Burghardt/2012-2014#Sfrac_template_renders_slash_and_horizontal_line_in_mobile_view, and then again at mw:MobileFrontend/Feedback), but wasn't successful in the end: I just noted that my last question is still unreplied at the latter page's top. At the former page, when you click on "ask another question on your talk page" in the box, you'll get an explanation on how to use the {{helpme}} template on your talk page.

If you are familiar with javascript (I'm not), maybe mw:How_to_contribute or somewhere below is a good starting point for you. To me, it looks as if it would take some days or weeks to become familiar with the overall architecture, the coding conventions, etc.

Since your reviewers are impatient, why not dropping the "collapsible collasped" mechanism for now, referring the reviewers to the bug. As an alternative temporal remedy, you could create a subpage (like for a local image) containing only the proof and link it in the footnote. - Regards - Jochen Burghardt (talk) 18:30, 15 November 2018 (UTC)

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Successor function

I saw that you added {{clarify}} to successor function and am a bit confused. I understand where it might be confusing, though it is said exactly the same way in the ref I provided. If that statement needs further explanation, regarding the formulas in the ref that lead to the conclusion about commutativity and/or other properties, please inform me or someone at WP:WPMATH who may be more familiar with writing such explanations than I am. Thank you. ComplexRational (talk) 22:33, 16 December 2018 (UTC)

In the lead of successor function, the definition H₀(a, b) = 1 + b is given. In the paper Rubtsov.Romerio.2004, a different definition may be given. I had a glance at the paper, but couldn't find the definition. — The operation H₀ from the lead is obviously non-commutative, e.g. H₀(8,1) = 1+1 = 2 ≠ 9 = 1+8 = H₀(1,8). - Jochen Burghardt (talk) 11:20, 17 December 2018 (UTC)

Anymore

On this change.

Oxford Advanced Learner's Dictionary, 4th edition (1989), page 44, on any" indef adv… any 'more (US anymore) …

Not sure what dictionary you have, but Oxford has it! And no, I don't mind. Jeblad (talk) 19:57, 2 February 2019 (UTC)

I looked into an old Langenscheidt Dictionary English-->German; I am not sure whether it contains Americanisms, too. Feel free to redo your edit. However, as for "don't care"-term, I would still prefer this short form as more common; actually, I never saw the long form "do not care"-term. In contrast, in explanations like "these are terms we don't care about" or similar, Wikipedia prefers the long form. - Jochen Burghardt (talk) 13:33, 3 February 2019 (UTC)

Hilbert 10th

I am currently double checking who did the Isabelle proof. The current reference is an easy chair paper. Its only a paper, not the proof. But fortunately it matches quite well the end-result: https://gitlab.com/hilbert-10/eucys-18/tree/master/code . Can GitHub be referenced from within Wikipedia? Jan Burse (talk) 18:44, 2 March 2019 (UTC)

I added your above link; I think it makes sense since it is apparently unmentioned in the EasyChair paper. I'm not sure whether "source code" is the proper word; please improve if necessary. - Jochen Burghardt (talk) 12:58, 3 March 2019 (UTC)

Wrong identity of Jacob Tamarkin

Hi, I am afraid a recent paper here, has presented a convincing argument that the image taken at the First International Topological Conference in Moscow, 1935 has been mistakenly identified as Jacob Tamarkin when it is in fact of Lev Tumarkin. Unfortunately Hassler Whitney made an error on this, and I am doing my best to correct this on Wikipedia. Leutha (talk) 19:57, 14 April 2019 (UTC)

IIRC

... stands for "if I recall correctly" or "if I remember correctly". You'll have to guess which one I meant :-) --Trovatore (talk) 16:55, 11 June 2019 (UTC)

@Trovatore: Thanks! Actually, *I* didn't recall correctly the powerset of {}. Sorry for the confusion! - Jochen Burghardt (talk) 08:50, 12 June 2019 (UTC)

No problem. Actually there could still be an open issue here. There are arguments on both sides as to whether a one-element structure with the signature of a Boolean algebra can properly be called a Boolean algebra, and more to the point there may be sources on both sides. My guess is that it's more usual to require "True" and "False" to be distinct elements, but I'm not sure.

If you felt like digging into this, it would be a service. I'm not interested enough at the current time. --Trovatore (talk) 19:46, 12 June 2019 (UTC)

I guess, algebraists would prefer to accept the one-element BA, in order to avoid a non-equational axiom "False≠True", but logicians would the prefer to forbid them, for the very same reason. I'd prefer the latter view; I had just a false memory about powerset({}). - Jochen Burghardt (talk) 09:53, 13 June 2019 (UTC)

"Equal to itself and different from all others"

Years ago, in Talk:Hindley–Milner type system, you said that the phrase "it is equal only to itself and different from all others" was tautological, but it's not. With ordinary numeric variables, it can be true that ${\displaystyle a=b}$, and so ${\displaystyle a}$ is equal to an "other" variable ${\displaystyle b}$. The sentence quoted is, I think, trying to clarify that this does not occur with type variables: that if they are different symbols, they are not equal. --Doradus (talk) 13:37, 26 June 2019 (UTC)

Oops, I don't remember that discussion, and I guess it is settled meanwhile. Anyway, to defend my viewpoint in your example, I'd merely say that ${\displaystyle a}$ and ${\displaystyle b}$ hold equal values, but have non-equal names. So ${\displaystyle a}$'s value is not different from ${\displaystyle b}$'s, while their names are different. - Jochen Burghardt (talk) 14:57, 27 June 2019 (UTC)

External academic review and publication of Wikipedia pages

Hi, This is a note to ask: would you be interested in submitting any articles for external, academic peer review to improve their accuracy and generate a citable publication?

The WikiJournal of Science (www.wikijsci.org) aims to couple the rigour of academic peer review with the extreme reach of the encyclopedia. For existing Wikipedia articles, it's a great way to get additional feedback from external experts. Peer-reviewed articles are dual-published both as standard academic PDFs, as well as having changes integrated back into Wikipedia. This improves the scientific accuracy of the encyclopedia, and rewards authors with citable, indexed publications. It also provides much greater reach than is normally achieved through traditional scholarly publishing.

The WP:WikiJournal article nominations page should allow simple submission of existing Wikipedia pages for external review. T.Shafee(Evo&Evo)^talk 04:02, 28 August 2019 (UTC)

Infinite domain of individuals and syntax rules of a formal language

Hi, Jochen! I have noticed your comments at talk:quantifier (logic) and talk: Formal language and I ask your input re the equivalences of quantifiers with logical conjunction and disjunction, especially for an infinite domain of individuals where an infinite sequence of conjunctions and disjunctions appears. Thanks!--109.166.134.237 (talk) 14:12, 1 September 2019 (UTC)

Kolmogorov complexity jw (talk) 21:20, 7 September 2019 (UTC)

hello, you reverted my edit to the definition section of Kolmogorov_complexity.

Thank you ... but ... in fact there were two separate objectives which I would like to discuss with you.
My original objective was to make the string example easier to read and understand.

-1- I felt that the use of the terms "Example 1" and "Example 2" add nothing to the explanation. We can do without these labels, which led me to be bold and edit to

"Consider the following two strings of 32 lowercase letters and digits:

abababababababababababababababab

and 4c1j5b2p0cv4w1x8rx2y39umgw5q85s7

The first string has a short English-language description, namely "ab 16 times", which consists of 11 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, which has 32 characters."

• • • would you agree to me doing this change? - or if you don't like it, I would suggest calling the two strings String1 and String2 (not Example1 and Example2), and actually using these names in the ensuing explanation. jw (talk) 21:20, 7 September 2019 (UTC)

-2- For the second example, you say that " the 2nd string above ", which has 20 characters is not self-contained.

-2.i- But the first description is not truly self-contained either since it should probably be specified that the first string is "the (string) result of concatenating the two-character string ab 16 times". Otherwise -I am deliberately pushing this to absurd limits- the expression "ab 16 times" might also be interpreted as

ab16×

or

ab ab ab ab

ab ab ab ab

ab ab ab ab

ab ab ab ab

-2.ii- The article doesn't say anything about whether or not descriptions should be self-contained (in addition I do not think this fact adds much to basic understanding of the simple example).

• • • Perhaps we should either -a- accept my suggested algorithm (which is still longer than the descriptor for the first string), OR -b- add something about self-contained descriptions and include a more rigourous descriptor for each of the strings ... What do you think ? jw (talk) 21:20, 7 September 2019 (UTC)

Reply

-1- I agree to that. My reason for reverting it were that the strings are no longer aligned to each other, so that it is no longer obvious that they have equally many characters. So, I'd not have problems with "String1" and "String2"; even moving the "and" up to the line of the first string would be ok for me.

-2-i- You are right that my term "self-contained" isn't fully adequate, as it doesn't make clear that references to other texts are not allowed while references to certain elementary operations (like repeating) are. The formal definition of Kolmogorov complexity presupposes a fixed Turing machine T and considers the length of the shortest program that, when executed by T, results in the given string. The example tacitly assumes that repetition ("repeat ... times") of some action can easily be programmed, while looking up the contents of Wikipedia pages ("the ... string above") is not possible at all, for T. If you think of T as a machine just understanding the C programming language, string 1 can be obtained by the program for (int i=0; i<16; ++i) printf("ab"); (38 characters) while string 2 can be obtained only by programs like printf("4c1j5b2p0cv4w1x8rx2y39umgw5q85s7"); (43 chracters) or printf("4c1j5b2p0cv4w1x"); printf("8rx2y39umgw5q85s7"); (55 characters). Relations become more obvious if the strings are made longer (e.g. "ab" 1600 times), but that doesn't fit into the article's introductory section.

-2-ii- When reverting your edit I tought about inserting "self-contained" somewhere, but it didn't fit in nicely anywhere in the sentence, so I left that task open for the future. Right now, I'm still unsure about it, since the more elaborated explanation, as I tried in the above reply to -2-i-, is rather complicated and close to the formal definition. I think including it would mess-up the introductory example. On the other hand, a motivating example may ignore some subtleties. - Jochen Burghardt (talk) 15:18, 8 September 2019 (UTC)

Reply to Reply

-1- thank you / done ... but ... I again fell to temptation and made a few simplifications (I hope) to other wording too. I hope you accept that this section with English-language pseudo-algorithms is now concise and self-contained, and clear enought for non-mathematicians too (which was my original intent). jw (talk)

-2- I fully understand your statements and explanations. I shall leave you to consider how to fit it all in nicely - and I might add that your reply shows how difficult it may be to define this properly :) ... I shall also (slowly) give this some more thought jw (talk) 19:33, 8 September 2019 (UTC)

Ordered proposition set?

Hi there! I see your edits at talk:mathematical induction re a proposition set of the form {p(0), p(1), p(2),... p(n)} and I ask you to comment on the conclusion that seems to emerge from the enumeration of the propositions elements of the set, namely that the various increasing values of n present as index to the propositions of the set is just/only an ordering generator, a number of order of the propositions involved in the math induction method. Thanks! --93.122.249.16 (talk) 19:11, 4 October 2019 (UTC)

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Boolean algebra (structure) revert

Hi, reason for my edit to Boolean algebra (structure) was that the PMID given, PMID 16577445 and its corresponding PMC, PMC 1076183 aren't for the AMS paper cited. Is the other paper at pubmed relevant to keep as a separate citation? Thanks Rjwilmsi 18:17, 3 November 2019 (UTC)

@Rjwilmsi and David Eppstein: Thanks to both of you - I hadn't notice the difference.

As for a separate citation: the 1933 TAMS paper refers to the 1932 pubmed/PNAS paper on p.275, as an abstract describing the "fourth set" of axioms of boolean algebra (the TAMS paper persents a total of 6 such sets). Since the fourth set is discussed in detail (p.280-286) in the TAMS paper, it appears that the pubmed/PNAS pdf might only serve as evidence for Huntington having devised the fourth set already in 1932. So I don't think it needs to be included. - Jochen Burghardt (talk) 13:36, 4 November 2019 (UTC)

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With regards to this edit

I removed <math>S_1</math> because it did not appear in the Media Viewer caption. Instead, one would see Representation of a finite-state machine; this example shows one that determines whether a binary number has an even number of 0s, where is an accepting state.. Your recent edit has corrected this issue and kept the style appropriate. Thank you. Regards, GUYWAN ( t · c ) 18:26, 25 November 2019 (UTC)

This appears to be a bug of the media viewer. I don't use that feature, anyway, so I never noticed it. - Jochen Burghardt (talk) 10:23, 26 November 2019 (UTC)