Talk:Sheffer stroke

Requested move (to Logical NAND)

Voting

Add *Support or *Oppose followed by an optional one sentence explanation, then sign your vote with ~~~~

• Oppose Charles Stewart 20:11, 7 December 2005 (UTC) --- Moving to less common name: see comment below.
• Oppose Sheffer naming is more common in maths. Kusma (talk) 23:42, 7 December 2005 (UTC)
• Support There are a few reason to support the move.
• Support why should one particular boolean operation be listed under the name of the symbol that is used to indicate it? "logical and" is not listed under "ampersand" or "dot" or "upsidedown V". The Sheffer Stroke article, if it remains, ought to be simply an article on the history of the sheffer stroke symbol itself and how it came to be used to indicate a logical "not and".

First, though "logical NAND" and "bitwise NAND" may be less commonly called than "Sheffer stroke" (in some, NOT all english countries only, but for other english countries or other countries that use english, the situation is totally opposite), and "NAND" is more familiarly used than "Sheffer stroke" in logic, maths, computer, and engineering. But "NAND" is a acronym which may need disambiguation, so I do not support the move from "Sheffer stroke" to "NAND". However, "NAND" is a term which belongs to "logic", so I strongly encourage the move from "Sheffer stroke" to "logical nand".

Second, as user R. Koot stated, it would be best to keep it consistent with Peirce arrow (which redirects to logical nor). I suppose that the consistency should be a important factor to decide whether the content could be moved from "Sheffer stroke" to "logical nand". QQ 12:07, 8 December 2005 (UTC)

NAND is currently a redirect to Sheffer stroke. If the article were to be moved to NAND and articles on topics with acronym NAND were to appear, we could create a page NAND (disambiguation) to handle this case. --- Charles Stewart 15:47, 8 December 2005 (UTC)

Postscript The basis in popularity for naming an article a particular way for en.wikipedia is just for the popularity in english. How other languages do thiungs is relevant to other language wikipedias, not here. --- Charles Stewart 15:49, 8 December 2005 (UTC)

• Support The term "logical NAND" is more comprehensive. 203.186.238.228 09:00, 9 December 2005 (UTC)
• Support In my secondary school and university, I have not even heard the term "Sheffer stroke", but I have heard the term "logical nand" and "NAND" instead. Therefore when I watched this page, I felt very strange and confused. Moreover, when I saw the stroke notation (|) for representing "NAND", I encountered bewilderment. The reason of this are: 1. I have learnt that the stroke notation (|) is used for representing "A given B", and 2. I mostly use the notation ∧ for representing "NAND", which can be referred from unicode standard. 203.186.238.129 09:16, 9 December 2005 (UTC)
• Support why should one particular boolean operation be listed under the name of the symbol that is used to indicate it? "logical and" is not listed under "ampersand" or "dot" or "upsidedown V". The Sheffer Stroke article, if it remains, ought to be simply an article on the history of the sheffer stroke symbol itself and how it came to be used to indicate a logical "not and".

Remark. I crossed out votes which seem to be by the same person using a changing IP, and also the unsigned votes. I don't think they should be considered. Oleg Alexandrov (talk) 03:41, 10 December 2005 (UTC)

Discussion

Add any additional comments

• Comment - The phrase "logical NAND" is used in computer science to distinguish from "bitwise NAND". According to Google, however, this phrase is much less common than "Sheffer stroke" used by logicians, which in turn is far less common than plain "NAND". I think the reason the redirect exists is due to a piece of misplaced tidymindedness, namely all the boolean logic operators should be similarly named, and and and or are disambig pages, hence each must be logical something or other. I'd be better disposed to moving this page, as well as Logical nor to NAND and NOR, though it feels wrong to me to document the non-engineering material for this topic under this title. --- Charles Stewart 20:11, 7 December 2005 (UTC)

• Comment. I don't have a strong opinion on the name, but I think it would be best to keep it consistent with Peirce arrow (which redirects to logical nor). —R. Koot 21:39, 7 December 2005 (UTC)

It would be better, but Peirce arrow is a much less well known term than Sheffer stroke, and there is very little material at that article that doesn't fit well with the title NOR, compared to the situation with NAND. I'm not all that bothered by this bit of untidyness. --- Charles Stewart 15:52, 8 December 2005 (UTC)

• Comment. I'm not a wikipedian, but I have to say that I'm beyond puzzled to see Logical NAND go to a page about a specific notation. "History of the stroke" and whatever aren't what you need when you are looking for logical and math functions. Did you guys move "Addition" to "Plus Sign"? Get this outta here. These are two VERY distinct things, a math function, and a notation related to it. Totally disjoint. So frustrating to see stuff like this. — Preceding unsigned comment added by 192.35.35.35 (talk) 05:06, 5 December 2014 (UTC)

  I agree. Authors like Jayne discuss NAND and NOR in terms of probability theory and it becomes the basis for the emerging argument for Bayesian statistical analysis over traditional statistical analysis found in Clayton's Bernoulli's Fallacy.

  Also the result is the lack of parallel with the wikipedia entry Logical NOR. Rmj03 (talk) 21:06, 11 December 2022 (UTC)

Result

It was requested that this article be renamed but there was no consensus for it to be moved. WhiteNight ^{T | @ | C} 20:05, 29 December 2005 (UTC)

Alternative, not joint, denial

Contrary to the first paragraph, Sheffer stroke is not 'joint denial' but rather 'alternative denial'. The joint denial of P and Q is $\lnot p\land \lnot q$ which is equivalent to NOR. The alternative denial of P and Q $\lnot p\lor \lnot q$ which is equivalent to NAND (the Sheffer stroke).

Sheffer, in his paper talks about rejection as the negation of a disjunction. So not what you wrote ( i think ) but ¬(p∨q). Which by De Morgan's Law turns into ¬p∧¬q. mmick66 —Preceding undated comment added 12:08, 12 March 2011 (UTC).

NAND symbol shape is non-standard

The NAND gate symbol shown in the upper-right illustration does not conform to industry standards for a NAND gate. The straight horizontal edges should be longer. See page three of the IEEE document http://www.ddpp.com/DDPP3_pdf/IEEEsyms.pdf .

Olmsfam 16:12, 15 March 2007 (UTC) edit: Ive taken the liberty to create and upload these for consideration, but i know not how to upload them to WIKI and there for leave it up to the more knowlegable to replace the larger and blurrier existing nand.jpg with one of the following:

Exactly same as nand.jpg only smaller file size and in png: File:Http://www3.telus.net/public/olmsfam/NAND.png

Closer to the IEEE standard File:Http://www3.telus.net/public/olmsfam/NAND 1.png

Logical nand is a more common name

This is the simple reason why I moved the article from Sheffer stroke to Logical nand. And after that, I did some innovative changes, but however, some people just reverted the changes and ignored the improved article!!!!! User:203.186.238.228

Nonetheless the move was improperly performed. See WP:MOVE for the policy: in particular WP has facilities for moving pages unavailable to anonymous users: you can request page moves at WP:RM (requested moves). What's wrong with what you did is that blanking pages by hand and copying contents spoils the connection of contributed content to the edit history, and this connection is considered important for content licensing purposes.

Note that while NAND is a very common name for this, it is usually counted as an electronic gate, and the phrase "Logical nand" is fairly rare, according to google much rarer than Sheffer stroke. --- Charles Stewart 19:17, 7 December 2005 (UTC)

I have to say, I find this Sheffer stroke title for the article quite surprising. I have never heard of Sheffer stroke, and I studied Computer Science and Electrical Engineering for my BS. This included lots of abstract math, and I never encountered it, such that I would remember it, nor have I ever heard anyone utter that phrase. No matter what Google may say about it, I think it's a rather uncommon phrase, compared to "Logical NAND" or just NAND. Interesting, yes, but Logical NAND would be much preferable name for the article, and Sheffer and his stroke can figure prominently, of course! JoGusto 22:52, 18 April 2006 (UTC)

Which term is more common depends on what field you're in. "NAND" is more common in your fields, "Sheffer stroke" is more common among logicians, both those in philosophy departments and those in math departments. I have no opinion as to how that should affect the name of the page. To me, the most important thing is that "Logical NAND", "NAND", and "Sheffer stroke" all take you to the same place, either directly or by redirect. --JMRyan 23:34, 24 April 2006 (UTC)

I've never heard of Sheffer stroke either, but by google it's something like 10 times more popular, if i didn't divide wrong. --M1ss1ontomars2k4 ^{(T | C | @)} 01:04, 4 June 2006 (UTC)

When I came to this page when searching for NAND, I thought Wikipedia had messed up for the first time, and that it was the wrong page. I support renaming this page as NAND. As a senior software engineer, I have never heard of Sheffer stroke. Todd 12:04, 14 November 2007 (UTC) Sounds more like a medical term - "the Sheffer stroke following an open heart surgery"! ;-) Todd (talk) 10:30, 22 November 2007 (UTC)

JA: I probably learned the terms ampheck, NAND, and Sheffer stroke all about the same time, and remain fond of all the historical connections, but frequency of use is not the only consideration, as I'm finding out as I try to develop some consistency of treatment across the pages on the 16 functions. Considering them as a group of related articles, it would just help the exposition a little to have "logical NAND" on a par with "logical NOR" and all the others. Jon Awbrey 11:38, 4 June 2006 (UTC)

Protection

I protected the Logical nand page due to several cut and paste move attempts recently. I will now unprotect it since it looks like it's part of a move debate. Thanks. --Woohookitty^{(cat scratches)} 09:27, 9 December 2005 (UTC)

I protected Logical nand and now this page. Whoever is putting half a gig onto these pages STOP NOW. It's so large and has so many script errors that it's literally making browsers crash. --Woohookitty^{(cat scratches)} 10:20, 9 December 2005 (UTC)

Misterious removals

Somebody removes links to Sheffer stroke and XNOR from the list of mathematical topics and other lists. That person using an ever-changing IP address, so it is hard to track. Oleg Alexandrov (talk) 16:53, 9 December 2005 (UTC)

To the anonymous contributor

Please make an account. Each time you contribute you use a different IP address. I counted at least five. It is a mess, and it is impossible to get in touch with you. Please make an account like everybody else and let us discuss. Thanks. Oleg Alexandrov (talk) 16:56, 9 December 2005 (UTC)

Distinction between signs or symbols and functions or operators

• JA: It is very important to distinguish the roles of signs and symbols and so on, which are semiotic or syntactic things, from the roles of functions and operators and so on, which are formal or mathematical objects. In particular, the Sheffer stroke, which probably should be written with quotes, as "|", in the article, is a signlike thing, which is just one of many signs that may denote the corresponding mathematical object. Jon Awbrey 15:00, 19 January 2006 (UTC)

Name Change : Sheffer Stroke → Logical NAND

JA: The more I work on standardizing the formats across the various 2-place operators, the more it looks like it would be a service to the reader to use "Logical NAND" as the title of choice for the Sheffer stroke operation. We can always mention the other name in the first line without much ado. I don't really want to go through all that voting business unless there's some kind of prior con-sense among interested parties that it makes sense to do this. So, what do folks think as of the present moment? Jon Awbrey 16:46, 18 May 2006 (UTC)

The title needs changing anyway, because the topic of the article is not a symbol, it is a sentential operation. Nortexoid 18:33, 18 May 2006 (UTC)

JA: Yes, it's a practice that began as a harmless form of loose speech among practitioners who had no doubt what they were actually talking about, and probably couldn't imagine how creative their epigones would be in confusing themselves about it. So, I can put you down for a Yea? Jon Awbrey 18:46, 18 May 2006 (UTC)

I think it is IMPOSSIBLE to change name of this article, because the voting result is to OPPOSE this suggestion. In addition, SOME "logician" use their "force" to prevent the name change, as the term "Sheffer Stroke" may be more comfortable to them (but it ought to be more painful to other people). QQ 14:35, 28 May 2006 (UTC)

Shouldn't the articles for Logical NAND and Logical NOR both be treated equally? Now the NOR article emphasizes the actual operation while the NAND article emphasizes the denotational symbol (Sheffer stroke). 130.234.177.217 16:14, 13 October 2006 (UTC)

Roots of the naming issues

JA: There is a set of methodolodical questions that have been boiling under the surface of the naming issues that periodically erupt here and elsewhere. I don't think that the article-specific name-change voting format is very good way to handle these broader issues, so I think it might be good to start up a more comprehensive discussion here, and to reflect on the wider consequences of whatever policy we adopt. Jon Awbrey 14:24, 29 May 2006 (UTC)

JA: First off, splitting the article is clearly a bad idea, so I'll vote "Oppose" on that if and when the proper voting boilerplate is instituted. Jon Awbrey 14:28, 29 May 2006 (UTC)

Reference to German Wikipedia article seems to be wrong

The "Deutsch" link is to http://de.wikipedia.org/wiki/NAND-Gatter (NAND-Gate). However the article says "This article is about NAND in the logical sense."

The parallel German article is probably:

http://de.wikipedia.org/wiki/NAND

Big move

I did a big edit. I want to center around the logical operators as the key concept around which the entries are organized. There are standard sections for each of them. Everything nand related is in one place. The links to "NAND gate" will go directly to that section. Gregbard 04:19, 24 June 2007 (UTC)

Proposed project

I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at: Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also see Talk:Logical connective.

I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts.

Gregbard 08:45, 28 June 2007 (UTC)

Natural language subsection

This section, currently comprising the following text, makes little sense to me:

NAND is not used in everyday sentences because it exhibits an inherent inversion, which makes it confusing like a double negative. Here's an example of a sentence using:

NAND operator: We will surely die if we have food nand water.

Common terms: We will surely die if we do not have both food and water.

Or, by DeMorgan's Law: We will surely die if we lack either food or water.

(1) "NAND is not used in everyday sentences because..." "NAND" not used in everyday sentences because it's not an English word. What is really meant by this statement?

(2) It seems to me that in ordinary English, "We will surely die if we do not have both food and water" and "We will surely die if we lack either food or water" mean two different things. The DeMorgan version is much clearer (although it would be that much more reflective of the truth table if it said, "We will surely die if we lack either food or water or both"). The "common terms" version sounds like it means that death will result only if BOTH food and water are lacking, but death will not result if food is present and water is lacking, or food is lacking and water is present. This interpretation is no congruent with the truth table. —Preceding unsigned comment added by 65.192.31.130 (talk) 21:57, 18 January 2008 (UTC)

To make the confusion perfect, to me, the natural way to phrase the statement in English would be, "We will surely die if we have neither food nor water." Benja (talk) 20:21, 18 April 2008 (UTC)

The "overbar" symbol

A 19th century algebra textbook, Olney's Algebra, used the overbar as a grouping operator, equivalent to pairs of parentheses. It remains today as the horizontal stroke in a square (or other) root symbol. It's also called a vinculum. (Off-topic, but of some interest, is that that book gave procedures for extracting cube, 5th, and 7th roots "by hand", as elaborations of the square-root procedure. However, as the order of the root increased, the procedure become progressively more elaborate, and became closer to guesswork (with more penalty for bad guesses!).

In 1960, I was a computer technician, working with the BMEWS DIP computer, which was an all-NAND-gate machine. Needless to say, Boolean expressions describing the machine's logic required a NAND notation, and while training, we used the overbar frequently.

Around 1978, I was an associate editor at Electronic Design magazine, where we sometimes had occasion to publish Boolean expressions, and we used only the overbar. It caused our printer considerable grief, because their typesetter simply was not designed to create the symbol. Back in the 19th century, before Linotype, it was probably easier to typeset. —Preceding unsigned comment added by Nikevich (talk • contribs) 19:42, 4 June 2008 (UTC)

Logical vs. binary interpretations

Although the first table presented in the article uses the binary symbols 0 and 1, the accompanying discussion refers to truth values "true" and "false." In fact, it doesn't seem that the article ever explains how to relate the two interpretations. Thus, for example, the uninformed reader would not understand that the first table is just another version of the truth table, using a different pair of symbols. Jumping over to the NOR article for comparison, note that there the binary symbols aren't used at all. Nor are these symbols mentioned in the umbrella article on logical connectives. I think that they should be, and perhaps all the articles about logical connectives should be edited for consistency on this point. Ishboyfay (talk) 21:30, 10 October 2009 (UTC)

Factual Error

This article is mistaken about what the Sheffer Stroke is. The Sheffer Stroke is equivalent to "Neither Nor", not to "Not Both." This is clear is you look at the original 1913 article by Sheffer, p. 487, first full paragraph. It is available at http://www.jstor.org/stable/pdfplus/1988701.pdf See also the discussion at http://undaimonia.blogspot.com/2009/02/sheffer-stroke-problem.html In my opinion, the whole article needs to be rewritten. PhiloBalk (talk) 16:41, 8 March 2010 (UTC)

I just now looked at Enderton's A Mathematical introduction to logic, p. 51. Enderton says "nand, not both A and B; the symbol is called the Sheffer stroke" Then I checked the CRC Consise Encyclopedia of Mathematics. The entire entry under "Sheffer stroke" is the word "NAND". Hinman's Fundamentals of matheamtical logic, p. 40, also says the Shefer stroke is NAND.

Just to double-check, I searched for sheffer strike nand on Google books; there are plenty of other results there.

So it's a little much to claim that Wikipedia is mistaken here. At best, usage is mixed. — Carl (CBM · talk) 16:56, 8 March 2010 (UTC)

In contemporary common usage (which Wikipedia follows), Sheffer stroke usually denotes NAND, whereas NOR is called Pierce arrow. It is true that in Sheffer's original paper he assigns it the NOR interpretation in the small part which deals with equivalence of his system to other formulations of Boolean algebra, nevertheless for the most part his approach is very formalistic and one cannot really tell from the axioms which of the two operations it denotes, because of self-duality of Boolean algebras.—Emil J. 17:15, 8 March 2010 (UTC)

Having said that, the History section needs fixing. done—Emil J. 17:21, 8 March 2010 (UTC)

I do think it is clear from the Sheffer paper that Sheffer means "neither." I also agree that common usage is mixed. (If you google books Sheffer Stroke NOR you get lots of hits too.) So since it is mixed, why not go with the one that follows Sheffer's intentions?. Thanks at least for fixing the history section. PhiloBalk (talk) 03:43, 9 March 2010 (UTC)

If the contemporary usage is to use "Sheffer stroke" to mean NAND, that's what we should follow here. There are many examples in mathematics where someone's name is attached by common usage to something different than that person actually did. Personally, I think this article should be titled "Logical NAND" to match Logical NOR. Does anyone object to that move? — Carl (CBM · talk) 11:45, 9 March 2010 (UTC)

Why would Wikipedia wish to propagate a citation error? As PhiloBalk rightly points out, Sheffer, the creator of the Sheffer stroke, defines it to be "neither nor": p | q means neither p nor q, that is, (not p) and (not q). It is true that many authors since Sheffer's time have confused his original definition, but this fact hardly excuses continuing the confusion. Proof that not all authoritative authors are propagating this error can be found in the 3-volume set Handbook of Boolean Algebras (J.D. Monk, ed., North Holland, 1989). On p. 27 of volume 1, Sheffer stroke is defined in the way Sheffer did originally. Also, proof of the fact that the term "Sheffer stroke" is intended to refer to Sheffer's original paper (reference given by PhiloBalk) can be found in Haskell Curry's classic logic text Foundations of Mathematical Logic (1977 reprint by Dover Publications). In that book, on p. 294, he gives the *incorrect* definition (the "NAND" definition) but actually claims that it comes from Sheffer's original paper, which Curry cites. This illustrates that at least one "authoritative" author really believes he is quoting Sheffer's original paper with this incorrect definition. At the very least, the Wikipedia article should acknowledge that there is an issue, historically, regarding the correct definition of "Sheffer stroke."

Hey guys I just read the part from Shefferd's paper indicated by PhiloBalk and I fear we might be mistaken. Sheffer talks about rejection (the operation we are considering) as the negation of a disjunction not of a conjunction as we are writing here!. He has the logical equation of p ^ q = ¬(p ∨ q) where ^ is rejection in this part of his paper for some reason). By De Morgan's Law we can turn the latter into ¬p ∧ ¬q which in a Venn diagram would mean only the outsie of the circles would be red. Am I confused or are we quoting Sheffer wrong? mmick66 —Preceding undated comment added 12:05, 12 March 2011 (UTC).

Sheffer Stroke Proof of Informal Logic

I suggest undoing the edits from IP 67.190.103.219 on Nov. 10 for the following reasons:

• Spelling, punctuation, capitalization, and other grammatical errors
• Poor formatting and references (e.g. I don't think Wikipedia is allowed to cite itself).
• Digressive writing; not much coherency

But most importantly:

• It's not clear what the point is or why this content belongs here. The content seems to be about the Sheffer Stroke proof of informal logic; what is the relevance to the Sheffer Stroke/NAND logical operation?
• Snide comment about the American judicial system; verging on vandalism (already reverted)

It's either that or smother it with tags saying "Fix me, Citation needed, clarification needed, improper style etc. etc." Rotiro (talk) 05:26, 10 November 2010 (UTC)

I agree it wasn't written in a way appropriate for this article. It has already been removed. — Carl (CBM · talk) 12:11, 10 November 2010 (UTC)

Unicode Nand ⊼

Unicode includes the negated and symbol: ⊼ (U+22BC NAND). Should we use it? 81.186.243.41 (talk) 15:37, 25 January 2013 (UTC)

I'd say yes. ↑ (2191 UPWARDS ARROW) can't be counted upon to look like anything like a Sheffer Stroke in most fonts I've used, e.g. PragmataPro, Fira, Noto, etc. Using | (007C VERTICAL LINE) is technically better except it usually means something different in programming languages. I was so happy when I discovered ⊼ on this talk page. Jartine (talk) 23:29, 17 December 2021 (UTC)

Confusing Citation

I find the following baffling: Stamm, Edward Bronisław [in Polish] (1911). "Beitrag zur Algebra der Logik". Monatshefte für Mathematik und Physik (in German). 22 (1): 137–149. doi:10.1007/BF01742795.

The puzzle is the [in Polish] remark. First, the article is obviously in German, as correctly noted after the title. Is this simply supposed to mean that Stamm himself, or his name, is Polish--a completely unnecessary remark? Or is it supposed to suggest that he used Polish notation (I'm not sure if he did, but again this is completely inappropriate to remark upon in a citation). But I'm also puzzled about how to remove it; I can't find the [in Polish] text anywhere on the editing page, so I hope someone who agrees with me that it is out of place and knows how or where this is encoded can remove it.ScottForschler (talk) 13:18, 17 July 2023 (UTC)

Requested move 5 December 2018

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this section.

No consensus. See no agreement below based on usage in reliable sources, just good faith "great idea" support with a valid stab at internal WP:CONSISTENCY ("would fit with other logical articles"), which must still jive with usage in reliable sources. In looking at this talk page and the move log (this article has been stable at this title since 25 February 2002), it appears that it will take someone with expertise on the subject who can correctly summarize the appropriate sources and describe it in language your average closer like me can understand if editors want to move this page. So this article will retain its stable title for now. As is usual with a no-consensus result, editors can work on the concerns noted below and try again in a few months to garner consensus to rename this article. Kudos to editors for your input, and Happy Publishing! (nac by page mover) Paine Ellsworth, ed.  ^put'r there  07:20, 23 December 2018 (UTC)

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Sheffer stroke → Logical NAND – Would fit with the other logical articles, easier to remember (Sorry) 108.58.186.110 (talk) 19:53, 5 December 2018 (UTC) --Relisting. Andrewa (talk) 01:38, 13 December 2018 (UTC)

• Support – This is a great idea! I don't understand why we would list an operation under its notation. Gigamicro (talk) 21:31, 6 December 2018 (UTC)

• Support – cherkash (talk) 16:04, 7 December 2018 (UTC)

• Relisting comment: In 17 years of seriously studying formal logic I never once heard this referred to as NAND, that was the usage in the electronics and computing science world, and more lately in some areas (not all) of mathematics. But I note that the nom and !votes to date are all just personal opinions and experience, as is my comment. We need to look at sources. (I note that this article leads off In Boolean functions and propositional calculus,...) Andrewa (talk) 01:38, 13 December 2018 (UTC)

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The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Another comment on the naming

There's a lot of context to understand where the "Sheffer" comes from, but absolutely nothing explaining why it's a "stroke". Very nearly had one [a stroke] while trying to grasp the context.

110.150.31.209 (talk) 11:14, 31 January 2024 (UTC)