text:
An Jung-geun

An Jung-geun (2 September 1879 – 26 March 1910), sometimes spelled Ahn Joong-keun, was a Korean independence activist and pan-Asianist. His baptismal name was Thomas.

He is remembered as a martyr in both South and North Korea for his 1909 assassination of the Japanese politician Itō Hirobumi, who had previously served as the Resident-General of Korea and first Prime Minister of Japan. An was imprisoned and later executed by Japanese authorities on 26 March 1910.

He was posthumously awarded the Order of Merit for National Foundation in 1962 by the South Korean government, the most prestigious civil decoration in the Republic of Korea, for his efforts for Korean independence.

Early accounts
An was born on 2 September 1879, in Haeju, Hwanghae Province, Joseon. He was the first son of An Taehun and Jo Maria, of the Sunheung An clan. Ahn is the 26th great-grandson of Ahn Hyang. His childhood name was (안응칠; 安應七; ). The name originated from seven dots on the chest and stomach, meaning that it was born in accordance with the energy of the Big Dipper. As a boy, he learned Chinese literature and Western sciences, but was more interested in martial arts and marksmanship. Kim Ku, a future leader of the Korean independence movement who had taken refuge in An Tae-hun's house at the time, wrote that young An Jung-geun was an excellent marksman, liked to read books, and had strong charisma.

At the age of 16, An entered the Catholic Church with his father, where he received his baptismal name "Thomas", and learned French. While fleeing from the Japanese, An took refuge with a French priest of the Catholic Church in Korea named Wilhelm (Korean name, Hong Seok-gu; 홍석구; 洪錫九) who baptized and hid him in his church for several months. The priest encouraged An to read the Bible and had a series of discussions with him. He maintained his belief in Catholicism until his death, going to the point of even asking his son to become a priest in his last letter to his wife.

At the age of 25, he started a coal business, but devoted himself to the education of Korean people after the Eulsa Treaty by establishing private schools in northwestern regions of Korea. He also participated in the National Debt Repayment Movement. In 1907 he exiled himself to Vladivostok to join in with the armed resistance against the Japanese colonial rulers, where he learned fluent Russian. He was appointed a lieutenant general of an armed Korean resistance group and led several attacks against Japanese forces before his eventual defeat.

Assassination of Itō Hirobumi

In October 1909, An passed the Imperial Japanese guards at the Harbin Railway Station. Itō Hirobumi had come back from negotiating with the Russian representative on the train. An shot him three times with an FN M1900 pistol on the railway platform. He also shot Kawagami Toshihiko (川上俊彦), the Japanese Consul General, Morita Jirō (森泰二郞), a Secretary of Imperial Household Agency, and Tanaka Seitarō (田中淸太郞), an executive of South Manchuria Railway, who were seriously injured. After the shooting, An yelled out for Korean independence in Russian, stating "Корея! Ура!" (Korea! Hurrah!), and waving the Korean flag.

Afterwards, An was arrested by Russian guards who held him for two days before turning him over to Japanese colonial authorities. When he heard the news that Itō had died, he made the sign of the cross in gratitude. An was quoted as saying, "I have ventured to commit a serious crime, offering my life for my country. This is the behavior of a noble-minded patriot." Wilhelm gave last rites to An, ignoring the bishop of Korea's order not to. An insisted that the captors call him by his baptismal name, Thomas.

In court, An claimed to be a lieutenant general of the Korean resistance army and demanded to be treated as a prisoner of war and not a suspected criminal. He insisted he did nothing wrong, reciting a list of 15 execution-worthy offenses he believed Itō had committed. An mistakenly believed Itō had ordered the assassination of Empress Myeongseong, an order which is attributed to Miura Gorō, although Miura Gorō did send a report to Itō after the execution.

"'15 reasons why Itō Hirobumi should be killed.

 * 1) Assassinating the Korean Empress Myeongseong
 * 2) Dethroning the Emperor Gojong
 * 3) Forcing 14 unequal treaties on Korea
 * 4) Massacring innocent Koreans
 * 5) Usurping the authority of the Korean government by force
 * 6) Plundering Korean railroads, mines, forests, and rivers
 * 7) Forcing the use of Japanese banknotes
 * 8) Disbanding the Korean armed forces
 * 9) Obstructing the education of Koreans
 * 10) Banning Koreans from studying abroad
 * 11) Confiscating and burning Korean textbooks
 * 12) Spreading a rumor around the world that Koreans wanted Japanese protection
 * 13) Deceiving the Japanese Emperor by saying that the relationship between Korea and Japan was peaceful when in truth it was full of hostility and conflicts
 * 14) Breaking the peace of Asia
 * 15) Assassinating the Emperor Kōmei.

I, as a lieutenant general of the Korean resistance army, killed the criminal Itō Hirobumi because he disturbed the peace of the Orient and estranged the relationship between Korea and Japan. I hoped that if Korea and Japan be friendlier and are ruled peacefully, they would be a model all throughout the five continents. I did not kill Itō misunderstanding his intentions.'"

Imprisonment and death
An's Japanese captors showed sympathy to him. He recorded in his autobiography that the public prosecutor, Mizobuchi Takao, exclaimed "From what you have told me, it is clear that you are a righteous man of East Asia. I can't believe a sentence of death will be imposed on a righteous man. There's nothing to worry about." He was also given New Year's delicacies and his calligraphy was highly admired and requested. After six trials, An was sentenced to death by the Japanese colonial court in Ryojun (Port Arthur). An was angered at the sentence, though he expected this outcome. He had hoped to be viewed as a prisoner of war instead of an assassin. On the same day of sentencing at two o'clock in the afternoon, his two brothers Jeong-geun and Gong-geun met with him to deliver their mother's message, "Your death is for the sake of your country, and don't ask for your life in a cowardly manner. Your brave death for justice is final filial regard to your mother."

Judge Hirashi, who presided over An's trial, had promised An that a stay of execution for at least a few months would be granted, but Tokyo ordered prompt action. Before his execution, An made a final request: that the wardens help him finish his essay, "On Peace in East Asia". Also he received Korean white clothes from his mother to die in during his execution. An requested to be executed as a prisoner of war, by firing squad. But instead, it was ordered that he should be hanged as a common criminal. An was executed in Ryojun, on 26 March 1910. His grave in Lu Shun has not been found.

During his imprisonment, An was excommunicated by the Catholic church for Ito's assassination, viewed negatively by the church. This excommunication was lifted posthumously in 1993.

An dictated in his will that his body be buried in Harbin Park in China and then relocated to his homeland if Korea achieved independence but his request was not honoured. According to records, he was buried near the prison; the Korean government has not received cooperation from the Japanese government regarding the location of his burial. Hyochang Park in Seoul contains a grassy mound that serves as an honorary grave for An.

Views
Some historians hold that Itō's death resulted in the acceleration of the final stage of the colonization process, but the claim has been disputed by some.

Pan-Asianism
An strongly believed in the union of the three great countries in East Asia, China, Korea, and Japan in order to counter and fight off Western imperialism, namely, Western countries that controlled parts of Asia, and restore East Asian independence. He followed the progress of Japan during the Russo-Japanese War and claimed that he and his compatriots were delighted at hearing of the defeat of one of the agents of western imperialism, but were disappointed that the war ended before Russia was totally subjugated.

According to Donald Keene, author of Emperor of Japan: Meiji and His World, 1852–1912, An Jung-Geun was an admirer of Emperor Meiji of Imperial Japan. One of the 15 charges An leveled against Itō was that he had deceived the Emperor of Japan, whom An felt desired peace in East Asia and Korean independence. An requested that Meiji be informed of his reasons for his execution of Itō in the hopes that if Meiji understood his reasons, the emperor would realize how mistaken Itō's policies were and would rejoice. An also felt sure that most Japanese felt similar hatred for Itō, an opinion he formed from talking with Japanese prisoners in Korea. During An's prison sentence and trial, many Japanese prison guards, lawyers, and even prosecutors were inspired by him.

An felt that with the death of Itō, Japan and Korea could become friends because of the many traditions that they shared. He hoped that this friendship, along with China, would become a model for the world to follow. His thoughts on Pan-Asianism were stated in his essay, "On Peace in East Asia" (東洋平和論; 동양평화론) that he worked on and left unfinished before his execution. In this work, An recommends the organization of combined armed forces and the issue of joint banknotes among Korea, Japan, and China. Sasagawa Norikatsu (笹川紀勝), a Professor of Law at Meiji University, highly praises An's idea as an equivalent of the European Union and a concept that preceded the concept of the League of Nations by 10 years.

Legacy

The assassination of Itō by An was praised by Koreans and many Chinese as well, who were struggling against Japanese invasion at the time. Well-known Chinese political leaders such as Yuan Shikai, Sun Yat-sen, and Liang Qichao wrote poems acclaiming An.

In the 2010 An Jung-Geun Symposium in Korea, Wada Haruki (和田春樹), an activist who once worked at Tokyo University, evaluated An by quoting Itō Yukio (伊藤之雄), a fellow history scholar in Kyoto University. In his text published in 2009, Itō Yukio claims that the reign by Itō Hirobumi resulted in strong resistance from Koreans as it was considered the first step for the annexation of Korea due to the cultural differences, and that An is not to be blamed even if he assassinated Itō without understanding Itō's ideology (2009, Itō).

On 26 March 2010, a nationwide centenary tribute to An was held in South Korea, including a ceremony led by the Prime Minister Chung Un-Chan and tribute concerts.

Ancestry
An's family produced many other Korean independence activists. An's cousin An Myeong-Geun attempted to assassinate Terauchi Masatake, the first Japanese Governor-General of Korea  who executed the Japan-Korea Annexation Treaty in 1910. He failed, however, and was imprisoned for 15 years; he died in 1926. An's brothers An Jeong-Geun and An Gong-Geun, as well as An's cousin An Gyeong-Geun  and nephew An Woo-Saeng , joined the Provisional Government of the Republic of Korea in Shanghai, China, which was led by Kim Ku, and fought against Japan. An Chun-Saeng, another nephew of An's, joined the National Revolutionary Army of China, participated in battles against Japanese forces at Shanghai, and joined the Korean Liberation Army in 1940. Later, he became a lieutenant general of the Republic of Korea Army and a member of the National Assembly of South Korea.

Meanwhile, An Jung-Geun's youngest son, Ahn Jun-saeng became a prominent businessman and Chinilpa during the Japanese occupation of Korea. He died in 1952 from tuberculosis, with his children immigrating to the United States of America after the war.

 * Grandfather
 * An In-su
 * Father
 * An Tae-hun
 * Mother
 * Jo Maria (趙瑪利亞, 조마리아) of the Baecheon Jo clan (6 May 1862 – 25 July 1927)
 * Sister
 * Younger sister: An Seong-nyeo (1881–1954)
 * Brother
 * Younger brother: An Jeong-geun (17 January 1887 – 17 March 1949)
 * Sister-in-law: Yi Jeong-seo
 * Nephew: An Won-saeng
 * Niece: An Mi-saeng
 * Nephew: An Jin-saeng (28 January 1916 – 24 December 1988)
 * Niece-in-law: Park Tae-jeong
 * Grandniece: An Gi-su
 * Grandniece: An Gi-ryeo
 * Younger brother: An Gong-geun (11 July 1889 – 30 May 1939)
 * Nephew: An Woo-saeng (1907–1997)
 * Nephew: An Nak-saeng (22 June 1913 – 1950)
 * Niece: Lady An
 * Nephew-in-law: Han Ji-seong
 * Niece: Lady An
 * Wife
 * Kim Ah-ryeo
 * Children
 * Son: An Mun-saeng
 * Daughter: An Hyeon-saeng (1902–1959)
 * Son-in-law: Hwang Il-cheong
 * Granddaughter: Hwang Eun-ju
 * Granddaughter: Hwang Eun-sil
 * Son: An Jun-saeng (1907 – November 1951)
 * Daughter-in-law: Jeong Ok-nyeo (1905–?)
 * Grandson: An Ung-ho
 * Granddaughter: An Yeon-ho (1938 – 6 February 2011)
 * Granddaughter: An Seon-ho (? – 2003)
 * Cousins
 * An Myeong-geun (안명근,安明根; 1879–1927)
 * An Hong-geun
 * An Bong-geun
 * Grandnephew: An Chun-saeng (12 August 1912 – 26 January 2011)

Calligraphic works
An is highly renowned for calligraphy works. While he was in prison, many prison guards such as Chiba Toshichi (千葉十七) who respected him, made requests to An for calligraphy works. He left many calligraphy works which were written in the jail of Lushun although he hadn't studied calligraphy formally. He would leave on his calligraphy works a signature of "大韓國人" (Great Korean) and a handprint of his left hand, which was missing the last joint of the ring finger, which he had cut off with his comrades in 1909 as a pledge to kill Itō. Some of the works were designated as Treasure No. 569 of the Republic of Korea in 1972. One of his famous works is "一日不讀書口中生荊棘" (일일부독서 구중생형극; Unless one reads every day, thorns grow in the mouth), a quote from the Analects of Confucius.

Memorial Halls
Memorial halls for An were erected in Seoul in 1970 by the South Korean government and in Harbin by the Chinese government in 2006. South Korean President Park Geun-Hye raised the idea of erecting a monument for An while meeting with Chinese President Xi Jinping during a visit to China in June 2013. Thus another memorial hall honoring An Jung-Geun was opened on Sunday, 19 January 2014 in Harbin. The hall, a 200-square meter room, features photos and memorabilia. Annual activities in memorial of An are held in Lüshun, where he was imprisoned and executed.

According to local sources in China dated on 22 March 2017, the An Jung-geun Memorial Hall located at Harbin Railway Station was recently relocated to a Korean art museum in Harbin City amid China's retaliation over South Korea's deployment of the U.S. THAAD antimissile system. The Memorial Hall has since been reopened in the Harbin Railway Station after renovation work.

Controversies
Historically, the Japanese government has generally deemed An Jung-geun as a terrorist and criminal, while South Korea has upheld An as a national hero. In January 2014, Yoshihide Suga, then a Japanese government spokesperson and former Japanese Prime Minister, described the Harbin memorial hall honoring An in China as "not conducive to building peace and stability" between East Asian countries. China, on the other hand has declared that An was a "famous anti-Japanese high-minded person" while South Korea's foreign ministry stated An was a "highly respected figure."

In February 2017, South Korean police were criticized for using a picture of An in posters put up in the city of Incheon. The poster warned of terrorism, and many South Korean citizens online criticized the police, asking "if it was meant to imply if An was a terrorist". A police officer in the Korea Times apologized and clarified that there was no intention to associate An with terrorism, and all posters were taken down.

In popular culture
In 1959, South Korean film King Gojong and martyr An Jung-Geun was the first movie about An Jung-geun, and is a dramatized story about the event. The 1979 North Korean film An Jung Gun Shoots Itō Hirobumi is another dramatized story of the event. The 2004 South Korean film Thomas An Jung-geun  is another dramatized story of the event. Released on September 10, 2004, it is directed by Seo Se-won. An Jung-Geun is played by actor Yu Oh-seong and Itō Hirobumi is played by Yoon Joo-sang.

A Chinese-South Korean co-production, The Age of Heroes, is being planned as a Korean drama for 2019. The Age of Heroes is planned to be 24 episodes long and entirely pre-produced with a budget of 30 billion won. Filming will begin by the end of 2018 with locations in South Korea, China, and North Korea.

A fictionalized explanation of the events is presented in an episode of the fifteenth season of The Murdoch Mysteries, a Canadian murder mystery show. In the episode, entitled Patriot Games, a dead body in a Toronto cellar leads to an explanation of An Jung-geun's assassination plot wherein rogue Russian agents play a part, requiring swift action to prevent the outbreak of a potential world war.

Hero (2022 South Korean film)

Harbin, a 2024 film directed by Woo Min-ho, stars Hyun Bin as An.

title: An Jung-geun


text:
David Rosenthal

David Rosenthal may refer to:

 * David Rosenthal (musician) (born 1962), American keyboardist, music producer, and songwriter
 * David H. Rosenthal (1945–1992), American author, poet, editor and translator
 * David M. Rosenthal (philosopher) (fl. 1970s to present), philosopher at the City University of New York
 * David M. Rosenthal (director) (born 1969), American filmmaker, writer and director
 * David S. Rosenthal (fl. 1990s to present), American television producer
 * David S. H. Rosenthal (born 1948), computer scientist

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: David Rosenthal


text:
Anton Alberts (architect)

Anton (Ton) Alberts (6 July 1927 – 16 August 1999) was a Dutch architect best known for the ING Bank (1982) in the Bijlmer district of Amsterdam and the Gas Corporation headquarters in Groningen.

Alberts was involved with Situationist International before being expelled in 1960. He had been involved with fellow Situationists Constant and Har Oudejans in setting up a labyrinth in the Stedelijk Museum of Amsterdam, but the project fell apart amidst acrimony. Officially he was expelled for designing churches, although Asger Jorn relates the expulsion more to the "Amsterdam affair".

In 1963 he founded the firm Alberts and Van Huut with Max van Huut, guided by the principles of organic architecture. His work also has its roots in the anthroposophical architecture of Rudolf Steiner.

Alberts offered to work for free on the Peace Parks in Bosnia and Herzegovina but was only able to create sketches before he died, aged 72, in Amsterdam. Still, by Albert's sketches the Peace Flame House, a community centre, was built in Tuzla, Bosnia and Herzegovina, as a gift by Peace Flame Foundation Netherlands to this after-war community.

title: Anton Alberts (architect)


text:
Talk:Division by zero

Wiki Education assignment: Computer Science Principles
— Assignment last updated by Annie.nguyen0811 (talk) 21:33, 27 October 2022 (UTC)

Error in Paragraph "Algebra"
In Paragraph "Algebra" there ist written:

"It follows from the properties of the number system we are using (that is, integers, rationals, reals, etc.), if b ≠ 0 then the equation a/b = c is equivalent to a = b × c. Assuming that a/0 is a number c, then it must be that a = 0 × c = 0."

This is wrong, since the assumption b ≠ 0 is already violated in the next sentence. Stephan Schief (talk) 20:15, 8 May 2023 (UTC)

 * The statement that the denominator of a fraction cannot be equal to zero in the number systems mentioned is a correct statement, but the sentence saying that is awkward enough so I can understand how it can be misread. I'll try to make it clearer. Rick Norwood (talk) 10:32, 9 May 2023 (UTC)
 * I agree that in the field structure of the reals (or rationals), if b≠0, then a/b=c implies a=b×c. But one can not use this argument to say that if a/0=c, then a=0×c. Because then one would use b=0, in contradicition to the assumption. Stephan Schief (talk) 10:50, 9 May 2023 (UTC)

 * As I'm sure you know, when showing something by way of contradiction, it is standard to violate the assumption, arrive at a contradiction, and so demonstrate that the assumption is correct. I've tried to rewrite the paragraph so make the hypothetical nature of the claim clearer. Rick Norwood (talk) 11:04, 9 May 2023 (UTC)
 * I did not realise that you were using an argument by contradiction! I am sorry about that. I like how you rewrote the paragraph, it is a lot clearer to me now. Thank you! Stephan Schief (talk) 11:13, 9 May 2023 (UTC)

Sources for proof assistants
My edit cites two sources: a blog post from Kevin Buzzard and and StackOverflow answer from Arthur Azevedo de Amorim. I'm not concerned about the authors, given that they are a Lean maintainer and an author of Software Foundations respectively. But I'm open to alternatives from more established publishers. Lambda Fairy (talk) 05:37, 2 December 2023 (UTC)
 * Blogs are not reliable sources. I have reverted your edit. To establish notability, such content needs more solid sources, such as textbooks or articles in peer reviewed journals. - DVdm (talk) 10:52, 2 December 2023 (UTC)
 * Correcting a mistake of Lambda Fairy: Kevin is not a Lean maintainer at all, but is still a subject matter expert (source: I am a maintainer for its math library).
 * Blogs are not reliable sources
 * Proof assistants are ultimately source code; would a permalink to the corresponding lines of code be sufficiently reliable? After all, there is no more reliable indicator of how a software system behaves than its source code.
 * I think the blog/SE post provides some interesting context beyond the simple proof that the statement is true
 * To establish notability
 * Presumably the fact that Coq and Lean have their own pages is some indication that this is sufficiently notable? Eric Wieser (talk) 17:51, 2 December 2023 (UTC)
 * If this has never been mentioned anywhere in a published paper or any secondary source, is it really that essential to the topic of division by zero in general? –jacobolus (t) 18:09, 2 December 2023 (UTC)
 * It seems just as relevant as mentioning the behavior of the Desmos graphing calculator, which is mentioned immediately above the proposed insertion point, without any references at all. If the problem is references to blog posts, would removing all references other than those to other Wikipedia pages (to match the Desmos example) suffice? Eric Wieser (talk) 20:31, 2 December 2023 (UTC)
 * It sounds like this section/article has become a magnet for un-encyclopedic trivia. The behavior of the Desmos graphing calculator certainly doesn't seem necessary here with or without a source. –jacobolus (t) 20:50, 2 December 2023 (UTC)
 * I split the section into floating point and integer subsections, and took out some of the trivia including the part about Desmos, which isn't about integer arithmetic at all. The rest of the section about integer arithmetic also needs sources. Material about proof systems probably belongs in a separate subsection, but it would be helpful to find a "reliable source" about it, not just documentation, code, or blog posts by the authors (though these could also be cited as a supplement). –jacobolus (t) 01:54, 3 December 2023 (UTC)
 * I think Buzzard's blog post is probably alright here, if we take a generous approach to "Self-published expert sources may be considered reliable when produced by an established expert on the subject matter, whose work in the relevant field has previously been published by reliable, independent publications". This blog post has been cited several other times, including e.g. in this peer-reviewed (but not yet published) paper https://pubs.rsc.org/en/content/articlepdf/2023/dd/d3dd00077j. It's perhaps worth having a fuller discussion of this topic, e.g. DJB criticizes Buzzard's claim here: https://cr.yp.to/papers/pwccp-20230909.pdf "in fact a mathematician is permitted to deduce b ≠ 0 from c = a/b, since a/b is undefined for b = 0. Redefining the notation to allow b = 0 breaks this. Unless it occurs to the author to state a conclusion c = a/b and a conclusion b ≠ 0, the proof assistant won’t check that b ≠ 0, whereas the reader will think that this has been checked."
 * There's some related material in Bergstra (2014) "Division by Zero and Abstract Data Types" and (2021) "Division by Zero in Logic and Computing", which cites Komori (1975) "Free algebras over all fields and pseudo-fields" and Ono (1983) "Equational theories and universal theories of fields". –jacobolus (t) 03:15, 3 December 2023 (UTC)
 * Thanks jacobulus. As for Buzzard's "work in the relevant field", I think his work formalizing perfectoid spaces is relevant, as well as his overview of schemes in Lean.
 * There is also a peer-reviewed source on n/0=0 here: https://arxiv.org/pdf/1506.04205.pdf, page 8. (Though that only says how it's defined, not why.) --Lambda Fairy (talk) 12:58, 19 January 2024 (UTC)
 * Do you want to take a crack at re-incorporating this topic? I think it's fine to cite Buzzard's blog post, but I don't think this should go in the "Computer arithmetic" section, but would probably be better to put into the "Alternative number systems" and/or "Higher mathematics" sections. –jacobolus (t) 15:12, 19 January 2024 (UTC)
 * Added it back, cheers!
 * Re placement: I think it does belong in "Computer arithmetic", actually, because IMO it's more an implementation detail than a fundamental change. Allowing n/0=0 does not change the overall "shape" of a proof; it merely shifts the proof obligations from the statement of a theorem to its body. The mainstream ring theory textbooks still apply. This is unlike e.g. replacing epsilon-delta limits with filters, which has much mathematical content, enough to fill a volume of Bourbaki.
 * Re DJB: I'm hesitant to include DJB's opinion alone—while his opinion is justified, it's not representative of the consensus among experts in proof assistants (who are largely supportive). --Lambda Fairy (talk) 12:46, 21 January 2024 (UTC)
 * Relatedly, regarding https://en.m.wikipedia.org/wiki/Special:MobileDiff/1197667226; Lean advertises itself both as a programming language and a proof assistant, so I'd weakly argue it does belong in this table. Eric Wieser (talk) 10:11, 22 January 2024 (UTC)
 * It's not about whether it technically satisfies some (made up) criteria; the question is whether including it there is on net helpful to readers, when we are already saying the same thing directly in the article text and when it's at least somewhat misleading to compare. (Frankly I think the table has questionable value and I'm considering entirely scrapping it.) –jacobolus (t) 16:19, 22 January 2024 (UTC)
 * @Eric Wieser I just took the table out altogether, and rewrote/reorganized the section a bit. What do you think? –jacobolus (t) 18:13, 22 January 2024 (UTC)

Research paper tag
the article reads like an academic paper or a teaching aid. it speaks to the reader as if the reader is a student. sections such as Elementary arithmetic epitomise this. The article needs to be rewritten to avoid being a research paper or a teaching aid as opposed to be encyclopedic. It should not posit that the reader considers examples. The Fallacies section goes into details of mathematical examples, which treats the section as an academic exercise instead of an encyclopedic article. PicturePerfect666 (talk) 17:56, 7 December 2023 (UTC)

To clear things up Wikipedia states as follows on what Wikipedia is not " [articles should not ] presented on the assumption that the reader is well-versed in the topic's field." the flede begtins as follows" "In mathematics, division by zero is division where the divisor (denominator) is 0|zero. Such a division can be formally expressed as, where $a$ is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by $0$, gives $a$ (assuming $a \neq 0$ ); thus, division by zero is undefined (a type of singularity). Since any number multiplied by zero is zero, the expression $\tfrac{0}{0}$ is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to $\tfrac{a}{0}$ is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst ('ghosts of departed quantities')." - directly from a maths teaching textbook or aid.

This is confusing and dense and challenging for the reader with limited initial knowledge of the topic to understand the subject of the article, hence it reads like something from academia. PicturePerfect666 (talk) 19:32, 7 December 2023 (UTC)

 * This article does not read like an academic paper, but like a (poorly written) encyclopedia article. The banner is not appropriate. It is entirely fine (indeed, extremely helpful) for encyclopedia articles to include concrete examples of abstract concepts and situations. If you would like to rewrite one or another section for style and clarity, please do so. –jacobolus (t) 18:09, 7 December 2023 (UTC)

 * I think a greater level of explanation as opposed to simply going the 'article does not read like an academic paper', is needed here. It is stated clearly by you that you believe this is a poor-quality article. Just stating that it is a poor quality is unhelpful, expand on why. Also, the shifting of burden here is something to be avoided, if you believe it is a poor quality article be bold and improve it. I am not a mathematician and this reads to me someone outside the heft of mathematics as an academic paper. You can disagree with that but assume good faith. PicturePerfect666 (talk) 19:20, 7 December 2023 (UTC)

 * The banner is facially absurd. The article does not read remotely like a research paper.  PicturePerfect, quit trying to force this.  If you have specific examples of language that needs to be improved, feel free to bring them up, or even correct them. --Trovatore (talk) 18:22, 7 December 2023 (UTC)

 * The banner is not 'Factually absurd" and stating so misses the points raised. the article does to the person who added it (me) fully believes this is the feel of academic. If you have expert knowledge on this topic fine, but I have not got a clue how to get through the academic density here with complex mathematical examples and mathematical theory in the article. PicturePerfect666 (talk) 19:20, 7 December 2023 (UTC)
 * Note, "facially absurd" (not "factually") means self-evidently incorrect and therefore immediately dismissible.
 * The "complex mathematical examples" begin with the integral division of a pile of cookies, then proceed to nontechnical historical material, then some middle school level algebra manipulation, and then some high school level calculus. Eventually we hit some discussion of the topic as it applies to undergraduate level and beyond, and some discussion of the computer engineering aspects of the topic.
 * No part of any of these is written anything like a research paper, which is why several editors here think that is an inappropriate banner.
 * It is expected, and valuable, for Wikipedia articles to include relatively comprehensive coverage of a topic, even though some aspects of that coverage are only accessible to a relatively narrow audience (we should try to make them as broadly accessible as practical). Less-technical readers can easily skip past parts with advanced prerequisites, but more-technical readers often need to look up or find out about advanced material and Wikipedia is a fine place for it. –jacobolus (t) 20:10, 7 December 2023 (UTC)
 * it is not "self-evidently incorrect and therefore immediately dismissible" which assumes bad faith on your part.
 * The rest of what you have said after this is do not quite fathom as it appears to be a non-sequitur, and more personal comments, which are again not relevant and seem to be cherry-picking of sections which you believe make things accessible, but It could equally not be something which makes smoothing accessible. This is user bias on the part of the examples listed. PicturePerfect666 (talk) 21:27, 7 December 2023 (UTC)

 * No, the article doesn't read "like an academic paper". It has its problems, but that's not one of them. XOR'easter (talk) 18:36, 7 December 2023 (UTC)

 * Please explain how it does not do what you are stating it does not do, simply saying "it does not", does not address the concerns raised. also if the article has other problems please expand on them so this article can be improved, don't be secretive or shy about the problems you think the article has. PicturePerfect666 (talk) 19:20, 7 December 2023 (UTC)
 * I can't "address" concerns that make no sense. Read academic papers, and read this article; the experience is not the same. (On the flipside, if you don't have experience reading them, then don't say it resembles one.) XOR'easter (talk) 19:26, 7 December 2023 (UTC)
 * You have stated above "It has its problems" - what are these problems you have identified then? I cannot read your mind to know what they are unless you state what they are. PicturePerfect666 (talk) 19:28, 7 December 2023 (UTC)
 * I'm not sure why you're going for such a confrontational tone; that won't actually help anybody. The article is already tagged with needing citations on multiple specific places, which is more helpful than slapping banners across the top of it or griping here. XOR'easter (talk) 19:31, 7 December 2023 (UTC)

If you believe I am being confrontational that is not my intention here and not the tone being aimed for...but remember to assume good faith. If you think that I am not acting in good faith then please consider why you believe this and re-evaluate, as I can assure you my actions are exclusively in good faith. I am simply asking for you to state what your concerns with the article are. You have said you think the article has problems, yet won't state what these are, so no one else can attempt to improve the issue you see the article as having. I may have used direct language, but this is because you won't tell anyone what you see the issues with the article are. Please share what you think the issues with the article are. No one here can read your mind. — Preceding unsigned comment added by PicturePerfect666 (talk • contribs)
 * No one here can read yours. You opened this thread; it's on you to say what you mean. (I have already pointed to one obvious problem.) What exactly are you finding too difficult to understand? Remember, this topic will naturally have a gradation in difficulty: some aspects can be understood by schoolchildren, while others might not be encountered until university. Ideally, the opening sections should be more widely comprehensible than the more demanding ones that follow, while the paragraphs before the first section break need to summarize everything that follows. XOR'easter (talk) 19:42, 7 December 2023 (UTC)
 * Indeed, as best as I can follow, your complaints are self-contradictory. How is the article supposed to be more accessible "for the reader with limited initial knowledge of the topic" without giving basic examples to help such a reader? XOR'easter (talk) 19:48, 7 December 2023 (UTC)

 * I am going to disengage from the discussion with you as it has become circular. Others are making improvements to the article and you will not state the issues you think the article has. I have provided examples above as to the issues I have and this discussion with yourself and myself is no longer helpful to the improvement of the article in its current form. If you would like to continue discussions please do so by stating clearly the issues you have with the article as opposed to assuming bad faith on my part and essentially attacking the content I have [put above in a manner which is unconstructive. Also please refrain from patronising statements such as the following "This topic will naturally have a gradation in difficulty: some aspects can be understood by schoolchildren, while others might not be encountered until university" as it assumes the person you are discussing with is an idiot, which is an assumption of bad faith and potentially a personal attack. Please withdraw or reword that section. PicturePerfect666 (talk) 19:46, 7 December 2023 (UTC)
 * @PicturePerfect666 about half of this article has been substantially rewritten since your previous comments. Did that address your concerns? –jacobolus (t) 18:56, 22 January 2024 (UTC)

List of general references tag
The end of the article contains a simple list of "Sources" which are not referenced in the article. It is therefor challenging to know what these refer to specifically or how they can be scrutinised as verifiable or simply padding. This needs to be updated and improved. PicturePerfect666 (talk) 18:03, 7 December 2023 (UTC)

 * Please feel free to read the article and hunt for sources about each section and/or read the provided sources to figure out which specific part each one discusses. If you are not willing to do that, then just pasting an eyesore banner that says "someone else please fix this for me" is not accomplishing anything except distracting and annoying readers. –jacobolus (t) 18:08, 7 December 2023 (UTC)

 * Not being a mathematician, this is like asking a Chinese Person who has never encountered Arabic or English to translate into English the Qur'an. Not everyone has the technical expertise to wade through the density of mathematics in this article. This is a very technical and dense topic and one I am not even remotely qualified at being able to decipher here on this platform or wade through even denser published research papers. PicturePerfect666 (talk) 19:24, 7 December 2023 (UTC)
 * Why would a Chinese person be trying to tell English speakers that they need a big disclaimer about the poor quality of the English translations of the Qur'an? To the extent this were really true that this article was totally over your head and conceptually impossible for you to make any sense of, you should probably go work on some other one and leave it to experts.
 * But frankly this is a misleading analogy. The most important parts of this article needing the most improvement are or should be accessible at a high school level, and are related to mathematical history, pedagogy, philosophy, and the most basic structures taught to schoolchildren and ultimately very formally specified in introductory courses for undergraduate students requiring no special prerequisites. You could certainly read and follow many relevant sources, and you shouldn't declare yourself a priori incapable of understanding them. –jacobolus (t) 19:54, 7 December 2023 (UTC)
 * The analogy is to describe the difficulty of understanding the complexities in this article. It is an analogy not something to be taken literally. Please also stop going on about education levels it is not relevant to the discussion. i have also not  "declare yourself a priori incapable of understanding". i have simply said it assumes a lot of knowledge as opposed to be accessible from the ground up. Wikipedia article shroud not rely on users going to complex and dense academic papers or specialist resources to understand an article. This is what I am saying this is not an article for mathematicians, it is a general access encyclopedia article. It also assumes that all mathematics globally is taught in the same way, which is a centric-view of wherever the person asserting the claim of this is at this level and this at this level etc. A form of unconscious bias if you will.  Please stop making assumptions as this is not benefiting the clarity or understandability of the article. PicturePerfect666 (talk) 21:23, 7 December 2023 (UTC)
 * Wikipedia [articles should] not rely on users going to complex and dense academic papers or specialist resources to understand [them]. This particular article doesn't require familiarity with "dense academic papers" to follow, though some sections assume familiarity with introductory textbook material about various topics, some of which are relatively advanced. But even if it did, Wikipedia articles should cover their subject reasonably comprehensively, including advanced material, while staying as accessible as practical in each section. Sometimes arcane and difficult prerequisites are necessary; we can't include the multiple years' worth of technical coursework in the middle of every article which would be necessary to make every part completely accessible to a lay audience. What we can do is cover the lay-accessible parts of the subject as clearly and completely as we can, organize them toward the top of the article if possible, and then strive to make more advanced parts accessible to the broadest audience we can without going excessively off topic to do so. –jacobolus (t) 23:43, 7 December 2023 (UTC)

Lead section
I'm trying to rewrite the lead section for clarity, but I don't think I've done an amazing job so far. Does anyone want to take another crack at it, or maybe polish up some of my sentences? For example, can someone improve this vague sentence I wrote without making it too long or technical? "When a real function involves division by a quantity that can become zero for some values, that is a type of singularity." @XOR'easter? –jacobolus (t) 19:47, 7 December 2023 (UTC)

 * Is that sentence necessary? I don't think the body text follows up on it in any serious way (unlike the concept of a limit in the next sentence). XOR'easter (talk) 20:03, 7 December 2023 (UTC)
 * Similarly, I think we should try to get the historical coverage right in the main text and then do a summary in the lead, rather than polishing lines in the lead that aren't elaborated upon later. XOR'easter (talk) 20:10, 7 December 2023 (UTC)
 * I like discussing the limit of $$1/x$$ in the intro before bringing up indeterminate forms. XOR'easter (talk) 21:03, 7 December 2023 (UTC)

"Analysis" section
I think this section would be better titled something like "other number systems", since the focus is the extended real numbers and the projectively extended real numbers, and the material about Wheel theory could be moved there.

It should IMO be preceded by a section (perhaps titled "Calculus") discussing the treatment in calculus and real analysis of the limits of functions with real numbers as the domain/codomain, where infinity is often treated as a limit but not a number per se. This section would discuss infinite singularities, and possibly contrast them with other kinds of singularities, and would then include material about indeterminate forms and L'Hospital's rule.

It might be worth adding a section about complex analysis and the idea of zeros and poles and meromorphic functions. –jacobolus (t) 23:20, 7 December 2023 (UTC)

 * I think "Calculus" is a more illuminating section heading than "Analysis". The former refers to a specific math subject (and even people who haven't studied it have heard of it as a math thing), whereas the latter has a general meaning of "thinking about" that could be confusing in this case. XOR'easter (talk) 00:12, 8 December 2023 (UTC)

Riemann sphere para
In regards to Jacobulus's edits, latest here: This article is about division by zero. Therefore acknowledgment that there is sometimes such a thing as division by zero should not be deferred to the fourth paragraph. I am also not sure why Jacobulus preferred to speak of the projectively extended real line rather than the more-used Riemann sphere (when the real line is extended it is more common to add a +∞ and a −∞, which doesn't allow division by zero because it isn't clear which one to pick). --Trovatore (talk) 00:22, 8 December 2023 (UTC)

 * (As an aside, the "Riemann sphere" is a confusing name to use for the extended complex numbers, and in my opinion extended complex numbers and Riemann sphere should be split into two separate articles, since the former number system is also commonly used to model flat and hyperbolic phenomena, not only spherical ones. But that discussion is off topic here.) The reason I think the projectively extended real numbers rather than extended complex numbers should be used as an example in the lead section here is that they are simpler, approximately as widespread, easier to draw pictures of, and don't involve as many conceptual prerequisites to make sense of. I absolutely think we should discuss both the affinely extended real numbers, the projectively extended real numbers, and the extended complex plane in this article about division by zero, along with a more extensive discussion of which types of geometric phenomena and other more abstract situations they are each good models for. (As another aside: there is also a reasonable complex analog of the affinely extended real numbers: the complex logarithm should arguably have the extended complex numbers as its domain, and a complex cylinder as a codomain, where $$\log(\infty) = +\infty$$ and $$\log(0) = -\infty,$$ two distinct values at opposite infinite ends of the real axis.) –jacobolus (t) 00:40, 8 December 2023 (UTC)
 * Confusing or not, I'm pretty sure Riemann sphere is the usual name. The reason to call it a "sphere" is that the structure itself is topologically a sphere, not that you'd apply it on a sphere.  I really don't think the one-point compactification of the reals is nearly as used (or useful).
 * In any case I don't think this material should be pushed so far down. --Trovatore (talk) 00:46, 8 December 2023 (UTC)
 * It's called the "Riemann sphere" because stereographic projection provides a bidirectional link between spherical geometry and complex analysis. For example it is common to adopt chord length or arc length on the sphere as an alternative metric for measuring distance between complex numbers, or in the other direction to use complex numbers and their arithmetic as a representation of points on the sphere so that the geometry of spherical objects can be treated numerically. The topological aspect is only one part of that.
 * don't think the one-point compactification of the reals is nearly as used it is used ubiquitously throughout most areas of mathematics and applications to science and engineering, but as a quirk of history is unfortunately rarely explained in a clear or systematic way. –jacobolus (t) 00:55, 8 December 2023 (UTC)
 * Hmm, I think you have an origin story for the name that I have never heard. It's shaped like a sphere; that's a good enough reason to call it a sphere, without needing to make any detailed connection to spherical geometry.
 * I'd need to see examples for your claim about the one-point compactification. Usually when you're working in the reals you know whether things are positive or negative.  (In fact the structure [0, +∞], which is fundamental to measure theory, is in my experience more useful than the "projectively extended reals"; unfortunately it doesn't seem to have a snappy name.) --Trovatore (talk) 01:01, 8 December 2023 (UTC)
 * shaped like a sphere – yes, exactly, it's shaped like a sphere. For example, the natural setting for "Möbius transformations" (which, contra Wikipedia's article, should fundamentally be defined geometrically, as general transformations generated by reflections and circle inversions) is the "inversive plane" a.k.a. Möbius plane, which can be naturally modeled either by the Euclidean plane with a single extra point at infinity or by the 2-sphere; as it happens the inversive geometry of these, because all of the relevant relationships are preserved by the stereographic projection, is the same. If we want to represent Möbius transformations numerically, one natural representation is using complex numbers.
 * I'd need to see examples for your claim For example, any time you see the trigonometric tangent function (or in general the slope of a geometric line) you are properly dealing with the projectively extended real numbers, which is the natural codomain there. –jacobolus (t) 04:05, 8 December 2023 (UTC)
 * About the ordering: I think it's clearer to roughly order the article (and the lead) in an order from less to more advanced material, which means talking about the conventional number system taught to every high school student first, including its appearance in introductory calculus, and then talk about relatively niche alternative number systems not seen until the middle of an undergraduate pure math degree until after that. I also was aiming to make the lead section as legible and jargon-free as I could. Maybe this paragraph could be rephrased to make the alternative number systems seem more important or to explicitly mention more of them though. –jacobolus (t) 00:46, 8 December 2023 (UTC)
 * @Trovatore: Maybe it would be clearer for this paragraph to lead with something like, "As an alternative to the convention of leaving division by zero undefined, ...". –jacobolus (t) 09:22, 9 December 2023 (UTC)
 * Just looked at this again, and I still think it's entirely unacceptable to defer discussion of when division by zero makes sense to the fourth paragraph. I hope we can come to an agreement here. --Trovatore (talk) 17:20, 5 January 2024 (UTC)
 * Do you have a concrete idea for how the lead should go? Feel free to paste a draft in here, in a subpage of this talk page, in user space, or the like. (Or, as always, boldly edit the article.)
 * The reason I think this is fine is because division by zero is typically treated as undefined / nonsensical in most of mathematics (and pretty much universally at the high school / early undergraduate level), and it's worth being clear about that in this article and its lead. I would not expect readers to be confused or misled by the current text. [I'm not against division by zero. The projective real numbers are one of my main mathematical interests.] –jacobolus (t) 19:47, 5 January 2024 (UTC)
 * I think the ordering of the lead is pretty much fine as it stands now, on the general philosophy that stuff one doesn't see until the later years of a math major can wait until after the basic arithmetic. XOR'easter (talk) 21:18, 5 January 2024 (UTC)
 * I still think the structures in which the topic of the article makes sense are not prominent enough. It might be a solution to expand the first paragraph with a sentence that says that in the most usual contexts, the expression is undefined, but that contexts in which it makes sense do exist.  Then we can elaborate later in the lead section.  --Trovatore (talk) 21:29, 5 January 2024 (UTC)
 * Can you make a concrete proposal? I was trying to do more or less what you are suggesting, but at a bigger scale: start with describing why division by zero is considered undefined for real numbers, then later discuss alternative structures where it is defined, and then elaborate on that further down the article. –jacobolus (t) 21:49, 5 January 2024 (UTC)
 * One thing that might be helpful could be rewriting the "meaning of division" section for clarity, and expanding it to include other kinds of places where division (or ratio) is used, including those where a ratio like 1 : 0 can be meaningfully interpreted. –jacobolus (t) 21:53, 5 January 2024 (UTC)
 * I'm thinking something like adding two sentences to the end of the first para, so it reads something like:
 * "In mathematics, division by zero, division where the divisor (denominator) is 0|zero, is a unique and problematic special case. Using fraction notation, the general example can be written as $\tfrac a0$, where $a$ is the dividend (numerator). In ordinary arithmetic, for example on the real numbers, the result of this operation is undefined. However, there are other mathematical contexts in which division by zero is allowed."
 * Then we could probably trim some of the language in the second para as redundant. Later in the lead, I would prefer to speak explicitly of structures rather than just conventions, but that's a second-order point. --Trovatore (talk) 07:13, 6 January 2024 (UTC)
 * I think a turnabout in the very first paragraph would confuse more people than it would help. XOR'easter (talk) 15:40, 6 January 2024 (UTC)
 * Not sure what you mean by a "turnabout". I think it is essential to acknowledge in the first paragraph that the topic of hte article does sometimes make sense. --Trovatore (talk) 20:30, 6 January 2024 (UTC)
 * @Trovatore nearly every mathematics source aimed at laypeople or students for the past ~100 years says something like "in mathematics, division by zero is not allowed, because it leads to absurdities". It's potentially more confusing if we lead by saying "In mathematics, division by zero is sometimes not allowed, but sometimes it is". –jacobolus (t) 20:38, 6 January 2024 (UTC)
 * That's just going to confound people who have barely grasped the real numbers and never gone beyond that, i.e., most people who are looking up the topic of "division by zero". XOR'easter (talk) 20:38, 6 January 2024 (UTC)
 * This sounds like you're trying to make things easier for middle-school math teachers. That's not what we do.  We don't tell lies to children.  The first paragraph should give a fair top-level summary of the whole situation. --Trovatore (talk) 20:43, 6 January 2024 (UTC)
 * First, making life easier for middle-school math teachers is a good idea. Heaven knows they've got it hard enough. Second, it's not a "lie to children" to hold off on the projective real line and the Riemann sphere until the fourth paragraph. XOR'easter (talk) 21:26, 6 January 2024 (UTC)
 * It's something like a "lie to children by omission" if you let people read the first para or two and come away with the impression "you just can't divide by zero, period", because that's just not true.
 * As for the teachers, sure, they do a hard job and should be valued for it, but it sounds like you're worried about a scenario where Jenny raises her hand and says, "Mr. Simmons, you told us you can't divide by zero, but I looked it up in Wikipedia and it says sometimes you can, and now I'm confused".
 * Well, that's productive confusion. It's not our job to try to blunt the confusing nature of reality for the benefit of learners.  Maybe Jenny will be bothered enough by it that she'll go and learn something on her own.  Or maybe not; either way it shouldn't affect our writing.  We should summarize the whole picture early in the article, while leaving the details for later. --Trovatore (talk) 21:41, 6 January 2024 (UTC)
 * If someone can't be bothered to read a few short paragraphs, I can't see how a vague half-sentence is going to help them come to a better understanding. –jacobolus (t) 21:42, 6 January 2024 (UTC)
 * My objection is that the omission reinforces the false claim, which as you note is standardly taught to youngsters, that division by zero is never allowed. --Trovatore (talk) 21:45, 6 January 2024 (UTC)
 * From what I can tell the current lead section doesn't make any false claims. It just first discusses arithmetic of fields, and then later discusses alternative arithmetics. –jacobolus (t) 21:49, 6 January 2024 (UTC)
 * That's why I said "by omission". Lies by omission aren't technically lies at all, but we still should want to avoid them. --Trovatore (talk) 21:51, 6 January 2024 (UTC)
 * Nothing's being omitted. It's just being organized in a way that's probably somewhat better for the most likely audience. XOR'easter (talk) 21:58, 6 January 2024 (UTC)
 * It's not better if they can come away thinking division by zero is never allowed. --Trovatore (talk) 21:59, 6 January 2024 (UTC)
 * One reason I think it's okay to hold off is that arguably treating projective quantities as representing "division" per se is already an abuse. Really the desired concept here is ratio, and what we want is a ratio 1:0, not a "number" ∞, but division has been shoehorned in because modern mathematics has all but done away with ratio as a separate concept, especially at the high school / undergraduate level, instead putting all its eggs in the "real numbers" basket. This streamlining is a trade-off: fewer overlapping abstractions, but not quite so well tailored to the specific circumstance. –jacobolus (t) 21:41, 6 January 2024 (UTC)
 * I mean, that's a possible perspective; I'd have to think about it more. In any case the sources do call it division. --Trovatore (talk) 21:47, 6 January 2024 (UTC)
 * @Trovatore I added a bit about slopes of lines in the "meaning of division" section. Does that help at all? –jacobolus (t) 20:36, 8 January 2024 (UTC)
 * Not for the point I'm trying to get at, which is that the possibility of division by zero making sense should be addressed early in the lead. --Trovatore (talk) 20:40, 8 January 2024 (UTC)

Overlooked proof
Let imagine a graph (1/x) is divided into 2 halves where the negative half is x<0 and the positive half is x>0. The primary proof against 1/0 being a defined value is that the two halves directly contradict one another (negative half shows -∞ but positive half shows ∞) so it must be an undefined value right? No, so lets change our way of thinking. We will be adding a new rule which states: "Any division that might return a negative result shall be written in a way in which a negative number will never be dividing another or divided against.". Since this only applies to HOW we write down or calculate the equations, this does not change anything ((wrong) 2÷-5 = -0.4 --> (correct) -(2÷5) = -0.4). By applying the rule, we would never actually divide by the negatives which completely removes the negative half. This will leave only the positive half with nothing contradicting it, which could only mean x/0 = ∞.

I don't study math like a mathematician but this is easy. I need yall to say im wrong rn holy moly. Also the rules are made ambiguous, think of the best case scenario of my explanation as the primary one. SussusMongus (talk) 04:52, 16 December 2023 (UTC)

 * It's not "wrong" per se. You are welcome to define your own new number system that behaves however you want. It's just that most mathematicians and other technical professionals have settled on a few conventional choices of number system which were found to be the most convenient in the broadest class of existing uses, and your proposed system is not one of them. (Your number system is quite limiting in that you have to constantly check that you aren't dividing by negative numbers, which is even more burdensome than checking to not divide by zero, and there are many kinds of algebraic manipulation that have the potential to introduce illegal divisions which you will have to either disallow or be very careful about. Many of the most convenient and useful tools of algebra are going to be made much more troublesome, if they aren't entirely broken.)
 * I'd recommend you take this kind of question to Reference desk/Mathematics, since it's not really about improving this article per se. –jacobolus (t) 05:05, 16 December 2023 (UTC)
 * I am going to reply since i already posted this and the rule actually NEVER specified about when you check, you just need to know that before you actually divide it. If it's a variable then just look if it have a sign. Afterall, the variable itself might be negative but the value might NOT be negative (or vise-versa) and the rule never specified any of that. This reply is the primary example of why I left the phrase "The rules are made ambiguous" there (i knew my initial post isnt going to be accurate at conveying what i literally meant, especially the little details). SussusMongus (talk) 06:28, 19 December 2023 (UTC)

Note: SussusMongus copied this discussion over to Reference_desk/Mathematics. Seems fine to let the conversation live over there.–jacobolus (t) 07:26, 19 December 2023 (UTC)

0/0 = 0
if a/b=c then cb=a, right? then, 0/0=0 as 0*0=0. anyone find any sources for this?49.37.202.122 (talk) 16:07, 5 January 2024 (UTC)

 * I realise my mistake. 0/0 is 0, 1, i, and every number. 49.37.202.122 (talk) 16:14, 5 January 2024 (UTC)
 * going from cb = a to a/b = c is only valid if b<>0. Dhrm77 (talk) 16:15, 5 January 2024 (UTC)

rewritten "meaning of division" section
I split this section up and rewrote the first part (the second half, now titled 'Inverse of multiplication') still needs a rewrite). Does it make sense to folks? This kind of informal discussion about concrete interpretations of division and the way zero might fit in seems valuable to me to include up front, but I'm just one person here. Hopefully it doesn't seem like belaboring the point or getting to far into the weeds. I'll try to find and insert a few relevant reliable sources if I can. –jacobolus (t) 01:41, 7 January 2024 (UTC)

 * @XOR'easter (or anyone else reading along) do you mind giving the first half of this article another once-over? I tried to add some more accessible examples and informal discussion, but I can't promise it makes more sense to anyone other than myself. –jacobolus (t) 01:40, 10 January 2024 (UTC)
 * Looks OK to me. XOR'easter (talk) 03:23, 10 January 2024 (UTC)

A reason why "Division is the inverse of multiplication" is an incorrect sentence
Multiplication of two real numbers $$x$$ and $$y$$ is a function $$f:\R^2\to\R$$. Does it have the inverse? No, because it's not a bijection.

That being said, we can define a function, say, $$f(x)=2x$$, which is a bijective function $$f:\R\to\R$$ and thus it has the inverse $$f^{-1}(x)=\frac{x}{2}$$, but the function $$f(x)=2x$$ is not a multiplication (of two numbers), it's a multiplication by a specific number.

I hope this explains why we can't say "Division is the inverse of multiplication", because this sentence doesn't specify the specific number. For example, we could say something like this: "Division by 2 is the inverse of multiplication by 2", but I haven't seen such usage (it's much simpler just to write the function in such cases). — Preceding unsigned comment added by Robertas.Vilkas (talk • contribs) 21:35, 24 February 2024 (UTC)

 * The word "inverse" in this context is not being used to mean the same as "inverse function". Calling division the "inverse operation" as multiplication is widely accepted by reliable sources, including by mathematicians, scientists, schoolteachers, mathematics education researchers, etc. If anyone cared enough the term could be precisely formally defined. I think it's fine to just use the plain-English meaning; no claims here depend particularly strongly on making the term's definition precise. Edit: however, I added a quick inline definition. –jacobolus (t) 22:17, 24 February 2024 (UTC)

 * Division is the inverse of multiplication in the same way that subtraction is the inverse of addition. This language is standard. Rick Norwood (talk) 11:01, 25 February 2024 (UTC)

 * Pretty standard indeed:
 * {| class="wikitable" style="text-align: center"

! Google !! Scholar !! Books
 * division "inverse of multiplication"
 * 1250
 * 8990
 * }
 * - DVdm (talk) 11:38, 25 February 2024 (UTC)
 * - DVdm (talk) 11:38, 25 February 2024 (UTC)

Calculus paragraph
I am hoping someone can fix the following issues in the intro paragraph starting with "Calculus":

It's not correct that a positive ratio of functions whose denominator tends to 0 tends to infinity, because the numerator could be going to 0 faster.

There is no reason to require a "positive fraction". (It would even be OK for it to be complex; one just needs the denominator to be nonzero in a punctured neighborhood. Can someone figure out a nice way to say this without getting bogged down in details?)

We should avoid conflating "becoming arbitrarily large" and "tending to infinity". The function sin(1/x)/x as x approaches 0 becomes arbitrarily large but does not tend to infinity.

It is 0/0 that is the indeterminate form, not the quotient of functions. So the last sentence of the paragraph needs to be rewritten. Ebony Jackson (talk) 21:31, 9 March 2024 (UTC)

 * @Ebony Jackson I don't think it's all that important to make these two sentences completely airtight as far as exact correctness is concerned. We're just trying to introduce the subject, not make a full formal specification. It's probably fine to also cut the note about sign expressing $f(x) \to \pm \infty$ as $$x \to c$$ as "tends to infinity" (we can leave "from the right" in the image caption). I think it's entirely fine to conflate this with "arbitrarily large", since we are talking in an informal loose way here. Likewise, specifying that the numerator can't tend to zero is wordier and more confusing (than just not mentioning the numerator) without really much benefit in my opinion. We can be more precise in the dedicated section below. I don't think there's any advantage in mentioning complex numbers in this paragraph. –jacobolus (t) 22:42, 9 March 2024 (UTC)
 * If you want to try to add a caveat in about limits of fractions with functions in the denominator which tend to zero but whose sign continues to oscillate even in arbitrarily small intervals, so that in the affinely extended real numbers there is no well defined limit, that would be fine with me, though also doesn't seem totally necessary; I'm generally not that excited about pedantically emphasizing the most unusual obscure counterexamples, though I know some mathematicians really enjoy it. I expect anyone who is curious about this is going to be able to find their way to e.g. essential singularity. –jacobolus (t) 22:50, 9 March 2024 (UTC)

 * The second sentence of the paragraph currently claims, for example, that $$\frac{x^2-4}{x-2}$$ tends to infinity as $$x \to 2$$. Surely we would want to correct this?  This is not some obscure counterexample!  WP:PROVEIT requires an inline citation to a reliable source for questionable statements, whether or not they are in the lead, and we're not going to find a reliable source supporting false statements like this. Ebony Jackson (talk) 04:26, 10 March 2024 (UTC)
 * It emphatically does not currently claim that. That is an aggressively pedantic intentional misreading. (There's even a clarification about precisely this case in the immediately following sentence!) –jacobolus (t) 04:47, 10 March 2024 (UTC)
 * Hi, sorry that we don't seem to be understanding each other yet. Just to make sure we are talking about the same sentence: I am referring to
 * "When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to tend to infinity, a type of mathematical singularity."
 * Are you arguing that it would be unreasonable for a reader to think that the hypothesis
 * "When a real function can be expressed as a fraction whose denominator tends to zero"
 * applies to a function such as $$\frac{\sin x}{x}$$ as $$x \to 0$$ (to give another example)?

 * I do see that two sentences later, there is a separate statement about a quotient of functions both tending to zero, but as written it doesn't seem clear that it is meant to restrict the applicability of the earlier statement above. Ebony Jackson (talk) 08:44, 10 March 2024 (UTC)
 * No, I am arguing that: (a) The immediately following sentence which you keep cutting out of your quotation/discussion directly clarifies this point. Here's the whole paragraph in its current form:
 * Calculus studies the behavior of functions in the limit as their input tends to some value. When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to "tend to infinity", a type of mathematical singularity. For example, the reciprocal function, $$f(x) = \tfrac 1x,$$ tends to infinity as $$x$$ tends to $$0.$$ The quotient of two functions which both tend to zero at the same input is called an indeterminate form, as the resulting behavior depends on which functions are being considered.
 * Maybe the last sentence could be reworded to more closely parallel the first though, e.g. "If both the numerator and denominator of the fraction tend to zero at the same input, ..."
 * I am also arguing that (b) making a fully precise statement here is going to be awkward and excessively detailed for the context of this lead-section summary, and readers trying to understand what this sentence means are entirely capable of looking a few sections down to a (hopefully) clearer and more precise description in the relevant topical section. Your replacement version wasn't in my opinion appropriate to the full intended range of the audience of this article, which could plausibly include e.g. middle school students. –jacobolus (t) 16:31, 10 March 2024 (UTC)
 * I've reworded this to:
 * Calculus studies the behavior of functions in the limit as their input tends to some value. When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to "tend to infinity", a type of mathematical singularity. For example, the reciprocal function, $$f(x) = \tfrac 1x,$$ tends to infinity as $$x$$ tends to $$0.$$ When both the numerator and the denominator tend to zero at the same input, the expression is said to take an indeterminate form, as the resulting limit depends on the specific functions forming the fraction and cannot be determined from their separate limits.
 * Is that any better? –jacobolus (t) 19:40, 10 March 2024 (UTC)

Seems to be an error.
In the "Elementary arithmetic" section; "The meaning of division" - there is, and I quote: "Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle 1:0}" - I suppose a mathematical function was put there, but has failed for reasons beyond my comprehension. I hope someone may be able to fix it? Or was it only on my browser? I used two browsers and both showed this error.

Althuios (talk) 14:58, 29 April 2024 (UTC)

 * These errors are transient, and there's nothing editors can really do about them. –jacobolus (t) 15:15, 29 April 2024 (UTC)

title: Talk:Division by zero


text:
Francis Bond Head

Sir Francis Bond Head, 1st Baronet KCH PC (1 January 1793 – 20 July 1875) was Lieutenant-Governor of Upper Canada during the rebellion of 1837.

Biography
Head was an officer in the corps of Royal Engineers of the British Army from 1811 to 1825; as such he earned a Waterloo Medal. Afterwards, he attempted to set up a mining company in Argentina. Head rode between Buenos Aires and the Andes twice, from which he was given the nickname "Galloping Head".

Head was born to parents, James Roper Mendes Head and Frances Anne Burgess. He was descended from the Spanish Jew Fernando Mendes, who accompanied as her personal physician Catherine of Braganza in 1662 when she came to England to marry Charles II. His grandfather Moses Mendes married Anna Gabriella Head and took on the Head name following the death of his wife's father, Sir Francis Head, 4th Bt. He married Julia Valenza Somerville in 1816, and they eventually had four children.

King William IV knighted him in 1831 after he demonstrated the military usefulness of the lasso. In 1834, Head was appointed as an assistant Poor Law Commissioner in Kent. While serving in this capacity, he drew up a document called Plan of a Rural Workhouse for 500 Persons, which established separate areas for males and females but mingled sick and well, young and old, sane and insane. He argued that provisions for the poor should not be superior to those earned by the independent labourer. The rooms, for example, were to hold eight residents in a 15' x 10' space, and the diet was to be strictly for subsistence, resulting in the kind of gruel portrayed in the workhouse scenes of Oliver Twist by Charles Dickens.

Head was appointed Lieutenant-Governor of Upper Canada in 1835 in an attempt by the British government to appease the reformers in the colony, such as William Lyon Mackenzie, who wanted responsible government. He appointed reformer Robert Baldwin to the Executive Council, but that appointment was opposed by the more radical Mackenzie. In any case, he ignored Baldwin's advice, and Baldwin resigned; the Legislative Assembly of the 12th Parliament of Upper Canada then refused to pass any money bills and so Head dissolved the government. In the subsequent election campaign, he appealed to the United Empire Loyalists of the colony, proclaiming that the reformers were advocating American republicanism. The Conservative party, led by the wealthy landowners known as the "Family Compact", won the election to the 13th Parliament of Upper Canada.

In December 1837, Mackenzie led a brief and bungled rebellion in Toronto. Sir Francis Bond Head later boasted that despite the evidence that poured in from every district in the province, he allowed Mackenzie to prepare a revolt. He further claimed that he encouraged the outbreak by sending all the troops from the province, laying a trap for Mackenzie, despite there being no troops, and the York Militia had been preparing for an attack. Head sent the colonial militia to put down the rebellion, which they did within four days. In response to the rebellion, Britain replaced Head as Lieutenant-Governor with Sir George Arthur and then Lord Durham. Head returned to England and settled down to write books and essays.

In later life Head lived at Duppas Hall, overlooking Duppas Hill in Croydon, where he organised protests against the proposed outlawing of horse-riding in the area. He was appointed to the Privy Council in 1867.

Legacy
Several places in Ontario are named for Sir Francis Bond Head:
 * Bond Head, an unincorporated area northwest of Toronto in the town of Bradford West Gwillimbury, Simcoe County
 * Bond Head, a cape on Lake Ontario in the municipality of Clarington, Regional Municipality of Durham, to the east of Toronto, which gives its name to the adjacent settlement of Bond Head, and a local park west of the cape and east of the Port of Newcastle harbour.
 * Three streets in the town of Oakville, Ontario named Francis, Bond, and Head. (Only Bond and Head remain.)
 * Two streets in the city of St. Catharines, Ontario named 'Bond' and 'Head'. Though both streets are short, they intersect.
 * The community of Frankford, on the Trent River, was named after Head after he crossed the river there while travelling.

Works

 * Life of Bruce (London, 1830), a biography of Scottish traveler James Bruce
 * Bruce, James, Travels (1830), an abridged version of the 1790 work, edited by F. Bond Head.
 * Head, Francis Bond. (1826). Rough Notes Taken during some Rapid Journeys across the Pampas and among the Andes. Murray (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00161-8)
 * "Bubbles from the Brunnens of Nassau, by an Old Man" (1834), travel in Germany
 * Head, Francis Bond. (1846). The Emigrant. London: John Murray.
 * Head, Francis B[ond]. (1852). A Fortnight in Ireland.
 * ''The Defenceless State of Great Burray, 1869.

title: Francis Bond Head


text:
Balkan Bulgarian Airlines

Balkan Bulgarian Airlines (Балкан) was Bulgaria's government-owned flag carrier airline between 1947 and 2002. During the 1970s, the airline became a significant European carrier. The company encountered financial instability following the fall of communism in Central and Eastern Europe. Despite managing to continue operations, following the start of the 21st century and a controversial privatisation, it declared bankruptcy in 2002. Balkan was liquidated in late October 2002. Bulgaria Air was appointed Balkan's successor in December 2002.

Early years
Bulgaria had a short-lived airline (Bunavad) in 1927, yet the country could not afford investing in modern air transport until after World War II. In 1946, the Ministry of Transport and Communications formed an Administration of Air Communications (Дирекция на въздушните съобщения (ДВС), Direkcia na vazdushnite saobshtenia (DVS)). Since Bulgaria was regarded as a combatant on the defeated Axis side, the DVS could only contract with France for the supply of several Atelier d'Avions Coulombe Toucan aircraft (French-built versions of the Junkers Ju 52). In interpretation of their delivery, Bulgarian airmen practised by flying the nation's first long-distance flights: to Paris, transporting government officials to peace negotiations, being conducted there. These flights used German-built Ju 52 aircraft (Bulgarian service designation Сова or Sova, = Owl), delivered before the war to the На Негово Величество Въздушни войски [НВВВ] or His majesty's Air Force, and captured during the war from retreating German forces.

DVS officially launched services under the Bulgarian Air Lines (Български въздушни линии, Balgarski vazdushni linii) name on 29 June 1947 with a Ju 52 flight from Sofia via Plovdiv to Burgas. Other services soon followed. By the close of the year, the DVS had ordered several Soviet-built Lisunov Li-2 variants of the Douglas DC-3 and at least 13 were operated until 1968. The Soviet forces stationed in Bulgaria took interest in DVS, and by late 1947, had taken DVS into joint ownership, as had been done with all airlines of East-European countries formerly allied with Nazi Germany. The resulting airline was called TABSO (ТАБСО), an acronym for "Transportno-aviacionno balgaro-savetsko obedinenie" (Транспортно-авиационно българо-съветско обединение, Bulgarian-Soviet Transport Aviation Corporation). The Ju 52s gradually phased out from service as TABSO re-equipped with Li-2s. These more modern planes allowed the airline to expand services.

The 1950s and 1960s
Soviet equity in TABSO was reacquired by the Bulgarian government in 1954. The airline with this brand name survived until the end of 1967, often in the shadow of the headline phrase Bulgarian Air Transport. In 1956, TABSO bought its first Ilyushin Il-14 aircraft. These aircraft, along with Li-2s, were deployed on services to seven domestic destinations, including Burgas, Gorna Oryahovitsa, Ruschuk, Plovdiv, Sofia, Stara Zagora and Varna; and international destinations Amsterdam, Athens, Beirut, Belgrade, Berlin, Bucharest, Budapest, Damascus, Frankfurt, Kiev, Moscow, Odessa, Prague, Vienna and Warsaw.

In 1962, it began services with the Ilyushin Il-18; these and the expansion of Bulgaria's inclusive-tour tourism industry began to put the airline's name on the European and world map. The turboprop type crossed the Equator to Kenya and the Atlantic to Peru. By 1967, Antonov An-24s had arrived for domestic and regional flights. By the mid-1960s, tourism was a major hard currency earner for Bulgaria and TABSO faced home-grown competition. Executives of the Teksim trading company had decided to start their own aviation business which included crop-spraying and inclusive-tour charter airline operations under the name of Булер (Bulair). Despite trying to buy Sud Aviation Caravelle jet airliners, Bulair ended up buying more Il-18s turboprops under heavy Soviet and Bulgarian political pressure. These were operated to several Western European countries to bring holiday makers to Bulgarian resorts.

The Teksim venture proved a success and a thorn in the side of TABSO. By 1967, TABSO had the inside track in government circles, and the Teksim operation was largely disbanded by 1970. Amid rumours of scandal and embezzling several Teksim directors were sent to jail, accused of performing capitalism-ruled economic behaviour. Their venture had operated under the TABSO banner for reasons of expediency (not least international rights). The last Bulair-branded aircraft had been rebranded as TABSO machines by 1972.

The carrier bought three Tupolev Tu-134 jets in late 1967. On 1 January 1968, TABSO was rebranded Balkan Bulgarian Airlines (Балкан – Български въздушни линии, Balkan – Bulgarski vazdushni linii). The wider commercial aviation scene was put under Balkan's control via subsidiaries such as the aforementioned Bulair, Селскостопанска авиация [ССА] or Selskostopanska aviacia [SSA] (the Agricultural Aviation Company) and a separate profit centre which performed ad hoc aviation contracting, mostly with helicopters.

The first Tu-134 was put into service in November 1968, initially flying scheduled services between Sofia and London. The airline became the first foreign customer of the type, leading to a close association with the Tupolev design bureau that lasted two decades. There were several reasons why Bulgaria was allowed to put a new Soviet type into service ahead of more important Soviet-bloc nations. Andrei Tupolev was President of the Soviet-Bulgarian Society. He had cemented personal links with his Bulgarian counterpart, formidable wartime Resistance figure and Politburo member Tsola Dragoycheva. She lobbied him for delivery preferences in return for campaigning before the Bulgarian authorities to buy his products rather than Western or other Soviet aircraft types. Indeed, Balkan never bought the Ilyushin Il-62 long-range airliner, preferring to misuse its Tu-154s for long-range work. Similarly, it eschewed Ilyushin's Il-86 wide-body despite arguably having the precise role for it on its sea or ski charter flights.

The 1970s
At March 1970, Balkan served countries in Africa, Asia and Europe plus  domestic destinations. At this time, the fleet included Antonov An-2s, An-10s and An-24Bs, Ilyushin Il-14s and Il-18s, Tupolev Tu-134s, Z-37 Cmelaks and Mil helicopters. Lazar Beloukhov was the general manager. On 18 January 1971, an Ilyushin Il-18 crashed and caught fire while attempting to land at Kloten Airport in fog; only two people survived the crash. During 1971, Balkan was the first airline beyond the USSR borders to operate the Tupolev Tu-134A. On 21 December, the crash of another Il-18 during takeoff left fatalities.

Again in 1972, this time with the Tupolev Tu-154, the carrier became the first foreign customer to incorporate a new Tupolev aircraft into its fleet. The latter type was deployed first on charter flights, and later on scheduled services. By 11 the same year, Balkan had two of these aircraft in service. It also launched non-Soviet use of the Tu-154A, Tu-154B, Tu-154B-2 and Tu-154M. Balkan was a useful test-bed for new ideas by the Tupolev bureau. The airline pioneered the use of three-person flightdeck crews on the Tu-154 by removing navigators (flight crew members whom the designers had intentionally inserted into the Tu-134 and Tu-154) between 1972 and 1976. Balkan also removed the Tu-154's concrete ballast trim on which conservative Tupolev engineers had insisted. In the mid-1980s, a team of Bulgarian engineers interlinked the automatic flight control systems of the airline's Tu-154s with OMEGA Navigation System receivers, enabling very accurate automatic long-range overwater navigation. In the 1990s, Balkan was among the first to fit GPS navigation to its Tu-154 fleet. A Tu-154B was flown non-stop from Montreal to Sofia, a distance of over 7000 km and a record for the type, during a charter flight.

As the Soviet-bloc economies gradually entered into stagnation in the 1970s, Balkan continued growing apace. In 1974, the airline's route network was 74500 mi long. By the mid/late 1970s, it was carrying three million passengers a year, more than any Soviet-bloc airline other than some Directorates of Aeroflot. The fleet comprised aforementioned types plus Antonov An-12s for cargo (since late 1969) and Yakovlev Yak-40 regional jets for short-haul routes (since 1974). The comprehensive route system covered Europe, North Africa and the Middle East. With the delivery of more Tu-154s, Balkan opened longer-range routes, including ones to Zimbabwe, Angola and Nigeria in sub-Equatorial Africa, and to Sri Lanka and Vietnam in Southern Asia.

The 1980s
In 1986, Balkan was restructured as part of a wholesale shakeup of the late Socialist economy in an attempt to make it more productive and manageable. The airline was divorced from functions such as running airports. It had suffered disastrous traffic falls after the Comecon fuel crisis of 1979, when the number of passengers carried collapsed to under a million. By the late 1980s, loads were back up to 1970s levels. Of the three million annual passengers, a third were carried on domestic services, another third on charter flights, and the remaining million on scheduled international routes.

Balkan joined the International Air Transport Association (IATA) in 1988, becoming its 175th member worldwide. On 10 November 1989, Bulgaria's long-ruling leader Todor Zhivkov was removed from power and Bulgaria began moving away from the Soviet bloc. Within a year, Balkan had been restructured yet again, with Hemus Air emerging from within it as a "second force" state-owned airline with mainly domestic and regional flights. Private airlines began to appear, most important among them Singapore-backed Jes Air which launched services to New York and Singapore using Airbus A310s.

The 1990s
By mid-1991, Balkan had leased two Boeing 767-200ERs from Air France to compete with failing Jes Air on North American and Southern Asian routes. At the same time Balkan acquired four Airbus A320s from Oryx. The Soviet-build types remained in service alongside the new arrivals.

The 1990s were a time of headlong decline at Balkan. The airline suffered in Bulgaria's transition to a market economy. Former managers of state-owned industry began forming private companies to supply the industries they had once managed (at high prices), and yet other private companies to purchase their production (at low prices). The aim was to control both supply and sales, charging high prices and paying low prices to strangle state companies and then privatise them at very low prices. The entire Bulgarian economy was in deep recession. This was due to severe political instability at home and protracted wars and economic sanctions in neighbouring Yugoslavia. These factors upset potential investment and tourism and cut off Bulgaria from many trading partners.

In March 1995, Balkan had a fleet of four Airbus A320-200s, three Antonov An-12Fs, fourteen Antonov An-24s, three Boeing 737-500s, two Boeing 767-200ERs, six Ilyushin Il-18s, five Tupolev Tu-134A-3s, fifteen Tupolev Tu-154B-2s and seven Tupolev Tu-154Ms. At this time, the company had 3,889 employees and the route network included 52 destinations. By 1998, Balkan's 767s returned to Air France and the A320s were passed on to other lessees. The Tu-154B fleet was overdue for replacement, and the Tu-154M was aging. Bulgaria's government appeared to pledge some funds for Airbus A310 acquisition so that long-range services could be sustained, but nothing came of this.

Late in 1998, the company was ready to be sold to a holding named Balkan Air, comprising Bulgarian and US investors, but the transaction was later suspended. All through the decade, there had been rumours of investor interest in Balkan. These rumours consistently named Russian and German airline interests which were said to be eager to buy the carrier. There was also lobbying by the airline's managers for a management buyout. Nevertheless, a consortium comprising two Israeli companies —the Zeevi investment group and Knafaim-Arkia (the owner of Arkia Israel Airlines) — was assigned a 75 percent stake in Balkan Bulgarian in mid-1999 for a bargain price of US$150000, with the commitment of investing US$100 million in the airline over the following ten years. Arkia left the consortium once title in the airline was transferred. It was disclosed in 2001 that Balkan had been declared bankrupt months prior to the sale.

2000 and beyond
Balkan had 3,889 employees at March 2000. At this time, the fleet included three Antonov An-12s; six Antonov An-24Bs and an An-24RV; two Boeing 737-300s and three 737-500s; an Ilyushin Il-18 and an Il-18D; three Let L 410 UVP-Es; and fourteen Tupolev Tu-154Bs and ten Tu-154Ms. These operated services to Abu Dhabi, Accra, Algiers, Amsterdam, Athens, Bahrain, Bangkok, Belgrade, Berlin, Bourgas, Brussels, Budapest, Cairo, Casablanca, Chisinau, Colombo, Copenhagen, Dubai, Frankfurt, Helsinki, Istanbul, Kyiv, Kuwait, Lagos, Larnaca, London, Madrid, Male, Malta, Milan, Moscow, Paris, Prague, Rome, Sofia, Stockholm, Tehran, Tel Aviv, Tripoli, Varna, Vienna, Warsaw and Zürich. The Israeli connection led to difficulties in operating the Arab routes. Its assets seemed to be being sold-off in an asset-stripping manner and by early 2001, Balkan's fleet was not even up to the task of meeting the airline's summer charter commitments, despite taking on some used 737-300s. In February 2001, the Zeevi group ceased funding the carrier and initiated legal action against the Bulgarian government over a US$100 million debt. Although the company was grounded and entered receivership,  it resumed flying later that year.

Short of cash, in 2002 Balkan's six weekly slots for Heathrow airport were sold to British Airways for US$6 million. In 10 that year, creditors turned down a restructuring plan and voted for the closure of the airline, which was liquidated. The number of employees at the time of closure was 1,269. Balkan was succeeded as Bulgaria's national carrier by the newly formed Bulgaria Air.

Fleet
Until 1990, Balkan's signs were carried both by normal airliners and special government detachment, agricultural aviation, sanitary wings, cargo planes. Here follows the fleet except An-2 /281 pieces/ and Ка-26, as well as civil Mi-8s /17 pieces/, Mi-17 /1 piece/, Mi-2, training L-410s.

Accidents and incidents
, Aviation Safety Network records 15 occurrences and four hijackings for Balkan, and two fatal accidents plus one hijacking for TABSO. Only events that led to fatalities, wrote off the aircraft involved, or both, are presented in the list below.

title: Balkan Bulgarian Airlines


text:
User:Popsracer

My name is Richard I currently live in New Zealand. In the past I have lived in Sydney, Australia and London, England. My username 'Popsracer' comes from a character from the tv show Speed Racer.

Significant Contributions
Charles Upham - Alfred Hulme - Sky Tower - Harrods - Auckland International Airport - Naval Communication Station Harold E. Holt - Omega Navigation System - Cherie Blair - Isaac Isaacs - Macau Tower - James Packer - Blaster worm

Images Added
HMS Warrior - HMS Belfast - Lamma Island - Walsall - All Souls College, Oxford - Christ Church, Oxford - HMS Victory - Brighton - Canary Wharf and One Canada Square - Thames Barrier - Rangitoto Island - Highgate Cemetery - Imperial War Museum - Hong Kong Tramways - Beaches of Hong Kong - Devonport, Auckland - Waikato River - Macau Tower - The Mall (London) - Mumbles - Newgrange - Canary Wharf tube station - Cape Reinga - Huntly, New Zealand

Works in Progress
Raglan - Cambridge, New Zealand - Huntly, New Zealand - Tauranga, New Zealand - Invercargill, New Zealand - List of people associated with World War I - Bernard Freyberg - Peter Blake (yachtsman) - Bruce Farr - Volvo Ocean Race - Robert Semple - Denny Hulme - Simon Fuller - Colin Meads - Death Row Records - Leslie Andrew - Jonah Lomu - International Rugby Board - Harold Gillies - Alastair Campbell - Keith Park - Bill Hamilton (engineer) - Charles Goldie - George Grey - Simon Cowell - Sergei Prokudin-Gorskii - Len Lye - Robert FitzRoy - Kilmainham Jail - Terry Lloyd -

To be added in Future

 * Cyril Bassett
 * Jean Batten - Aviator
 * Alim Khan - Emir of Bukhara
 * Iceberg Slim

title: User:Popsracer


text:
Talk:List of electoral systems by country

United States — maps are wrong
The United States does NOT use the "majority bonus system" for the House of Representatives or the Senate. Both bodies are elected First Past The Post. Party primaries may use a variety of systems, but the OFFICIAL election (not the primaries) are all FPP. David Cannon (talk) 04:07, 12 June 2022 (UTC)

 * There are not just party primaries but jungle primaries as well. There are also elections with the two round system, which means the runoff is after the first round general election and the general election (jungle primary is before the only round of the general election, but essentially the same)
 * Therefore not all "official" elections are FPTP, some are two round, some are IRV
 * The maps show "varies by state" (shade of grey) not "majority bonus" (which is a shade of blue/purple)
 * for head of state (POTUS) the table shows this greenish blue which is indirect election by electoral college, which is also true, no matter which state uses which system(s) to elect their winner(s) Rankedchoicevoter (talk) 05:21, 12 June 2022 (UTC)

Sst
Brief notes about the elections conducted in three countries 111.223.27.144 (talk) 14:11, 5 June 2023 (UTC)


text:
Talk:Chinese Canadians

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 * Added archive https://web.archive.org/web/20070310063144/http://www.canada.com/vancouversun/news/story.html?id=711165cc-78b3-49af-8e24-15869021c39a to http://www.canada.com/vancouversun/news/story.html?id=711165cc-78b3-49af-8e24-15869021c39a
 * Added archive https://web.archive.org/web/20160322222706/http://www.canada.com/vancouversun/story.html?id=ffd98428-9fa0-42e8-84b4-4a8417fb9f65 to http://www.canada.com/vancouversun/story.html?id=ffd98428-9fa0-42e8-84b4-4a8417fb9f65
 * Added archive https://web.archive.org/web/20121103054129/http://www.canada.com/vancouversun/story.html?id=94cb22cb-98d1-47ef-8f3d-ecca40d11a60 to http://www.canada.com/vancouversun/story.html?id=94cb22cb-98d1-47ef-8f3d-ecca40d11a60
 * Added archive https://web.archive.org/web/20070310061924/http://www.canada.com/vancouversun/story.html?id=94cb22cb-98d1-47ef-8f3d-ecca40d11a60&p=2 to http://www.canada.com/vancouversun/story.html?id=94cb22cb-98d1-47ef-8f3d-ecca40d11a60&p=2

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Cheers.— InternetArchiveBot  (Report bug) 01:48, 9 December 2017 (UTC)

>Wrong word
At least I think it might be the wrong word..........

The Canadian media in the late 19th and early 20th centuries depicted the Chinatowns in lucid and sensationalist terms...

This was written by User:A.S. Brown.

Is "lucid" the right word here? I rather think the context suggests that "lurid" may have been what was meant. If so, change it, please. Kelisi (talk) 21:44, 19 November 2021 (UTC)

Wiki Education assignment: Gender, Race and Computing
— Assignment last updated by Racoon dolphin (talk) 07:09, 12 November 2023 (UTC)

title: Talk:Chinese Canadians