User talk:Jochen Burghardt

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Hi! I see that the German page on Matematical induction has the name Vollständige Induktion. What is the exact meaning of this German word? What other possible shades of meaning exist beside complete? I see that Google Translate gives as equivalents full, complete, total, entire! Thanks!--109.166.135.99 (talk) 19:15, 4 January 2020 (UTC)[reply]

I'd translate it with "complete" in this context. However, in English "complete (mathematical) induction" means "strong (mathematical) induction" - in contrast to "plain mathematical" induction". In German "vollständige Induktion" just means "plain mathematical induction" - in contrast to "philosophical induction". The latter is what humans do in everyday reasoning, viz. inferring ∀n. P(n) from a few observations like e.g. P(1), P(2), P(3); this is deemed "unvollständig" (Engl.: "incomplete"). - Jochen Burghardt (talk) 19:33, 4 January 2020 (UTC)[reply]

Very interesting quote at WikiQuote from Florian Cajori, also says about vollständige Induktion and its use by Richard Dedekind.--109.166.135.99 (talk) 00:06, 5 January 2020 (UTC)[reply]

Hi again! Re math induction, I see that the French wikiarticle has a title that in translation would be reasoning by recurrence! (I see that also the recurrence wikipage mentions matematical induction at See also.) Have you encountered this name, perhaps even in German sources under a German translation?--109.166.135.99 (talk) 19:24, 4 January 2020 (UTC)[reply]

No, I'm not aware of that name. The closest association is primitive recursion, a way to define a function that is (in some sense) based on mathematical induction. - Jochen Burghardt (talk) 19:37, 4 January 2020 (UTC)[reply]

The name reasoning by recurrence seems to be due to similarity with a recurrence relation involved in the structure of math induction being based on the succesive implication from the i value to the next i+1 (and then from n to n + 1) , this transition from a value to next (+ 1) is like the recurrence relation for terms of a sequence.--109.166.135.99 (talk) 22:36, 4 January 2020 (UTC)[reply]

Very interesting quotes re math induction, presenting also history details at WikiQuotes.--109.166.135.99 (talk) 23:36, 4 January 2020 (UTC)[reply]

This help request has been answered. If you need more help, you can ask another question on your talk page, contact the responding user(s) directly on their user talk page, or consider visiting the Teahouse.

I believe to have found a bug in the algorithm computing the watchlist, and would like the programmers to check this. I'm using the {{help}} template because I don't know better how to reach them.

My observations are these (all times are German local time):

• In my preferences, I enabled the features "Hide bot edits from the watchlist" and "Hide my edits from the watchlist".
• At the page "Schröder–Bernstein theorem", the current top of the watchlist looks like this:

   19:03, 14 January 2020‎ AnomieBOT talk contribs‎ m 19,187 bytes +18‎ Dating maintenance tags: <{{Cn}}
   18:43, 14 January 2020‎ Wcherowi talk contribs‎ 19,169 bytes +6‎ →‎Alternate proof: needs citation
   10:57, 14 January 2020‎ Dunloskinbeg talk contribs‎ 19,163 bytes +13‎ →‎Alternate proof
   10:37, 14 January 2020‎ Dunloskinbeg talk contribs‎ 19,150 bytes +1,797‎ →‎History
   20:31, 11 January 2020‎ Jochen Burghardt talk contribs‎ 17,353 bytes -32‎ →‎History: fix another link

• I got a watchlist notice after the 10:57, 14 January 2020‎ Dunloskinbeg edit; this is ok.
• However, I didn't get a notice after the 18:43, 14 January 2020‎ Wcherowi edit; I consider this a bug.
• I didn't get a notice after the 19:03, 14 January 2020‎ AnomieBOT edit; this agrees with my preferences settings.

I suspect that AnomieBOT's edit may have masked out Wcherowi's edit. A later edit by myself masking a former would be ok; and possibly the algorithm computing the watchlist handles a later bot edit in the very same way, although for this case it is not ok. - Jochen Burghardt (talk) 11:46, 15 January 2020 (UTC)[reply]

You are correct, that is a bug: phab:T11790. It's been a known problem since since 2007, but fixing it isn't a current priority for any of the WMF development teams. --AntiCompositeNumber (talk) 17:10, 15 January 2020 (UTC)[reply]

Ok, I see. Thanks for the quick response. - Jochen Burghardt (talk) 20:36, 15 January 2020 (UTC)[reply]

Hi Jochen, I'm currently working on preparing Cantor's first set theory article for a nomination to featured article. While working on accessibility of information in a diagram, I used a screen reader to read the text and found it read both a_n and a_N as "a n" (I had hoped it would read the latter as "a cap n" or "a sub cap n" but it didn't). So my choice of a_N and b_N was bad for people who depend on screen readers. I think a_L and b_L would be better. I'm choosing "L" to stand for "last". I would greatly appreciate it if you could change the 4 places that need changing: 3 of them can be found by searching for "last interval". I could change these 3, but since the changes are in a published article, I think all 4 changes should be done at the same time. The fourth occurrence of a_N and b_N is within your file "Cantor's first uncountability proof Case 1 svg.svg". Thanks again for the work you have done on the article, my featured article mentor is quite impressed with the article and I believe that your diagrams contribute a lot to the key proof in the article. Thank you, RJGray (talk) 17:44, 18 January 2020 (UTC)[reply]

 Done I also changed the corresponding Pdf file. - Good luck with the review process! Jochen Burghardt (talk) 18:20, 18 January 2020 (UTC)[reply]

Thanks for taking care of it so quickly. On my screen, everything was changed except in the diagram where a_N and b_N had not changed. I tracked down the problem to my browser: I changed browsers from Chrome to Opera and everything worked fine. Chrome may have cached the old copy of the svg file somewhere. I've never had a problem like this before. Thanks for wishing me good luck on the review process -- the featured article process is much tougher than the good article process. My mentor started me off with 16 items to change or consider. It's a good learning experience and is already making me a better Wikipedia writer. —RJGray (talk) 21:36, 18 January 2020 (UTC)[reply]

I repeatedly had a similar problem when I uploaded a new version of an image to commons and viewed its imported copy at English wikipedia. Usually, doing a few times "refresh (no cache)" helps; in Firefox. it is encoded as "Control-Shift-r". - Jochen Burghardt (talk) 16:57, 19 January 2020 (UTC)[reply]

Thanks, Jochen. The refresh worked fine: Chrome encodes it as "Control-F5, which I've read is also an option used by some other browsers including Firefox and Internet Explorer. However, I noticed a typo on the Case 1 diagram: Above the number line, it has a "c" instead of a "y". This conflicts with the Case 1 text on the left: "every y in this interval ...". RJGray (talk) 13:52, 20 January 2020 (UTC)[reply]

 Done Oops - sorry! Maybe it was called "c" earlier, and I missed the renaming. - Jochen Burghardt (talk) 16:52, 20 January 2020 (UTC)[reply]

In fact, I found it very clear and convenient for generalizing it from sets to ∞-groupoids (https://homotopytypetheory.org/2020/01/26/the-cantor-schroder-bernstein-theorem-for-%e2%88%9e-groupoids). This reference has a proof in mathematical vernacular, and also a proof formalized in a proof assistant and verified by it. I didn't need to check any reference to make complete sense of it. I would like this proof to be reinstated (with a citation for it, if possible), so that my citation to it still makes sense. No further details for the proof are needed. It may be laconic, but it does have all the necessary information. And I like it very much, much better than the proof that produces three equivalence classes. This proof with two equivalence classes is much better and direct and intuitive. Thank you. — Preceding unsigned comment added by 31.185.241.7 (talk) 19:39, 10 February 2020 (UTC)[reply]

You should copy your above text to Talk:Schröder–Bernstein theorem, so that all editors involved can discuss it. - Jochen Burghardt (talk) 19:49, 10 February 2020 (UTC)[reply]

Hi Jochen, not sure I understand your objection:

your RHS expr. in the 1st def. of Y, viz. "\lambda f. (\lambda x.f (x x)) (\lambda x.f (x x))", wouldn't be a valid term, its valid prefix, viz. "\lambda f. (\lambda x.f (x x))", would have x as both a bound (1st occ.) and a free (2nd ,3rd occ.) variable; this isn't a fixed point combinator

1. As stated in Notation »the body of an abstraction extends as far right as possible«, so the outermost level of parentheses to the right of . are actually redundant.
2. The version that is there now, λf.( λx.(f(xx)) λx.(f(xx)) ), when fully parenthesised actually becomes λf.( λx.( (f(xx)) λx.(f(xx)) ) ) which is definitely not a fixed point operator. Instead, it's important that the two abstractions (λx.f(xx)) have an outer set of parentheses to limit the scope of the bound variable x.
3. As far as I can see my version made the definition of Y equal to the one in Recursion and fixed points.
4. I also fixed the »Y demonstration« to be parenthesised identically to the one in Recursion and fixed points and made analogous changes to the demonstration of the Θ computation.

I'm trying to understand where I'm going wrong, so would appreciate if you could point out the errors in more detail.

--Jocki84 (talk) 12:44, 14 February 2020 (UTC)[reply]

Oops, my fault. I matched your term syntax against the rules given in Lambda calculus#Lead, not against Lambda calculus#Notation. The former rules lead to the a context free grammar with rules

E ::= V
E ::= ( E E )
E ::= \lambda V . E
V ::= ((any variable name))

and to the following derivation for the 'valid prefix':

_________________E_________________
\lambda V. ____________E___________
\lambda f. ____________E___________
\lambda f. ( _____E______    E    )   
\lambda f. ( \lambda V. E    E    )    
\lambda f. ( \lambda x. E    E    )   
\lambda f. ( \lambda x. f ___E___ )
\lambda f. ( \lambda x. f ( E E ) ) 
\lambda f. ( \lambda x. f ( V E ) )
\lambda f. ( \lambda x. f ( x E ) )
\lambda f. ( \lambda x. f ( x V ) )
\lambda f. ( \lambda x. f ( x x ) )

The two rightmost occurrences of 'x' are then outside the scope of the '\lambda x'. This should explain my weird-looking edit summary text.

I'll revert my revert, and add a note that the syntax of Lambda calculus#Notation, rather than that of Lambda calculus#Lead is used throughout the article. Sorry for the confusion. - Jochen Burghardt (talk) 08:40, 15 February 2020 (UTC)[reply]

Ah, I had taken your reference to »convenience notation« in your template to refer to Lambda calculus#Notation, so I was confused. Thank you for explanation and re-revert, I'm happy now ;-) --Jocki84 (talk) 08:24, 16 February 2020 (UTC)[reply]

Hi sir, on the first reason that you reverted my change was that "an n-ary relation is the same as an n-ary boolean-valued function, no matter if written in infix or prefix notation". I disagree with your statement, assuming that you and I both talk about relation and function based on set-theoretic definition. According to Binary Relation, a binary relation R over two sets X and Y is a set of ordered pairs (x, y) consisting of elements x in X and y in Y. That is, it is a subset of the Cartesian product X × Y. Noted, a binary relation is indeed a 2-ary relation. According to Function, a function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y, and every element of X is the first component of exactly one ordered pair in G. In other words, function f is a binary relation G such that every element of X is the first component of exactly one ordered pair in G. Noted, a unary function f: X → Y or f(x) = y is indeed a 1-ary function, but also by definition, a binary relation. In other words, a 1-ary function is equivalent to a 2-ary relation. According to Arity, a function of arity n thus has arity n+1 considered as a relation.

On the reason for my original change, according to Predicate, a predicate P is a boolean-valued function P: X→ {true, false}. Since the distinction between relation and function is clearly shown above, I believe it is careless to say that predicate is logically equivalent to relation when from the set-theoretic view, it is not so.

Also, on the last reason that you reverted my change was that "the name 'predicate' is standard in textbooks (e.g. Hermes 1973, Introduction to Mathematical Logic)". I completely agree this is the case but with a claim that such usage should only be meant loosely and used sparingly, otherwise risk contradictions.

Noted, there are two notations for a function f:

1. f: X → Y
2. f(x) = y

The second notation is very useful in predicate logic because it allows us to define function f using variables x and y. Hence, this allows function f to play well with quantifiers, substitutions, building formulas etc...

However, the most common notation for relation R is: R ⊆ X x Y. If we allow set-builder notation, we also have: R = {(x, y) | x ∈ X and y ∈ Y}. Clearly, both notations are not very handy in predicate logic, such as building formulas. As such, in predicate logic, a predicate R' is written in the functional notation R'(x,y) to describe relation R above. Indeed, predicate R' itself is a boolean-value function that should be explicitly written as R'(x,y) = true if (x,y) ∈ R and R'(x,y) = false if (x,y) ∉ R. Predicate R' can be seen as an indicator function of relation R. In other words, the Cartesian product X x Y, which R is a subset of, is the domain of boolean-value function/predicate R' or R': X x Y -> {true, false}. Thus, we can describe predicate R' as a relation: R' ⊆ X x Y x {true, false}. This is where the real connection between relation R and predicate R' comes from. Also, according to Extension, relation R is indeed the extension of R'.

In conclusion, a relation R is the extension of predicate R' and Cartesian product X x Y such that R ⊆ X x Y is the domain of boolean-value function R'. Both relation and predicate, under consideration of both predicate logic and set theory, are closely related but not logically equivalent. I am looking forward to your opinion on this. Thank you so much for your time sir. Langtutheky (talk) 21:54, 16 April 2020 (UTC)[reply]

These descriptions are isomorphic: every subset of a Cartesian product can be associated a binary boolean function and vice versa. So it is a matter of taste which definition is used. As an analogy, real numbers can be seen as equivalence classes of Cauchy sequences or as Dedekind cuts; when real numbers are defined (e.g.) in a textbook, the exact choice of construction is considered, but later on, when they are used, no one cares about it.

Moreover, a signature is concerned not with functions, relations, or predicates at all, but with symbols for them. The name predicate logic originates from the use of predicate symbols. I'm not aware of any logic book that introduces "relation symbols" and explicitly delimitates this term from "predicate symbols", or vice versa, are you?

Best regards - Jochen Burghardt (talk) 11:28, 17 April 2020 (UTC)[reply]

All boolean-value functions are subset of a Cartesian product but not vice versa, for example, one-to-many relation (multivalued function) does not satisfy the definition of a function in Set Theory. On the other hand, I completely agree that there are isomorphic descriptions such as real numbers as you mentioned. However, in Set Theory, the definitions of function, relation and predicate are distinct and not isomorphic. Of course, a signature is concerned about symbols for functions, relations, or predicates, but at the same time, the underlying assumption is that readers must provide semantics to these terms themselves. You can't really talk about "function symbols" without implying the semantic of "function" under some system; similarly, you can't really talk about "relation symbols" and "predicate symbols" without implying their semantics. To say that "relation symbols" is equivalent to "predicate symbols" is to imply that the underlying semantics for "relation" and "predicate" are equivalent.

On semantics, I am aware that the origins of functions and relations predated Set Theory by centuries. Of course, if one is to choose any isomorphic descriptions of these terms from systems other than Set Theory, or even go as far as to treat them as primitive notions then there is no problem at all. However, Predicate Logic has an intimate relationship with Set Theory as it was found by Gottlob Frege, and later developed by Richard Dedekind and Giuseppe Peano, all of whom are also champions of Set Theory. It is very likely that the definitions of function, relation and predicate are rooted in Set Theory. If this is so then the problem I presented above is still there. As a matter of fact, most of the articles here on Wikipedia regarding Predicate Logics, not just on signature, all points to definitions of function, and relation that are heavily built on Set Theory, thus, all suffer this very problem.

On the traditions that logic books use predicates and relations in place of each other, as I mention above, its understandable why they do so but it does not mean there is no room for improvement to clarify doubts for folks like me who get confused when one treats boolean-value function as logically equivalent (biconditional) to relation under Set Theory. I simply suggest that we should avoid mixing them in the same discussion without the intention to clear the mentioned issue.

Lastly, I accept your revision so that we can just leave things as it stands right now. Thank you for your time.

Best regards, Langtutheky (talk) 16:42, 17 April 2020 (UTC)[reply]

Greetings Jochen Burghardt. You undid one of the edits to page "ordinal number" with the comment "introduced converse relation symbol without need." I don't agree with your undoing, so I undid it. In trichotomy, the emphasis should be on the relations, not the variables. If the example was about permutations, then switching the variables would be more appropriate. By switching the variables back and forth, row by row, it directs attention away from the relation between them. If you want to keep the equality relation on the middle row, I think that is an acceptable compromise, but changing the variables row by row is distracting and does not make for a clear reading. I hope you understand.

Regards, Jozef Putrycz. Jputrycz (talk) 12:47, 29 April 2020 (UTC)[reply]

@Jputrycz: My point is that the trichotomy law is about one relation and equality. Your edit introdoces the converse relation in addition (tacitly assuming the ">" is the converse of "<"). When the relation is called e.g. R, as in Trichotomy (mathematics)#lead ("... a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of xRy, yRx and x = y holds"), the point is even more obvious: the only way to avoid introducing a new notation like R^T is to swap the variables. - Jochen Burghardt (talk) 14:50, 29 April 2020 (UTC)[reply]

@Jochen Burghardt:

Jochen,

Thank you for the detailed reply. It is greatly appreciated because now I have a better idea of where you are coming from. There are a few things I would like to address in your response.

First off, yes, thank you for pointing out that when variables are fixed, the statement "x < y" is in fact not equivalent to "x > y"- that is the exact purpose of fixing the variables in place so as to make clear that the statements are not equivalent. The point here is to demonstrate that only one of the statements is true, and by fixing the variables, and drawing attention to the flipped symbol, it is quite obvious that the statements are different, simply because the relations are different. It is unambiguous, and demonstrates the concept even if it is "just" an instance of a more general form of the concept.

Second, since the focus of this section of the article is on only one of the statements being true, and by simply showing the relations to be different is sufficient, I do not see how focusing on the general form of trichotomous relations is in this particular section of the article appropriate.

Nowhere else in the article is the general form of any of the relations focused upon in the same way you are suggesting for this particular concept. If we are going to focus on the general form of the relation in one section, we must either explain to the reader in a dedicated section of the article why that particular concept was generalized and not others, or we must use the general form in all other sections.

Lastly, the generality of a trichotomous relation isn't what makes the definition of an ordinal number unique. A specific instance of a trichotomous relation allows for comprehension, so while generalities and generalization are of course necessary, they are not necessary in this particular definition for there to be comprehension. Focusing on the abstraction of a trichotomy would draw attention away from the properties of ordinal numbers rather than hone in on them. The general form of a trichotomy is more appropriate for an article on general relations, and of course, trichotomous ones.

Regards, Jozef Putrycz Jputrycz (talk) 15:39, 29 April 2020 (UTC)[reply]

Thank you for reviewing my edits to Set (mathematics). When I first read the article, I noticed that the unordered property of sets was not mentioned, so I added it. Then, as I was reading the talk page, I came upon this section, Talk:Set_(mathematics)#Unordered?, where another editor apparently made the same "improvement" as I just did. The objection was that "ordered lists are also sets." I attempted to avoid this objection by the qualification "Unless otherwise qualified."

In any case, I do not think the definition of "set" is complete, unless the unordered property is noted. I feel satisfied with changes you made to the article, but apparently another feels concerned we must allow for special cases of ordered sets.

I hope the unordered property does not get removed again.

I will watch this spot in case you wish to comment.

Thanks again for your work on this article. Comfr (talk) 03:52, 16 May 2020 (UTC)[reply]

Thanks for the hint to Talk:Set_(mathematics)#Unordered?. I don't agree that ordered lists are also sets, although the former can be implemented by the latter. As an analogy, rational numbers can be implemented by (pairs of) integer numbers, yet both aren't the same. I agree with you that the unordered property is essential for sets, and intend to defend that phrase in the article. - Jochen Burghardt (talk) 07:01, 16 May 2020 (UTC)[reply]

Thanks for your support. Comfr (talk) 15:40, 16 May 2020 (UTC)[reply]

I redlinked precisification in the vagueness article, which you reverted, and I've just restored. Here's my rationale. Clearly, its surface definition is simply "making more precise", but I think there's clearly more meaning to it as a philosophical/logical term: see [1], [2] and [3]. I don't know enough about these topics to start writing an article on them, but the term is certainly article-worthy. -- The Anome (talk) 11:47, 7 August 2020 (UTC)[reply]

(I answered at Talk:Vagueness#Rationale_for_precisification_redlink.) - Jochen Burghardt (talk) 12:08, 7 August 2020 (UTC)[reply]

Hi, I saw you left a note in the LL grammar page saying that whether a grammar G is regular is "and easily decidable problem". I am afraid that that is not the case. For a formal proof consult Theorem 14.6 (page 221) of Hopcroft & Ullman's Formal languages and their relation to automata, available freely through ACM on this link. The notion of regularity is precisely the one of type 3 regularity, and the terms regular set and regular partition are commonplace in literature, though they indeed seem to be missing from Wikipedia, which will need to be sorted out. They are introduced in the aforementioned book on page 15.

It is the case that the problem of whether G is regular is decidable for deterministic languages, but I would still not call the proof "easy"^[1], and sadly the context of LLR languages permits nondeterminism. 192.76.8.73 (talk) 20:31, 6 October 2020 (UTC)[reply]

Thanks for your prompt reply to my {{clarify}} request, and for the references. Theorem 14.6 states that it is undecidable whether a given context-free grammar happens to generate a regular language. In contrast, the question whether a given grammar obeys the rules for a regular grammar is quite different, and easily decided by looking at the grammar's rules. I understood your phrase in LL grammar#Regular case to refer to the latter question.

I'd agree that the term "regular language" is commonly used; and I can imagine that "regular set" is a synonym, which is confirmed on p.15. However, I didn't find the string "partition" anywhere in the book. Since you are apparently familiar with this notion, could you add a definition?

Moreover, I think decidibility of regularity for deterministic language is worth mentioning - at regular language, or at deterministic context-free language, or in both places. - Jochen Burghardt (talk) 09:46, 7 October 2020 (UTC)[reply]

Good morning. I am happy to do edit the relevant wiki entries.

You are absolutely right, now reading the page again the statement "this is due to the fact that deciding whether a grammar G is regular ... is undecidable" is indeed incorrect and should be changed to "... whether the language generated by a grammar G is regular ...". Many thanks for the edit. Best, 192.76.8.73 (talk) 10:35, 7 October 2020 (UTC)[reply]

Great! You might consider registering with wikipedia (with your real name or a phantasy name).

BTW: I found a publicly available version of Ginsburg's and Greibach's paper here.^[2] There is a section "Decision Problems" starting at p.645, and Theorem 5.1 says it is decidible whether a given deterministic languages equals a given regular language. However, I found no theorem saying that it is decidible whether a given deterministic languages equals any regular language; maybe I overlooked it? - Jochen Burghardt (talk) 10:43, 7 October 2020 (UTC)[reply]

Hi, and thanks for all you do for Wikipedia. I ran across the word "redices" in your edit here. I could find no definition for it. Is this a typo? Best regards -- LilHelpa (talk) 13:13, 10 October 2020 (UTC)[reply]

Oops, I believed this word to be the plural form of "redex", isn't that true? Now that you asked, I couldn't find an occurence in the WWW either. Maybe the (English) plural really is "redexes", as used in redex, while "redices" is used in German for the plural? - Jochen Burghardt (talk) 15:13, 10 October 2020 (UTC)[reply]

Ah, thanks for explanation! --LilHelpa (talk) 22:22, 10 October 2020 (UTC)[reply]

There was a misunderstanding on my part about a "typo". I misunderstood what was posted when and why. I am deeply sorry. LMSchmitt 09:13, 8 November 2020 (UTC)[reply]

No problem. - Jochen Burghardt (talk) 14:25, 8 November 2020 (UTC)[reply]

I greatly appreciate your observation of my deletion. I found that pic inappropriate for my article on the illogic of treating a single observation as a universal continuing factor. If, after reading my revision, you find it useful to restore that example and pic of the use rather than the logic of induction, I will be happy to discuss that and any other suggestions you have.TBR-qed (talk) 17:12, 15 November 2020 (UTC)[reply]

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Thanks sir for considering my edit everybody was continuously deleting my edit THANK YOU SO MUCH :-) — Preceding unsigned comment added by Prakharblue123 (talk • contribs) 04:09, 28 November 2020 (UTC)[reply]

Hello! I see your description of your edit at mathematical induction as unneeded links. Can you explain such a label? Also please see the talk page of the article re the structure of the inductive step as implication.--86.127.33.116 (talk) 12:22, 30 November 2020 (UTC)[reply]

Is the reversion mainly due to WP:EASTEREGGs and less to unneeded links?--86.127.34.116 (talk) 14:41, 30 November 2020 (UTC)[reply]

Oops, my revert was incomplete, while my edit summary referred to a complete revert; I fixed this meanwhile. Here are some more details of my reasons for the complete revert:

The link "sequence" is at best unneeded, possibly even misleading, since the target article mainly talks about properties of number sequences. Renaming "N" to "i" is pointless. WP:EASTEREGGs are strongly discouraged by Wikipedia's policy. Moreover, mathematical induction is a school-level introductory article, so details like the names of parts of implications needn't be introduced there. Moreover, the inductive step is not just an implication, but a universal quantification of an implication (but this needn't be mentioned in the article, either). The word "implication" is even used in Mathematical_induction#A_trigonometric_inequality; this should be sufficient. - Jochen Burghardt (talk) 16:07, 30 November 2020 (UTC)[reply]

I have to disagree re the mentioned details and the presumed status of school-level introductory article. Aren't logical operators acting on propositions and predicates included in this school-level? The article should also mention the interaction between implication(s) and universal quantification, even if this interaction is a bit subtle (or perhaps other attribute to be used instead of subtle?). Secondly, it doesn't seem to me that linked article sequence is mainly about number sequences. As long as the number n in P(n) is just a number of order of individual sentences (ordered by succesive implications), as I see you already said on the talk page, I don't think the link to sequence is such a bad thing, almost as if a vandalism. Also I do not quite understand why the renaming of "N" to "i" be considered pointless, N mainly being too close to the typeface/simbol of the whole set of natural numbers.

I see that talk page of the article hasn't been used in connection with the edits in the article. I'll mention there these aspects emerged from here, the school-level introductory article and the need to mention the parts of the implication and the interaction of universal quantification with the implication.--86.127.34.116 (talk) 23:02, 30 November 2020 (UTC)[reply]

(Also the need to make a total reversion is not quite OK, it gives the impression that you want to have the last word re the edits in the article.) So please propose a wording/formulation re the mentioned aspects or corrections to my proposed formulation which I'll put on the talk page of the induction article and possible talk pages of other articles like universal quantifier, material conditional, consequent, etc....--86.127.34.116 (talk) 23:02, 30 November 2020 (UTC)[reply]

I suggest to continue the discussion at Talk:mathematical induction. Feel free to link from there to the above discussion, or to copy it to there, if you like. - Jochen Burghardt (talk) 08:59, 1 December 2020 (UTC)[reply]

Done linking, from there to here.--86.124.195.101 (talk) 00:37, 2 December 2020 (UTC)[reply]

On page algebraic equation can you please clarify me the line written "polynomial equation is usually preferred to algebraic equation" please sir Prankher31 (talk) 14:00, 23 January 2021 (UTC)[reply]

Actually, I'm not an expert in this topic. That said, my understanding of the initial sentences is that (1) "algebraic equation" usually means the same as "polynomial equation", but (2) for equations involving more than one variable the latter name is usually preferred. I have no idea, why. Anyway, naming issues are unimportant in mathematics (see Hilbert's famous saying, e.g. at David_Hilbert#Axiomatization_of_geometry), they are merely a matter of history of mathematics. - Jochen Burghardt (talk) 15:47, 23 January 2021 (UTC)[reply]

1 more thing is that on on page equation it was written algebraic equation is of 2 types P=0 or P=Q which was wrong and I edited and wrote it P=0 is it okay Prankher31 (talk) 02:18, 24 January 2021 (UTC)[reply]

It is ok after D.Lazard has fixed it. - Jochen Burghardt (talk) 10:10, 24 January 2021 (UTC)[reply]

Sir in this page can you please see the last line written that " polynomial equation is referred to algebraic equation " what is use of writing this line when it is clearly mentioned above ? Prankher31 (talk) 13:38, 24 January 2021 (UTC)[reply]

It is creating confusion. Prankher31 (talk) 13:43, 24 January 2021 (UTC)[reply]

I have restored your note in Cantor's diagonal argument and completed the change by adding an item necessary for displaying it: Special:Diff/1004593039. --CiaPan (talk) 11:44, 3 February 2021 (UTC)[reply]

Hi Jochen, I have no objection to your change. You might be interested to know that this is a bit of a fraught point in the history of English grammar. If I recall correctly, Fowler initially insisted on is, but after hearing many objections, came to agree that are is also acceptable. I think some speakers tend to find a subtle difference in meaning, but I wouldn't be able to tell you exactly what it is. --Trovatore (talk) 21:11, 24 February 2021 (UTC)[reply]

Thanks for your explanation! In case "is" is possible, I'd prefer to use it, since my experience is that singular is most often more clear than plural. In the particular case, a set of operations cannot be commutative or non-commutative, but only a single operation can. - Jochen Burghardt (talk) 08:04, 25 February 2021 (UTC)[reply]

Hi, Jochen. I've started a discussion on the talk page of Alphabet (formal languages) based on your edit. Jason Quinn (talk) 03:24, 28 March 2021 (UTC)[reply]

Hello, regarding your recent edit of Local language (formal language): do you happen to have a copy of Sakarovitch (2009) available? I suspect the examples as currently presented do not agree with the book, judging by another edit which changed the example. --109.81.214.106 (talk) 17:41, 20 April 2021 (UTC)[reply]

No, I don't. I just assumed that the example was according to the book before, and that you might have changed it to, say, your favorite example without checking it with the book. The earlier edit indeed does look strange (I wasn't aware of it). - Jochen Burghardt (talk) 19:10, 20 April 2021 (UTC)[reply]

Dear Jochen,

What do we do now? Nobody seems to care about our dispute about this profound (I know that you find it, at least, profoundly disturbing) theorem?

How do we settle our dispute? It is clear to me that 2 and 3 objects is 5 objects, the same as that 3 and 2 objects. I can accept non-communing multiplication of matrices (units do not agree under multiplication), but addition? "nonisomorphic well-orderings of any infinite set"? We do not need that fantastic feature of ordinal numbers to count the objects in the ugly duckling theorem.

Guswen (talk) 21:11, 3 May 2021 (UTC)[reply]

Since I'm currently short of time, I suggest to wait for another week. Maybe we also should renew our call for help? - Jochen Burghardt (talk) 07:17, 4 May 2021 (UTC)[reply]

Dear Jochen,

Awesome ideas! Let's do both then.

Would you kindly renew our call for help, when only you find it suitable, or should I do it?

Guswen (talk) 15:56, 4 May 2021 (UTC)[reply]

@Guswen: Sorry for the delay. I don't want to stall, but I was away from my computer during the last week. I'll renew the call in a minute. I'd like to ask you to revert your recent edit (per WP:BRD) until the issue is settled. If you have other ideas whom to ask, please do as you like, and leave a link here for my convenience. Best regards - Jochen Burghardt (talk) 12:24, 12 May 2021 (UTC)[reply]

 Done renewing at Wikipedia_talk:WikiProject_Mathematics#Ugly_duckling_theorem. I hope I got you viewpoint right? - Jochen Burghardt (talk) 12:37, 12 May 2021 (UTC)[reply]

Dear Jochen,

Thank you for renewing the call, but I do not see a reason to revert my edit. We've been waiting two weeks to no avail. I really wish I knew someone, who could help us to settle our dispute.

At the moment I have two arguments: (1) ordinal numbers should not be used in the UDT, as they do not commute under addition, and (2) Woodward.2009.

You have only one: "subtraction is undefined for limit ordinals, let alone binomial coefficients". Also kindly note that the notion of a countable set includes (a finite number of) "n things in the universe", as in the previous edit.

Therefore, in my humble opinion, the burden of proof is on your side. If the issue is settled in your favor, my edit shall obviously be reverted, and I will be smarter by gaining a new information that 2+3 [things out of n things in the universe] is not the same as 3+2 [things out of n things in the universe].

Guswen (talk) 13:37, 12 May 2021 (UTC)[reply]

Thanks for removing my possibly confusing "in addition to"; I suppose I didn't think it through completely.

But I still don't think the present wording is optimal. Specifically, I don't know what "including all constant functions, projections, and the successor function" is supposed to mean, because I haven't read enough about this to know from elsewhere and the wording is unclear. Is this short for "including all constant functions, including all projections, and including the successor function"? Or is it "including all constant functions, including projections, and including the successor function"? I can't tell whether "all" applies to "projections"; I assumed it did and edited the sentence accordingly to make that clear, but the actual wording, with no conjunction between "constant functions" and "projections," suggests that "all" does not apply to "projections," since it clearly does not apply to "the successor function."

If my interpretation is correct, then perhaps a better wording without the problematic "in addition to" would be "including the successor function and all constant functions and projections," if the order isn't important.

(I hope you're not too angry that I edited an article without fully understanding what I was editing—I mean, it seemed highly unintuitive that some, but not all, projections would be included, so I assumed it was just sloppy wording.)—GreenWeasel11 (talk) 15:52, 5 June 2021 (UTC)[reply]

Thanks for your remarks. Your assumptions are correct, and I tried to change the sentence to make it more clear. I hope it is ok now? Indeed, the order of inclusion is not important. (I consider edits of non-mathematicians to mathematics articles valuable, since they help to detect our blind spots; so I'm thankful for your original edit and your above remarks.) - Jochen Burghardt (talk) 14:29, 6 June 2021 (UTC)[reply]

Thank you for your edit[4]. Beware that Alfred Galois is recently (allegedly) reborn and comes with "new tools" to "revolutionize" mathematics starting with attacking Peano Axioms and Goldbach, but he is extremely powerful. ibicdlcod (talk) 23:55, 6 July 2021 (UTC)[reply]

Junk mathematicans ignore foundations and Peano Axioms.

When Évariste Galois were alive mathematics have many symbols but they ultimately represent numbers. Junk mathematicans embed numbers in symbols in their way of thinking, which made Évariste sick, and he liberated the symbols. But they still must have relations (otherwise you can't do any mathematics, and the symbols would be dead), so he got group theory.

But people still learn numbers at very young age.

0's status as a number/natural number were controversial, since it is pathological.

No counter-revolutionary could realize 1 is also pathological.

When translating Évariste's work from French to English Google can't even distinguish (context: degree of equation) "one" and "prime".

There is no reason to define 0 as the empty set.

There is no reason to define 1 as anything other than the set of all prime natural numbers.

Of course, you need to well-define all prime natural numbers (or all natural numbers >= 2) without ever using 1 or 0, which is the extremely difficult part.

NATURAL NUMBERS -> "NATURAL NUMBERS"

Alexander Grothendieck tried to do mathematics with as little "natural numbers" as possible.

The "ring" vs "line" is useless because it uses a predefined 0 and thus "ring" is also useless in the eyes of revolutionaries. ibicdlcod (talk) 00:45, 7 July 2021 (UTC)[reply]

I do not know of a method. I believe assigning labels is not incouraged in MOS because of the maintenance issues. An automated method does align with the philosphy of authomated ref and note numbering. User-duck (talk) 16:20, 12 August 2021 (UTC)[reply]

I like how you assumed good faith. I wasn't sure myself, as shown be the note left in the parentheses.Nononsense101 (talk) 19:09, 6 September 2021 (UTC)[reply]

Should aliquotSum in the box in "Correctness (computer science)" be divisorSum? Thx. — Preceding unsigned comment added by 24.205.134.231 (talk) 03:36, 10 October 2021 (UTC)[reply]

Yes; I just corrected that - Thanks! - Jochen Burghardt (talk) 07:37, 10 October 2021 (UTC)[reply]

"Modern formal logic has its roots in the work of late 19th century mathematicians such as Gottlob Frege." https://en.wikipedia.org/wiki/Logic "...and is understood by many to be the father of analytic philosophy..." https://en.wikipedia.org/wiki/Gottlob_Frege — Preceding unsigned comment added by 150.135.165.49 (talk) 22:00, 19 October 2021 (UTC)[reply]

I copied your post to Talk:Propositional_calculus#Propositional_calculus_as_branch_of_modern_formal_logic_as_branch_of_analytic_philosophy, so that all involved editors can discuss. Please keep to former version until the discussion is stelled, per WP:BRD. - Jochen Burghardt (talk) 09:53, 20 October 2021 (UTC)[reply]

Hello! Voting in the 2021 Arbitration Committee elections is now open until 23:59 (UTC) on Monday, 6 December 2021. All eligible users are allowed to vote. Users with alternate accounts may only vote once. The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate in the 2021 election, please review the candidates and submit your choices on the voting page. If you no longer wish to receive these messages, you may add {{NoACEMM}} to your user talk page. MediaWiki message delivery (talk) 00:36, 23 November 2021 (UTC)[reply]

A discussion is taking place to address the redirect Convolution (formal languages). The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 November 27#Convolution (formal languages) until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. Macrakis (talk) 17:01, 27 November 2021 (UTC)[reply]

An automated process has detected that when you recently edited Archie Blake (mathematician), you added a link pointing to the disambiguation page Bulletin of the AMS.

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Hey there, I see you reverted my change but your comment is incorrect more than 1 clause can be handled the lookup table is used as a template and then other clauses simply reference it. Could you please give me a hand explaining it better. I get a lot of people telling me it is impossible and am tired of explaining myself over and over again for years. So thought I would put it in the wiki but haven't edited one before. Fiveworlds2 (talk) 22:58, 24 December 2021 (UTC)[reply]

Before you continue, you should be aware of the policy Wikipedia:No original research: if your thoughts are really new, Wikipedia is the wrong place to publish them first, and you are wasting your time learning wiki editing. The best way is to prepare a PDF document explaining your thoughts and loading it up to arXiv or to wikimedia commons:Category:Boolean satisfiability problem.

Independent of the previous issue, you should know that the Boolean satisfiability problem is around for at least 50 years, and no algorithm is known with a worst-case runtime less than O(2^m), where m is the number of distinct variables in the input formula. You speak of O(n) worst-case runtime for your approach, but it is not clear what your n refers to, and if you mean the runtime for looking up one clause, or for deciding the satisfiability of the whole formula.

A third issue is that work under construction should better be prepared in your sandbox (particularly when you are unable to provide a previously published source). I strongly suggest that you move your new version to your sandbox (my topmost line in the browser shows "Talk   Sandbox   Preferences   Beta   Watchlist   Contributions   Log out" on the right, yours should look similar, just click on "Sandbox" and then paste your stuff there).

By the way: the first picture in NP-completeness shows an example formula of 26 clauses and 17 distinct variables. Could you demonstrate your approach on that formula? Would you need significantly less than 2¹⁷ steps? - Jochen Burghardt (talk) 10:23, 25 December 2021 (UTC)[reply]

Hi, Jochen. Regarding your edit summary "once a notion is introduced, definite articles are used", what part of the MOS is that in? Jason Quinn (talk) 00:25, 29 December 2021 (UTC)[reply]

I didn't take that from any Wikipedia policy, it is just (my understanding of) common use of English (and German) language. To provide examples, I randomly picked the lead of Computer program: "[2nd par.:]The resulting file is called an executable. ... [3rd par.:] If the executable is requested for execution, then the operating system loads it into memory and starts a process.[3] The central processing unit will soon switch to this process...". In the second example ("process"), nobody would say "... will soon switch to a process ...". That is all I meant; do you disagree? - Jochen Burghardt (talk) 11:13, 29 December 2021 (UTC)[reply]

Ah, I see your intent now. Thanks. Good edit. Thanks for clarification. Jason Quinn (talk) 14:41, 29 December 2021 (UTC)[reply]

Hi, I'm not sure I understand your reversion of Proxagonal here: https://en.wikipedia.org/w/index.php?title=Function_%28mathematics%29&type=revision&diff=1063176171&oldid=1063139766. It seems to me that in common English usage, the original wording to which you reverted ("assignment of an element of Y to each element of X") has exactly the same meaning as Proxagonal's version ("assignment of one element of Y to each element of X"), except that Proxagonal's version is more emphatic. The original version cannot mean that more than one element is assigned ("an" element is still just one element) but it doesn't draw attention to the fact that only one is assigned. Thus Proxagonal's version is mathematically the same as the original. The emphasis, however, is important. Many of us who lurk on the fringes of maths, using it without quite understanding what we're doing, will be used to the idea that a function might have multiple results (we'll think of the square root function immediately - which is handled much further down in the article, under Multi-valued functions). But the 5th illustration on the right hand side of the page makes it very clear that a function can have only one member in the codomain for each member in the domain, illustrating it and adding the words: "...does not define a function. One reason is that 2 is the first element in more than one ordered pair, (2, B) and (2, C), of this set" (my emphasis). I'm strongly inclined to think that Proxagonal's edit was helpful; it prevents people like me from reading the initial sentences of the lead while remaining stuck in what I suspect is a very common misconception. I'm pretty sure that >99% of non-mathematicians would see no reason why a square root isn't an example of a thoroughly boring, nothing-special function, no different to x^2 (to be honest, a lot of readers live in a world where "function" means "thing with the format =something() in Excel"). I'm not sure what should be done about this? Elemimele (talk) 18:29, 1 January 2022 (UTC)[reply]

@Elemimele and Proxagonal: My reason for reversion was in the first place that I didn't see Proxagonal's motivation for his/her edit (no summary given), and I couldn't immediately come up with an idea why it should be an improvement.

While I appreciate your above argument, I'm still afraid that "one" gives too much emphasis, that is, can be misunderstood as meaning "first chose one element of Y, then assing this element to every element of X" (i.e. a description of a constant function). I think, this kind of misunderstanding is discouraged by "an".

An alternative could be to reverse the order, as in the initial sentence of Function_(mathematics)#Relational_approach ("... associates to each element of X exactly one element of Y" - the words "exactly one" are even more precise than "an" or "one"). However, this sentence can't be used literally in the lead, as it presupposes the notion of binary relation. Maybe you can come up with a wording that joins both advantages? - Jochen Burghardt (talk) 18:57, 1 January 2022 (UTC)[reply]

I see the problem; it's hard to make it clear without being unduly emphatic. It is hard to know how different people will read the same sentence. It didn't occur to me to choose one element of Y and assign an X - my understanding was to take each element of X in turn, and assign one, and one only, element of some universal set, the codomain then being the set Y of all the elements we've had to assign, in order to deal with every member of X. I wonder whether we should leave the existing sentence as it is, but add an extra sentence to the lead, using the terminology you suggested: "Strictly defined, a function associates to each element of X exactly one element of Y. The concept of the function may sometimes be extended to multi-valued functions, where one element of X is associated with multiple elements of Y". Perhaps this is over-egging the pudding, but it might help to prevent a lot of readers starting off with a big misconception? I appreciate that mathematicians don't seem to like the terms one-to-many, many-to-one, one-to-one etc.;, but perhaps they might be useful to those readers who've come here with more experience of databases or logical-links like that?? I'm really not sure. Elemimele (talk) 19:19, 1 January 2022 (UTC)[reply]

I think your suggested extra sentence could be used as the introductory one, if nobody insists on reading there "a functions is ...". I'll give it a try.

As for one-to-one etc.: these notions should be understood by most mathematicians; they are used in set/relation theory, I believe. However, I'm afraid, novices won't understand them without explanation (unless they work in e.g. database theory), so using them in the lead wouldn't help much. - Jochen Burghardt (talk) 19:37, 1 January 2022 (UTC)[reply]

 Done - Jochen Burghardt (talk) 19:44, 1 January 2022 (UTC)[reply]

I like it! Thanks! Let's hope others find it clear too; I may just be weird. Best wishes, Elemimele (talk) 23:18, 1 January 2022 (UTC)[reply]

Hi Jochen, maybe you can have a look at Draft:Constraint_Decision_Model_and_Notation ? It's also about knowledge representation. Pcarbonn (talk) 17:40, 4 February 2022 (UTC)[reply]

Hi Pcarbonn, I'm far from being an expert in knowledge representation, let alone in business applications of computer science.

Nevertheless, after reading your draft (and glancing at Decision Model and Notation), I'd suggest to consider including the former as a section (named e.g. "Generalization") into the latter.

I wonder why your example (graph coloring) is from a non-business area. If cDMN is intended to be used outside that area, too, you should state that in the lead, and list possible application areas.

I didn't understand your explanations about "determinism" and "solutions"; none of these notions appears in the DMS article, and I wonder how a "model" or a "notation" can have a "solution". The notion of "determinism" seems to indicate some relationship to finite automata; if I'm right, I'd suggest to elaborate on that.

In the example, I didn't understand "E* hit policy", I wondered what the leftmost column (in particular the "1") is about, how a country can be negated (i.e. "not(c1)" should be "c2 != c1"?), and likewise for a color. Apparently, the leftmost 4 columns (including the "E*" column) define the constraint, and the rightmost column defines some action constraint's antecedent, and the rightmost column defines its consequent, you should mention that. "The first two columns" doesn't count the "E*" column - why not?

You could also give an overview over the available constructs in the language (e.g. what about disjunctions, existential quantifiers, functions and relations? Are they user-definable?).

Can you characterize the expressiveness of cDMN models (e.g. can each first-oder theory be modelled by cDMN?)

That's all that came to my mind (as you see, no business-related thoughts among them); I hope some remarks are helpful. - Jochen Burghardt (talk) 22:08, 4 February 2022 (UTC)[reply]

Thanks. I'm not the author of the Draft:Constraint_Decision_Model_and_Notation article, so I'll forward your comment to him. Pcarbonn (talk) 09:11, 7 February 2022 (UTC)[reply]

Hi, sorry I didn't manage to comment on your inquiry in the time specified, I am kind of a busy person.

I believe your understanding of rule 8 is incorrect, please double-check on that.

Also if this comment satisfied you, please revert it, I would probably forget about it myself. — Preceding unsigned comment added by 2001:718:2:22:0:0:0:52 (talk) 20:46, 15 February 2022 (UTC)[reply]

Hi, there is a notable nightclub that is called ∄. I wanted to see that anyone who might be looking for it on Wikipedia can find it, which is why I had it in the 'see also' section of the Existential quantification article. Please can we discuss this?

Victor Grigas (talk) 18:15, 29 March 2022 (UTC)[reply]

Meanwhile, PamD has added a hatnote mentioning K41. This is the most appropriate way to handle the situation, imo. - Jochen Burghardt (talk) 08:11, 30 March 2022 (UTC)[reply]

I posted my explanation on the Talk:Mathematical induction page. I agree with part of your reversion but not all. I hope we can have a discussion of points of disagreement on the Talk:Mathematical induction page. Zaslav (talk) 21:32, 10 April 2022 (UTC)[reply]

I propose to restore the redlink to modal collapse; there seem to be a number of papers that have been published on the topic, and it is discussed in several books: see this Google Scholar search and this Google Books search for some examples. — The Anome (talk) 20:29, 25 April 2022 (UTC)[reply]

Both searches seem to have yielded only philosophical papers reflecting about modal collapse, often in relation to religion. (I guess most, or even all, of them reflect about Gödel's ontological proof.) However, an article modal collapse would be a mathematical one, since it is a mathematical concept. And from a mathematical point of view, I guess there is not much to be said, except for the definition. None of the found papers coud contribute to that. - Some of the search results might be worth to be incorporated into the article Gödel's ontological proof, though. - Jochen Burghardt (talk) 15:40, 26 April 2022 (UTC)[reply]

As you say, it's more of philosophical interest than mathematical interest, but I think its interest goes well beyond just Gödel's ontological proof. I've created a stub for modal collapse; let's see how that develops as it gets expanded over time. — The Anome (talk) 08:42, 28 April 2022 (UTC)[reply]

This help request has been answered. If you need more help, you can ask another question on your talk page, contact the responding user(s) directly on their user talk page, or consider visiting the Teahouse.

There is a discussion about birth country and nationality of Igor Stagljar. The discussion is found at User talk:Cola 63, who is the main contributor.

Imo, Cola 63 is wrong in that people can choose (the name of) their birth country at will, and moreover hasn't given any evidence for the claims about Stagljar's preferences (unless both are identical).

I need some external help in mediating this conflict, allthemore as I'm not an expert in Wikipedia's biography policies. Many thanks in advance! - Jochen Burghardt (talk) 10:02, 6 June 2022 (UTC)[reply]

Please see my response on the user's talk page. Local Variable (talk) 13:53, 6 June 2022 (UTC)[reply]

Hey Jochen. I didn't mean that factorization was used in Logic Optimization, I meant that logic optimization is a form of factorization. I find it's good form to link a specific form of knowledge to a broader, more ancient, and thoroughly reviewded form of that knowledge.--TZubiri (talk) 01:21, 20 June 2022 (UTC)[reply]

I don't see how logic optimization is a form of factorization. But even if you had a point, the page factorization you linked to is about a much narrower sense of the word. So I still think the article is not helpful to anybody wishing to learn about logic optimization. - Jochen Burghardt (talk) 11:27, 20 June 2022 (UTC)[reply]

Well I was probably naive in thinking that x and not x being reduced to true is both a factorization and a logic optimization, but I suppose there's cases where a circuit representing an unfactored expression might be faster.

Although, for the constraint of reducing the amount of components in a circuit, which is recognized as correlated to reduced execution time, I think factorization would be synonymous.

At any rate, since it elicited restraint, it would require a source at this point. TZubiri (talk) 18:12, 20 June 2022 (UTC)[reply]

x and not x reduces to false, not to true. Anyway, this reduction doesn't resemble anything you'll find in the factorization article. - Jochen Burghardt (talk) 20:59, 20 June 2022 (UTC)[reply]

An editor has identified a potential problem with the redirect Narrowing (computer science) and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 September 19#Narrowing (computer science) until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. Mdewman6 (talk) 21:24, 19 September 2022 (UTC)[reply]

Regarding the {{Citation needed}} template on the Cardinality article, my apologies for not examining its history closely enough. The original template was added 2022 April 15 [5] to the phrase "The continuum hypothesis is a prominent focus of study". I changed that text April 16 [6] to read "Research continues to study how the cardinalities of different infinite sets compare to each other.", and removed the template. You restored the template October 9 [7] to the changed text, and I removed it a week later, thinking that its presence was related to the sentence that had been edited out. I've now removed the statement entirely. I thought (well, assumed, to be honest) that there were surely open questions still. Given that nobody (including 250 page watchers) has addressed the template with an actual citation, I thought it best to delete my essentially original research. My apologies again. _signed, Willondon (talk) 18:40, 17 October 2022 (UTC)[reply]

I posted a note on this at talk:Cardinality#(G)CH and research. --Trovatore (talk) 20:23, 20 September 2023 (UTC)[reply]

Reading through "Radical Behaviorism: The Philosophy and the Science" right now. Dr. Chiesa goes in depth on the topics of deductive and inductive reasoning.

I noticed you changed the inductive reasoning wiki back to *certain* after I made a change to *valid* in regard to the sentence "If the premises are correct, the conclusion of a deductive argument is...".

Everything that I'm reading says that sentence should be ending with valid and not certain. What's the thought process behind certain? 2601:804:8403:C820:D8:24DB:84DA:3411 (talk) 01:11, 6 November 2022 (UTC)[reply]

I was offline since 6 Nov - please apologize my delayed reply. I briefly explained my thoughts in my edit summary of 5 Nov: (1) "valid" links to a disambiguation ("DAB") page, such links should be avoided. (2) Trying to resolve the disambiguation, I found that validity (logic) would be most appropriate; however, this page explains that validity is a property of arguments (like modus ponens, etc.), while "the conclusion of a deductive argument" is a sentence (like "Bob will go on to University" in Inductive_reasoning#Statistical_syllogism). So I still believe that "certain" is the better choice here. - Jochen Burghardt (talk) 09:14, 19 November 2022 (UTC)[reply]

Hello! Voting in the 2022 Arbitration Committee elections is now open until 23:59 (UTC) on Monday, 12 December 2022. All eligible users are allowed to vote. Users with alternate accounts may only vote once.

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If you wish to participate in the 2022 election, please review the candidates and submit your choices on the voting page. If you no longer wish to receive these messages, you may add {{NoACEMM}} to your user talk page. MediaWiki message delivery (talk) 01:09, 29 November 2022 (UTC)[reply]

Hello!

I noticed that you chose to delete my note about the advanced capabilities of Business Rules Engines for adding and editing rules.

I believe that the current statement "they still had a formal syntax where a misplaced comma or other character could cause havoc as with any other computer language" maybe true for the 70s-80s, but it neglects the significant advances made in the late 90s and later. The tools for rules editing, reviewed in the reference I added, provide easy prompts and selection bars to avoid the need of writing rules in "source code".

I recommend returning the deleted note, or some improved version of it, otherwise the description remains insufficient. שפוי (talk) 17:13, 15 December 2022 (UTC)[reply]

I saw lots of commercial advertisements like the page you cited making similar promises which turned out to be exaggregated, so I'm rather skeptical. "Prompts and selection bars" sounds like just a graphical user interface like e.g. Wikipedias "Insert" bar in edit mode. Can you give an example of advanced editing? If there had been any substantial progress towards error-tolerant syntax, why didn't it influence programming language design and/or editor design at all? - Jochen Burghardt (talk) 18:25, 15 December 2022 (UTC)[reply]

Take, for instance, Pegasystems' self-guided tour at https://www.pega.com/platform-tour/ שפוי (talk) 22:32, 15 December 2022 (UTC)[reply]

Jochen, I believe I 'reasonably addresses some aspect of those concerns' that the code sample is too complex. As opposed to the C++ code, the C# is about entirely readable as proper English. Instead of programming constructs like switch statements, the lookup table is a verbatim copy of that table from the text and the rules and symbols are strings and characters and readily recognizable.

In the C++ code otoh there are needles everywhere such as the stupid enum prefixes, shouting uppercase identifiers, abbreviations like ss, pointers with stars and whatnot, etc etc etc. For non-programmers especially, that C++ is a huge hurdle because you have to parse every little few characters carefully.

The reason I wrote this C# is that the text surrounding the C++ sample and the C++ code itself are not as digestible as you apparently assume and I believe my C# has none of these problems. 2A02:A45E:1569:1:30EB:ABCC:7DF4:2369 (talk) 15:38, 15 January 2023 (UTC)[reply]

I copied your above post to Talk:LL_parser#C#_code_sample, such that all interested editors can discuss it there. - Jochen Burghardt (talk) 16:45, 15 January 2023 (UTC)[reply]

Let ${\displaystyle L=\{a^{n}:n\in S\}}$, with ${\displaystyle S\subset \mathbb {N} }$. If ${\displaystyle L}$ is CF and contains a nonempty word ${\displaystyle a^{n}\in L}$, then by pumping lemma, there exists ${\displaystyle 1\leq i\leq n}$ such that ${\displaystyle a^{n-i},a^{n},a^{n+i},...\in L}$, thus ${\displaystyle S}$ contains an arithmetic progression (not finite arithmetic progression). pony in a strange land (talk) 16:44, 19 February 2023 (UTC)[reply]

Oops - you are right, if S is additionally required to be infinite. I'll re-insert your paragraph at Pumping lemma for context-free languages, with that addition. - Jochen Burghardt (talk) 20:48, 19 February 2023 (UTC)[reply]

Hello. I saw you reverted my edit to the short description on Proof by contradiction. I totally agree that the previous version was more descriptive, but that's simply not the purpose of the short description. It's intended use is more along the lines of quick disambiguation of search results, not to summarize or define the article's subject. That's what the lead is for. See the guidelines on WP:SHORTDESC, specifically WP:SDNOTDEF. Even something like "Concept in Mathematics" would be appropriate, as indicated under miscellaneous in the Examples section. Donko XI (talk) 18:52, 24 February 2023 (UTC)[reply]

What advantage would you new version have? It is of about the same length but less descriptive. - Jochen Burghardt (talk) 19:16, 24 February 2023 (UTC)[reply]

It more clearly and quickly indicates the field covered by the article. For instance, someone searching for Proofing (baking technique) might see the short description and immediately know it's not the right article because it says "math" right at the start. This example is admittedly contrived, but this is the sort of thing the short description is made for. The short description is just glanced at while searching, so it should be very simple to parse by someone with no subject matter background. Being more descriptive than necessary only makes it worse in this regard. Donko XI (talk) 19:40, 24 February 2023 (UTC)[reply]

The main aim of a short description is to help readers to decide if they are interested in the article, withthout opening it. So, it is useless and misleading for readers not specifically interested in logic, to give, as you did, the same short description ("concept in logic") to all articles related to logic. This may prevent readers to read the relevant articles, when encountering quantifiers in an elementary mathematical textbook.

I have fixed some of the SD that you have changed, but a similar work is needed for the others. (I have not reverted your edits since, in general, the previous SD is not really better than yours). D.Lazard (talk) 23:11, 24 February 2023 (UTC)[reply]

The redirect Meru Prastara has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Anyone, including you, is welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 May 8 § Meru Prastara until a consensus is reached. Pichpich (talk) 22:59, 8 May 2023 (UTC)[reply]

"Undid revision 1164690965 by Epachamo (talk): misleading: Literal (computer programming) refers to (multi-character-)identifier for values, while terminal symbols are almost always considered to have length one)" This is not quite correct. Terminal symbols are often multi-character. Think of a lexical analyzer in a compiler. Terminal symbols include things like "if", "then", "for", "function", etc. As the article states, terminal symbols are Lexical items, which are more often than not more than one character. Epachamo (talk) 05:20, 12 July 2023 (UTC)[reply]

I copied your above message to Talk:Terminal_and_nonterminal_symbols#reverted_edit; it is better to discuss it there. - Jochen Burghardt (talk) 09:13, 12 July 2023 (UTC)[reply]

Good morning Jochen. In the Model (logic) article you have deleted the link to model. Could you explain your reasoning please? 2A00:23C6:54D3:DA01:884B:665D:F8BB:F43E (talk) 06:30, 5 September 2023 (UTC)[reply]

Sorry, I forgot to add an edit summary. My reasoning was that Model#"Model"_in_specific_contexts lists some unrelated meaning of "model" which aren't helpful, and one relevant link, viz. Model (logic). The latter, however, is a redirect back to the article the reader is currently reading, so this link isn't useful either. - Jochen Burghardt (talk) 16:50, 5 September 2023 (UTC)[reply]

Thanks for the explanation. As a Wikipedia reader, I am interested what the connection is between a Model (logic) and a Model (person) etc. By deleting the link, the reader will not be able to find the connection if they are on the Model (logic) page. Would you agree to reinstating the link? 86.153.41.116 (talk) 19:29, 5 September 2023 (UTC)[reply]

Mixing in here — 86.153.41.116, I suspect your interest here is linguistic? You're interested in how the word "model" came to be used for both these things? That's a fine interest for you to have, but it seems to me that it's not particularly on point for an encyclopedia article about models in the sense of logic. So I would prefer not to have such a link. --Trovatore (talk) 19:34, 5 September 2023 (UTC)[reply]

Indirectly, yes, it is a linguistic interest but with a didactic purpose. Understanding how a word is used in a (mathematical) language makes it easier to learn and retain the concepts, rather than having a "black box" which you learn today and forget tomorrow because it does not connect with any other brain cell. This is especially true of mathematics if one is not a full-time mathematician. Many Wikipedia articles devote a few lines to explain the origins of a term and to disambiguate terms, not only in the case of model which has such a wide application in English. So in the medium term I would like to persuade you to agree to a Model link. However in the short term, i.e. now, I would like to ask you how you, as a mathematician, see the connection between Model (logic) and Model (structural design/ Bauplan) from 16th century English. In other words, why did mathematicians choose the word model? 86.153.41.116 (talk) 20:10, 5 September 2023 (UTC)[reply]

In my opinion this is not a topic we should cover in the article under discussion. (Note that I'm not Jochen.) --Trovatore (talk) 20:33, 5 September 2023 (UTC)[reply]

Could you answer my question please? Or if you do not know the answer, could you point me towards where I might find the answer? 86.153.41.116 (talk) 20:47, 5 September 2023 (UTC)[reply]

Hello, thank you for your feedback on the C (programming language).

The two statements I considered likely to become outdated were:

• Since 2000, C has consistently ranked among the top two languages in the TIOBE index
• C has been standardized by ANSI since 1989

If I understand correctly, these statements may not be true in the future. Therefore I updated them according to MOS:SINCE using the {{as of}} template. Lightbloom (talk) 11:59, 9 September 2023 (UTC)[reply]

How could any of these statements become false in the future? For example, the start of C standardization is 1898, and nobody can change this. - Jochen Burghardt (talk) 14:55, 9 September 2023 (UTC)[reply]

"Since" implies it is ongoing, therefore if the standardisation stops, the reader may incorrectly infer that the standardisation is still occurring in the present. So one should either remove usages of relative terms (e.g. "since", "currently") as per MOS:RELTIME, or keep the usages of "since" or "as of" and use the template as mentioned in MOS:SINCE. Lightbloom (talk) 15:16, 9 September 2023 (UTC)[reply]

Ok, I wasn't aware of this subtlety of English language. So we should rephrase the sentences such that they no longer indicate ongoing intervals. What about

• From 2000 up to {{update after|2023|text=now}}, C has consistently ranked among the top two languages in the [[TIOBE index]]
• Standardization of C by ANSI began in 1989

I don't think that {{as of}} is appropriate for the start dates, since they never will be changed. - Jochen Burghardt (talk) 18:36, 9 September 2023 (UTC)[reply]

I think you are right that we should keep the language the same in these instances, because the information will be the same, and only the date will change if it stops for example. As for the relative time phrasing, I think relative time such as "since", "as of" should only be used for long periods as per MOS:SINCE, so preferably these should be replaced with more precise language, but I have opened a help topic here to get clarification. Lightbloom (talk) 18:42, 9 September 2023 (UTC)[reply]

I agree with Jochen here. "As of" is misleading wording for the start date of the standardization of a programming language, as the sentence is stating a verifiable well-established date. "As of" is appropriate when there is uncertainty about the exact time/date when an event occurred, or for events that occurred gradually without a clear before/after threshold. ISO will very likely be in charge of the stardardization of C and C++ for as long as ISO and these languages exist, so the "as of" wording is awkward and misleading in these cases. Fbergo (talk) 14:54, 10 September 2023 (UTC)[reply]

You undid my new image to the page, saying that the image does not represent the concept of a set. However, it does (as a base logical fact). In fact, it illustrates the concept in a clearer way than the previous image.

The brackets in set notation contain the elements of the set, and the elements are clearly delineated from one another using the commas. In my mind, when I visualize a set with discrete elements, I visualize the notation using brackets and commas.

For students of mathematics that understand basic groupings in the real world, the previous image has less meaning than the image with notation: The existence of a set does not depend on items in the set being different than each other, or even that there should be more than one element. 96.227.223.203 (talk) 18:55, 20 September 2023 (UTC)[reply]

I suggest you copy your argument to Talk:Set (mathematics) to see what other editors think. Personally, I'm not convinced of them. - Jochen Burghardt (talk) 19:05, 20 September 2023 (UTC)[reply]

My edit in Big O notation was "Finding the median value for a list of sorted numbers" as an example for O(1). You reverted that, with the reason "finding the median of n numbers needs O(n) time, not O(1)". Please note the word sorted is in my change. If the list is sorted, finding the median is O(1). Note that there is a topic on the talk page for that article "Determining if a binary number is even or odd changed to finding median". SlowJog (talk) 21:56, 29 October 2023 (UTC)[reply]

Oops, indeed I overlooked "sorted" - sorry. I'll redo your edit (since "table lookup" is already present, indicating a random-access computation model, rather than Turing's tape-model, the latter would still require O(n) time for both problems). - Jochen Burghardt (talk) 07:17, 30 October 2023 (UTC)[reply]

Finding the median for an array of sorted numbers would be O(1). For a linked list, it would not. "List" is somewhat ambiguous, and in Python it means an array, but we should not assume this. —David Eppstein (talk) 07:25, 30 October 2023 (UTC)[reply]

Hey,

Wondering why you reverted my contrib? Oneequalsequalsone (talk) 19:54, 30 October 2023 (UTC)[reply]

I find the link to the typographic article Turnstile (symbol) irrelevant in a mathematical article. As an analogy, in Polynomial interpolation, we don't link the "+" symbol. - Jochen Burghardt (talk) 08:14, 31 October 2023 (UTC)[reply]

It's supposed to provide further context to people not quite familiar with the notation. The ⊢ isn't really as common as the + Oneequalsequalsone (talk) 10:56, 31 October 2023 (UTC)[reply]

You currently appear to be engaged in an edit war according to the reverts you have made on C (programming language). This means that you are repeatedly changing content back to how you think it should be although other editors disagree. Users are expected to collaborate with others, to avoid editing disruptively, and to try to reach a consensus, rather than repeatedly undoing other users' edits once it is known that there is a disagreement.

Points to note:

1. Edit warring is disruptive regardless of how many reverts you have made;
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes and work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases, it may be appropriate to request temporary page protection. If you engage in an edit war, you may be blocked from editing. —DIYeditor (talk) 13:12, 8 November 2023 (UTC)[reply]

A discussion was opened on the talk page per WP:BRD. Please do not edit war to restore you preferred version and follow Bold, Revert, Discuss. Please do not use edit summaries to carry out a conversation about disputed content. —DIYeditor (talk) 13:13, 8 November 2023 (UTC)[reply]

I'm not edit warring; cf. my recent replay at Talk:C (programming language). - Jochen Burghardt (talk) 14:06, 8 November 2023 (UTC)[reply]

Out of curiosity, how could malloc be implemented in a language that merely has arrays but not does allow arrays to be treated as pointers to arrays or the memory location (or even size?) of said arrays to be modified in code? You say "every" language that support arrays are you sure about that? —DIYeditor (talk) 18:00, 9 November 2023 (UTC)[reply]

The following code should work. It does some first-fit memory allocation (returning the whole found block to the user rather than splitting off the requested size). A chunk in the free-list has a next index and its size at offset 0 and 1, respectively. The region [2...size) is available for the user. - Jochen Burghardt (talk) 14:57, 11 November 2023 (UTC)[reply]

int mem[memMax]; doesn't seem like a realistic implementation. —DIYeditor (talk) 22:41, 12 November 2023 (UTC)[reply]

If a language (like Algol 60) doesn't allow pointers, arrays are the only way to provide memory areas. The algorithms are essentially the same, this is what my code below was intended to demonstrate (btw: it is flawed as I've forgotten to remove the chunk from the free list before returning it to the caller; I won't fix that). Admittedly, having pointers is an important advantage of C in the area of system programming - but I guess this is already handled in C_(programming_language)#Rationale_for_use_in_systems_programming, and I'd agree with handling it there. - Jochen Burghardt (talk) 12:16, 24 November 2023 (UTC)[reply]

#define memMax (1024*1024*1024)
#define memNil (-1)

int mem[memMax];
static int memTop = 0;
static int memFree = memNil;

int malloc(
    int size)
{
    int chunk;

    /* try allocating from free list */
    for (chunk=memFree; chunk!=memNil; chunk=mem[chunk])
       if (mem[chunk+1]-2 >= size)
            return chunk+2;
    /* try allocating from top */
    if (memMax < memTop+2+size)
        abort();
    int const idx = memTop+2;
    mem[idx+1] = size;
    memTop += size+2;
    return idx;
}

void free(
    int idx)
{
    /* return to free list */
    mem[idx-2] = memFree;
    memFree = idx-2;
}

Many thanks, Jochen, for your improvements to my recent edits on the abductive logic programming page. They made me realise that I needed to expand on the negation as failure solution, which I have now done. They also showed me how to make nicer inline formating for Prolog text, which I will carry over to other edits.

Also a belated thanks for noticing and correcting the bad example of a Prolog program several months ago on the declarative programming page. Your correction got me started on my current campaign to improve the coverage of logic programming on Wikipedia.Robert Kowalski (talk) 09:22, 24 November 2023 (UTC)[reply]

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In answer to the question you asked in this edit summary, yes, your version is certainly more natural English. JBW (talk) 21:46, 7 January 2024 (UTC)[reply]

A discussion is taking place as to whether the article Fresh variable is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

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_signed, Rosguill ^talk 16:58, 19 January 2024 (UTC)[reply]

Which occurrences did i miss here?

https://en.wikipedia.org/w/index.php?title=Universal_instantiation&diff=prev&oldid=1198904870 Oneequalsequalsone (talk) 22:37, 25 January 2024 (UTC)[reply]

I don't understand your edit summary for this edit. Category:Wellfoundedness is certainly not an immediate subcategory of Category:Binary relations, nor as far as I can see is it a subcategory further down the category tree, but of course please correct me if I have missed a connection. JBW (talk) 19:54, 31 January 2024 (UTC)[reply]

The chain is (in upward direction): Category:Wellfoundedness - Category:Properties of binary relations - Category:Binary relations.

On commons (commons:COM:OVERCAT), this would suffice to remove Category:Binary relations from a page that is in Category:Wellfoundedness; as noted in my edit summary, I'm not quite sure about WP:OVERCAT. - Jochen Burghardt (talk) 12:47, 1 February 2024 (UTC)[reply]

Hi, I wanted to ask your rationale for the revert of my edit. I made the edit under the impression that it was more consistent with the rest of the article, as some other formulas used ≥ for this purpose. Theanswertolifetheuniverseandeverything (talk) 10:36, 15 February 2024 (UTC)[reply]

At the time when I reverted you, I didn't understand your motivation, since you didn't give an edit summary. I agree that using consistently >, or consistently ${\displaystyle \geq }$ (I don't have a preference here), is a good idea. However, before, as well as after, your edit, both relation symbols occurred. - Jochen Burghardt (talk) 13:31, 15 February 2024 (UTC)[reply]

Ah, I had overlooked that. Thanks for the clarification. Theanswertolifetheuniverseandeverything (talk) 18:33, 15 February 2024 (UTC)[reply]

modified photo. O Why did you crop the photo of my great uncle I uploaded many years ago? 70.50.152.163 (talk) 11:10, 20 February 2024 (UTC)[reply]

Which one? Please provide me a URL. - You can revert my crop at any time on the photo's description page. - Jochen Burghardt (talk) 12:50, 21 February 2024 (UTC)[reply]

Thanks for your revert, I assume it was a temporary error, since whatever the problem was, it seems to be fixed. Thanks, Cremastra (talk) 19:43, 11 April 2024 (UTC)[reply]

Hi, es geht wohl auch auf Deutsch oder? phase transition hat einen sehr viel allgemeineren Aspekt, als als bloss den physikalisch-chemischen, den Du unterstellst, nachzulesen z.B. auch hier: Evolution_of_a_random_network. Ich würde ja dementsprechend vorschlagen, Deine Rückgängigmachung rückgängig zu machen. What do you think? -- Kku (talk) 15:38, 28 April 2024 (UTC)[reply]

Na ja, aber im Artikel phase transition wird nur der chemische Aspekt besprochen, oder habe ich da was uebersehen? Falls nicht, koennte man ihn vielleicht umbenennen in phase transition (chemistry) und unter phase transition einen Disambiguation-Artikel stellen. Ich vermute, dass Du dazu einige Links beitragen koenntest. - Jochen Burghardt (talk) 11:09, 29 April 2024 (UTC)[reply]

Hello Jochen Burghardt, noticing your revert, you made me curious . Do these files fit into this article? If positive, they could be added to the same category on Commons. Thank you so much for your time. Lotje (talk) 04:17, 4 August 2024 (UTC)[reply]

Hi Lotje, which revert do you mean? I think the images currently shown in Subsumption lattice do fit there, as each of them illustrates some aspect of the lattice. As far as I know, there is no commons category commons:Category:Subsumption lattice, and I'm not sure there should be one. Best regards - Jochen Burghardt (talk) 06:16, 4 August 2024 (UTC)[reply]

Hello again, it this one. Not everybody looks as the side tab, hence my additions. Cheers. Lotje (talk) 06:19, 4 August 2024 (UTC)[reply]

Ok, I remember now. - Well, I look there, for example. Moreover, with your argument, we could duplicate the whole page contents, ("just in case that somebody didn't look at some text in the first copy, they should see it in the second copy"). - In software engineering, duplicating code is considered a design flaw (and even a security risk, as I recently learned at [9], found via footnote 7 of Common Weakness Enumeration; cf. also Duplicate code, most drawbacks listed there also apply to Wikipedia articles). - Jochen Burghardt (talk) 06:37, 4 August 2024 (UTC)[reply]

Thanks Jochen Burghardt, guess that means a bot will come and remove all the links to commons in the articles then Lotje (talk) 05:31, 5 August 2024 (UTC)[reply]

You reverted my use of the term "algebra" for formal power series, to "arithmetic". I don't care that much, but I would like to know why you think "arithmetic" is better than "algebra". I'm not aware of anyone using "arithmetic" for polynomial algebra. (When I manipulate f.p.s. I think I'm doing "algebra".) You might expand my understanding by explaining this. Zaslav (talk) 22:26, 14 September 2024 (UTC)[reply]

I think "arithmetic" is appropriate when we are concerned with no other operations than +, -, *, /, no matter what objects these operations are applied to. This seems to be supported by the introduction in Arithmetic.

However, I'm not quite sure. A search for wikipedia articles containing "arithmetic" in the title finds mainly articles about (operations on) natural numbers, like Modular arithmetic, Higher arithmetic, Peano arithmetic, Arithmetical hierarchy, Presburger arithmetic, Arithmetical set, ... - Jochen Burghardt (talk) 22:53, 14 September 2024 (UTC)[reply]

I believe you are mistaken here. The 'Arithemtic' article does specify 'numerical operations', and in the later in the 'Definitions' section, they make this clearer. Generally, the 'levels' go that arithmetic is based in, vaguely "numbers", meaning anything from naturals to reals, basic Algebra generalizes arithmetic by allowing variables (and sometimes other operations), then Abstract Algebra generalizes Algebra by allowing objects other than numbers.

When dealing with a structure that is concerned with no other operations than +, -, *, /, no matter what the objects they act on are, it is usually called a Field, which is considered an algebraic structure. Farkle Griffen (talk) 18:52, 15 September 2024 (UTC)[reply]

Based on decades of mathematical experience: "Arithmetic" has always meant with numbers. "Algebra" has always included algebraic operations with variables or indeterminates. It doesn't matter what the operations are; e.g., it could be exponentiation. Higher number theory sometimes is called "arithmetic", although that is not precisely the basic meaning. I have returned "algebra" to the Formal power series article, as it is certainly the right word. Zaslav (talk) 04:21, 17 September 2024 (UTC)[reply]

Hi Jochen,

You reverted the following edit I made: [10], which added a space to the construct "An operator is truth- (or falsity-)preserving if its value is truth (falsity) whenever all of its arguments are truth (falsity)."

For the life of me, I could not find any guidance on this exact constellation of punctuation in any of the style guides I have, nor online. But to my eye as a native English speaker and former technical writer, the space seems necessary — not because it looks good, but because not having it looks even worse. If the parentheses were not there, there definitely would not be a space. But it is extremely unusual to have both part of a hyphenated compound word and a conjunction within a parenthetical prefix. Even if there is no formal rule against it, it's certainly a very ugly construct to begin with, since it looks like a typo at first glance.

(I am also a fluent speaker of German, and unlike in English, I feel like that usage (no space) is somewhat common in German and doesn't look as "weird", likely because German does not use many open compounds. As someone who works full-time in an environment where I use hear, read, and write both German and English on a daily basis, including frequent communication with non-native speakers/writers of English, I am keenly aware of when German influences creep into English writing and punctuation. :P )

Anyway, I do not want to engage in an edit war over two options which are both bad, so I simply rewrote it to avoid the mid-sentence parentheses altogether. It's a bit wordier, but clearer. If you don't mind, please take a look to ensure the edit has not introduced an unwanted change in the meaning, since I am not an expert in the subject matter as such.

Grüsse aus Zürich,

— tooki (talk) 19:59, 15 September 2024 (UTC)[reply]

I didn't think deeper than "If the parentheses were not there, there definitely would not be a space". I'm not a native English speaker, so if your are, your opinion is likely to be right. Gruß aus Berlin - Jochen Burghardt (talk) 19:08, 17 September 2024 (UTC)[reply]

Yes, as I wrote above, I'm a native English speaker (and former technical writer/technical translator DE->EN). But as I said, despite my best efforts, I couldn't find any guidance on this very exotic constellation of punctuation, since "gut feeling" isn't the best last word on anything. :)

Are you able to verify that the meaning is still correct as rewritten? Thanks! — tooki (talk) 17:55, 18 September 2024 (UTC)[reply]

I checked it with Functional_completeness#Characterization_of_functional_completeness, and it seems ok. The original paper (by Post, 1941) uses a pretty different notation that is hard to understand. - Jochen Burghardt (talk) 10:28, 19 September 2024 (UTC)[reply]

Hi Jochen.

Thank you for reverting my change. It was only after my change that I noticed that there are not prime numbers in the table, but odd numbers, and that Gödel numbers are constructed differently than I thought. Although I found the numbering in another source (but it was not an scientific paper), I was not sure it is correct and that it was not copied from Wikipedia. Next time I'll think more before correcting what I'm not sure is wrong.

Kolarp (talk) 15:53, 16 October 2024 (UTC)[reply]

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