text:
Vanity Fair (novel)

Vanity Fair is a novel by the English author William Makepeace Thackeray, which follows the lives of Becky Sharp and Amelia Sedley amid their friends and families during and after the Napoleonic Wars. It was first published as a 19-volume monthly serial (the last containing Parts 19 and 20) from 1847 to 1848, carrying the subtitle Pen and Pencil Sketches of English Society, which reflects both its satirisation of early 19th-century British society and the many illustrations drawn by Thackeray to accompany the text. It was published as a single volume in 1848 with the subtitle A Novel without a Hero, reflecting Thackeray's interest in deconstructing his era's conventions regarding literary heroism. It is sometimes considered the "principal founder" of the Victorian domestic novel.

The story is framed as a puppet play, and the narrator, despite being an authorial voice, is somewhat unreliable. The serial was a popular and critical success; the novel is now considered a classic and has inspired several audio, film, and television adaptations. It also inspired the title of the British lifestyle magazine first published in 1868, which became known for its caricatures of famous people of Victorian and Edwardian society. In 2003, Vanity Fair was listed at No. 122 on the BBC's The Big Read poll of the UK's best-loved books.

Title
The book's title comes from John Bunyan's Pilgrim's Progress, a Dissenter allegory first published in 1678. In that work, "Vanity Fair" refers to a stop along the pilgrim's route: a never-ending fair held in a town called Vanity, which represents man's sinful attachment to worldly things. Thackeray does not mention Bunyan in the novel or in his surviving letters about it, where he describes himself dealing with "living without God in the world", but he did expect the reference to be understood by his audience, as shown in an 1851 Times article likely written by Thackeray himself. Robert Bell—whose friendship later became so great that he was buried near Thackeray at Kensal Green Cemetery —complained that the novel could have used "more light and air" to make it "more agreeable and healthy". Thackeray rebutted this with Evangelist's words as the pilgrims entered Bunyan's Vanity Fair: "The heart is deceitful above all things, and desperately wicked; who can know it?"

From its appearance in Bunyan, "Vanity Fair" or a "vanity-fair" was also in general use for "the world" in a range of connotations from the blandly descriptive to the wearily dismissive to the condemning. By the 18th century, it was generally taken as a playground and, in the first half of the 19th century, more specifically the playground of the idle and undeserving rich. All of these senses appear in Thackeray's work. The name "Vanity Fair" has also been used for at least 5 periodicals.

Plot summary
The story is framed by its preface and coda as a puppet show taking place at a fair; the cover illustration of the serial installments was not of the characters but of a troupe of comic actors at Speakers' Corner in Hyde Park. The narrator, variously a show manager or writer, appears at times within the work itself and is somewhat unreliable, repeating a tale of gossip at second or third hand.

In London in 1814, Rebecca Sharp ("Becky"), daughter of an art teacher and a French dancer, is a strong-willed, cunning, moneyless young woman determined to make her way in society. After leaving school, Becky stays with her friend Amelia Sedley ("Emmy"), who is a good-natured, simple-minded young girl, of a wealthy London family. There, Becky meets the dashing and self-obsessed Captain George Osborne (Amelia's betrothed) and Amelia's brother Joseph ("Jos") Sedley, a clumsy and vainglorious but rich civil servant home from the East India Company. Hoping to marry Sedley, the richest young man she has met, Becky entices him, but she fails. George Osborne's friend Captain William Dobbin loves Amelia, but only wishes her happiness, which is centred on George.

Becky Sharp says farewell to the Sedley family and enters the service of the crude and profligate baronet Sir Pitt Crawley, who has engaged her as a governess to his daughters. Her behaviour at Sir Pitt's house gains his favour, and after the premature death of his second wife, he proposes marriage to her. However, he finds that Becky has secretly married his second son, Captain Rawdon Crawley, but Becky very much regrets having done this; she had no idea that his father's wife would die so soon after. Sir Pitt's elder half sister, the spinster Miss Crawley, is very rich, having inherited her mother's fortune, and the whole Crawley family compete for her favour so she will bequeath them her wealth. Initially her favourite is Rawdon Crawley, but his marriage with Becky enrages her. First she favours the family of Sir Pitt's brother, but when she dies, she leaves her money to Sir Pitt's eldest son, also called Pitt.

News arrives that Napoleon has escaped from Elba, and as a result the stockmarket becomes jittery, causing Amelia's stockbroker father, John Sedley, to become bankrupt. George's rich father forbids George to marry Amelia, who is now poor. Dobbin persuades George to marry Amelia, and George is consequently disinherited. George Osborne, William Dobbin and Rawdon Crawley are deployed to Brussels, accompanied by Amelia and Becky, and Amelia's brother, Jos.

George is embarrassed by the vulgarity of Mrs. Major O'Dowd, the wife of the head of the regiment. The newly wedded Osborne is already growing tired of Amelia, and he becomes increasingly attracted to Becky, which makes Amelia jealous and unhappy. He is also losing money to Rawdon at cards and billiards. At a ball in Brussels, George gives Becky a note inviting her to run away with him (although this fact is not revealed until the end of the book). But then the army have marching orders to the Battle of Waterloo, and George spends a tender night with Amelia and leaves.

The noise of battle horrifies Amelia, and she is comforted by the brisk but kind Mrs. O'Dowd. Becky is indifferent and makes plans for whatever the outcome (for example, if Napoleon wins, she would aim to become the mistress of one of his Marshals). She also makes a profit selling her carriage and horses at inflated prices to Jos, who is seeking to flee Brussels.

George Osborne is killed at the Battle of Waterloo, while Dobbin and Rawdon survive the battle. Amelia bears him a posthumous son, who carries on the name George. She returns to live in genteel poverty with her parents, spending her life in memory of her husband and care of her son. Dobbin pays for a small annuity for Amelia and expresses his love for her by small kindnesses toward her and her son. She is too much in love with her husband's memory to return Dobbin's love. Saddened, he goes with his regiment to India for many years.

Becky also gives birth to a son, named Rawdon after his father. Becky is a cold, distant mother, although Rawdon loves his son. Becky continues her ascent first in post-war Paris and then in London where she is patronised by the rich and powerful Marquis of Steyne. She is eventually presented at court to the Prince Regent and charms him further at a game of "acting charades" where she plays the roles of Clytemnestra and Philomela. The elderly Sir Pitt Crawley dies and is succeeded by his son Pitt, who had married Lady Jane Sheepshanks, Lord Southdown's third daughter. Becky is on good terms with Pitt and Jane originally, but Jane is disgusted by Becky's attitude to her son and jealous of Becky's relationship with Pitt.

At the summit of their social success, Rawdon is arrested for debt, possibly at Becky's connivance. The financial success of the Crawleys had been a topic of gossip; in fact they were living on credit even when it ruined those who trusted them, such as their landlord, an old servant of the Crawley family. The Marquis of Steyne had given Becky money, jewels, and other gifts but Becky does not use them for expenses or to free her husband. Instead, Rawdon's letter to his brother is received by Lady Jane, who pays the £170 that prompted his imprisonment.

He returns home to find Becky singing to Steyne and strikes him down on the assumption—despite her protestations of innocence—that they are having an affair. Steyne is indignant, having assumed the £1000 he had just given Becky was part of an arrangement with her husband. Rawdon finds Becky's hidden bank records and leaves her, expecting Steyne to challenge him to a duel. Instead Steyne arranges for Rawdon to be made Governor of Coventry Island, a pestilential and disease-ridden location. Becky, having lost both husband and credibility, leaves England and wanders the continent, leaving her son in the care of Pitt and Lady Jane.

As Amelia's adored son George grows up, his grandfather Mr Osborne relents towards him (though not towards Amelia) and takes him from his impoverished mother, who knows the rich old man will give him a better start in life than she could manage. After twelve years abroad, both Joseph Sedley and Dobbin return. Dobbin professes his unchanged love to Amelia. Amelia is affectionate, but she cannot forget the memory of her dead husband. Dobbin mediates a reconciliation between Amelia and her father-in-law, who dies soon after. He had amended his will, bequeathing young George half his large fortune and Amelia a generous annuity.

After the death of Mr Osborne, Amelia, Jos, George and Dobbin go to Pumpernickel (Weimar in Germany), where they encounter the destitute Becky. Becky has fallen in life. She lives among card sharps and con artists, drinking heavily and gambling. Becky enchants Jos Sedley all over again, and Amelia is persuaded to let Becky join them. Dobbin forbids this, and reminds Amelia of her jealousy of Becky with her husband. Amelia feels that this dishonours the memory of her dead and revered husband, and this leads to a complete breach between her and Dobbin. Dobbin leaves the group and rejoins his regiment, while Becky remains with the group.

However, Becky has decided that Amelia should marry Dobbin, even though Becky knows Dobbin is her enemy. Becky shows Amelia George's note, kept all this time from the eve of the Battle of Waterloo, and Amelia finally realises that George was not the perfect man she always thought, and that she has rejected a better man, Dobbin. Amelia and Dobbin are reconciled and return to England. Becky and Jos stay in Europe. Jos dies, possibly suspiciously, after signing a portion of his money to Becky as life insurance, thereby setting her up with an income. She returns to England, and manages a respectable life, although all her previous friends refuse to acknowledge her.

Emmy Sedley (Amelia)
Amelia, called Emmy, is good-natured but passive and naïve. Pretty rather than beautiful, she has a snub nose and round, rosy cheeks. She is well-liked by men, and women when few men are around, as was the case when she was at school. She begins the work as its heroine ("selected for the very reason that she was the best-natured of all") and marries the dashing George Osborne against his father's wishes, but the narrator is soon forced to admit "she wasn't a heroine" after all as she remains soppily devoted to him despite his neglect of her and his flirtation with Becky.

After George dies in the Battle of Waterloo, she brings up little George alone while living with her parents. She is completely dominated by her increasingly peevish mother and her spendthrift father, who, to finance one of his failing investment schemes, sells the annuity Jos had provided. Amelia becomes obsessed with her son and the memory of her husband. She ignores William Dobbin, who courts her for years and treats him shabbily until he leaves. Only when Becky shows her George's letter to her, indicating his unfaithfulness, can Amelia move on. She then marries Dobbin.

In a letter to his close friend Jane Octavia Brookfield while the book was being written, Thackeray confided that "You know you are only a piece of Amelia, my mother is another half, my poor little wife y est pour beaucoup". Within the work, her character is compared and connected to Iphigenia, although two of the references extend the allusion to all daughters in all drawing rooms as potential Iphigenias waiting to be sacrificed by their families.

Becky Sharp (Rebecca)
Rebecca Sharp, called Becky, is Amelia's opposite: an intelligent, conniving young woman with a gift for satire. She is described as a short, sandy-haired girl who has green eyes and a great deal of wit. Becky is born to a French opera dancer mother and an art teacher and artist father Francis. Fluent in both French and English, Becky has a beautiful singing voice, plays the piano, and shows great talent as an actress. Without a mother to guide her into marriage, Becky resolves that "I must be my own Mamma".

She thereafter appears to be completely amoral and without conscience and has been called the work's "anti-heroine". She does not seem to have the ability to get attached to other people, and lies easily and intelligently to get her way. She is extremely manipulative and, after the first few chapters and her failure to attract Jos Sedley, is not shown as being particularly sincere.

Never having known financial or social security even as a child, Becky desires it above all things. Nearly everything she does is with the intention of securing a stable position for herself, or herself and her husband after she and Rawdon are married. She advances Rawdon's interests tirelessly, flirting with men such as General Tufto and the Marquis of Steyne to get him promoted. She also uses her feminine wiles to distract men at card parties while Rawdon cheats them blind.

Marrying Rawdon Crawley in secret was a mistake, as was running off instead of begging Miss Crawley's forgiveness. She also fails to manipulate Miss Crawley through Rawdon so as to obtain an inheritance. Although Becky manipulates men very easily, she is less successful with women. She is utterly hostile to Lady Bareacres, dismissive of Mrs. O'Dowd, and Lady Jane, although initially friendly, eventually distrusts and dislikes her.

The exceptions to this trend are (at least initially) Miss Crawley, her companion Miss Briggs, and her school friend Amelia; the latter is the recipient of more-or-less the only kindnesses Becky expresses in the work, persuading her to marry Dobbin in light of what Becky comes to appreciate to be his good qualities and protecting Amelia from two ruffians vying for her attentions. This comparative loyalty to Amelia stems from Becky having no other friends at school, and Amelia having "by a thousand kind words and offices, overcome... (Becky's) hostility"; 'The gentle tender-hearted Amelia Sedley was the only person to whom she could attach herself in the least; and who could help attaching herself to Amelia?'

Beginning with her determination to be her "own Mamma", Becky begins to assume the role of Clytemnestra. Becky and her necklace from Steyne also allude to the fallen Eriphyle in Racine's retelling of Iphigenia at Aulis, where she doubles and rescues Iphigenia. In lesser contexts, Becky also appears as Arachne to Miss Pinkerton's Minerva and as a variety of classical figures in the works' illustrations.

George Osborne
George Osborne, his father (a merchant, of considerably superior social status to Dobbin's grocer father, albeit self made, and ironically a mere corporal in the City Light Horse regiment of which Dobbin senior, by this time an alderman and a knight, is colonel), and his two sisters are close to the Sedley family until Mr. Sedley (the father of Jos and Amelia, and George Osborne's godfather, from whom the latter takes his middle name of 'Sedley') goes bankrupt following some ill-advised speculation. Since George and Amelia were raised in close company and were childhood sweethearts, George defies his father to marry Amelia. Before father and son can be reconciled, George is killed at the battle of Waterloo, leaving the pregnant Amelia to carry on as well as she can.

Raised to be a selfish, vain, profligate spender, handsome and self-obsessed, George squanders the last of the money he receives from his father and sets nothing aside to help support Amelia. After marrying Amelia, he finds after a couple of weeks that he is bored. He flirts with Becky quite seriously and is reconciled to Amelia only a short time before he is killed in battle.

William Dobbin
The best friend of George Osborne, Captain William Dobbin is tall, ungainly, and not particularly handsome. He is a few years older than George but has been friends with him since his schooldays, even though Dobbin's father is a fig-merchant (Dobbin & Rudge, grocers and oilmen, Thames Street, London - he is later an alderman and colonel of the City Light Horse regiment, and knighted) and the Osbornes belong to the genteel class and have become independently wealthy. He defends George and is blind to his faults in many ways, although he tries to force George to do the right thing. He pushes George to keep his promise to marry Amelia even though Dobbin is in love with Amelia himself. After George is killed, Dobbin puts together an annuity to help support Amelia, ostensibly with the help of George's fellow officers.

Later, Major and Lieutenant Colonel Dobbin discreetly does what he can to help support Amelia and her son George. He allows Amelia to continue with her obsession over George and does not correct her erroneous beliefs about him. He hangs about for years, either pining away over her while serving in India or waiting on her in person, allowing her to take advantage of his good nature. After Amelia finally chooses Becky's friendship over his during their stay in Germany, Dobbin leaves in disgust. He returns when Amelia writes to him and admits her feelings for him, marries her (despite having lost much of his passion for her), and has a daughter whom he loves deeply.

Rawdon Crawley
Rawdon, the younger of the two Crawley sons, is an empty-headed cavalry officer who is his wealthy aunt's favourite until he marries Becky Sharp, who is of a far lower class. He permanently alienates his aunt, who leaves her estate to Rawdon's elder brother Sir Pitt instead. Sir Pitt has by this time inherited their father's estate, leaving Rawdon destitute.

The well-meaning Rawdon does have a few talents in life, most of them having to do with gambling and duelling. He is very good at cards and billiards, and although he does not always win he is able to earn cash by betting against less talented gamblers. He is heavily indebted throughout most of the book, not so much for his own expenses as for Becky's. Not particularly talented as a military officer, he is content to let Becky manage his career.

Although Rawdon knows Becky is attractive to men, he believes her reputation is spotless even though she is widely suspected of romantic intrigue with General Tufto and other powerful men. Nobody dares to suggest otherwise to Rawdon because of his temper and his reputation for duelling. Yet other people, particularly the Marquis of Steyne, find it impossible to believe that Crawley is unaware of Becky's tricks. Steyne in particular believes Rawdon is fully aware Becky is prostituting herself, and believes Rawdon is going along with the charade in the hope of financial gain.

After Rawdon finds out the truth and leaves Becky for an assignment overseas, he leaves his son to be brought up by his brother Sir Pitt and his wife Lady Jane. While overseas, Rawdon dies of yellow fever.

Pitt Crawley
Rawdon Crawley's elder brother inherits the Crawley estate from his father, the boorish and vulgar Sir Pitt, and also inherits the estate of his wealthy aunt, Miss Crawley, after she disinherits Rawdon. Pitt is very religious and has political aspirations, although not many people appreciate his intelligence or wisdom because there's not much there to appreciate.

Somewhat pedantic and conservative, Pitt does nothing to help Rawdon or Becky even when they fall on hard times. This is chiefly due to the influence of his wife, Lady Jane, who dislikes Becky because of her callous treatment of her son, and also because Becky repaid Lady Jane's earlier kindness by patronising her and flirting with Sir Pitt.

Miss Matilda Crawley
The elderly Miss Crawley is everyone's favourite wealthy aunt. Sir Pitt and Rawdon both dote on her, although Rawdon is her favourite nephew and sole heir until he marries Becky. While Miss Crawley likes Becky and keeps her around to entertain her with sarcasm and wit, and while she loves scandal and particularly stories of unwise marriage, she does not want scandal or unwise marriage in her family. A substantial part of the early section of the book deals with the efforts the Crawleys make to kowtow to Miss Crawley in the hope of receiving a big inheritance.

Thackeray spent time in Paris with his maternal grandmother Harriet Becher, and Miss Crawley's character is said to be based on her.

Joseph Sedley
Amelia's older brother, Joseph "Jos" Sedley, is a "nabob", who made a respectable fortune as a collector in India. Obese and self-important but very shy and insecure, he is attracted to Becky Sharp but circumstances prevent him from proposing. He never marries, but when he meets Becky again he is easily manipulated into falling in love with her. Jos is not a courageous or intelligent man, displaying his cowardice at the Battle of Waterloo by trying to flee and purchasing both of Becky's overpriced horses. Becky ensnares him again near the end of the book and, it is hinted, murders him for his life insurance.

Publication history
Thackeray may have begun working out some of the details of Vanity Fair as early as 1841 but probably began writing it in late 1844. Like many novels of the time, Vanity Fair was published as a serial before being sold in book form. It was printed in 20 monthly parts between January 1847 and July 1848 for Punch by Bradbury & Evans in London. The first three had already been completed before publication, while the others were written after it had begun to sell.

As was standard practice, the last part was a "double number" containing parts 19 and 20. Surviving texts, his notes, and letters show that adjustments were made – e.g., the Battle of Waterloo was delayed twice – but that the broad outline of the story and its principal themes were well established from the beginning of publication.

 * No. 1 (January 1847) Ch. 1–4
 * No. 2 (February 1847) Ch. 5–7
 * No. 3 (March 1847) Ch. 8–11
 * No. 4 (April 1847) Ch. 12–14
 * No. 5 (May 1847) Ch. 15–18
 * No. 6 (June 1847) Ch. 19–22
 * No. 7 (July 1847) Ch. 23–25
 * No. 8 (August 1847) Ch. 26–29
 * No. 9 (September 1847) Ch. 30–32
 * No. 10 (October 1847) Ch. 33–35
 * No. 11 (November 1847) Ch. 36–38
 * No. 12 (December 1847) Ch. 39–42
 * No. 13 (January 1848) Ch. 43–46
 * No. 14 (February 1848) Ch. 47–50
 * No. 15 (March 1848) Ch. 51–53
 * No. 16 (April 1848) Ch. 54–56
 * No. 17 (May 1848) Ch. 57–60
 * No. 18 (June 1848) Ch. 61–63
 * No. 19/20 (July 1848) Ch. 64–67

The parts resembled pamphlets and contained the text of several chapters between outer pages of steel engravings and advertising. Wood engravings, which could be set along with normal moveable type, appeared within the text. The same engraved illustration appeared on the canary-yellow cover of each monthly part; this colour became Thackeray's signature, as a light blue-green was Dickens's, allowing passers-by to notice a new Thackeray number in a bookstall from a distance.

Vanity Fair was the first work that Thackeray published under his own name and was extremely well received at the time. After the conclusion of its serial publication, it was printed as a bound volume by Bradbury & Evans in 1848 and was quickly picked up by other London printers as well. As a collected work, the novels bore the subtitle A Novel without a Hero. By the end of 1859, royalties on Vanity Fair had only given Thackeray about £2000, a third of his take from The Virginians, but was responsible for his still more lucrative lecture tours in Britain and the United States.

From his first draft and following publication, Thackeray occasionally revised his allusions to make them more accessible for his readers. In Chapter 5, an original "Prince Whadyecallem" became "Prince Ahmed" by the 1853 edition. In Chapter 13, a passage about the filicidal Biblical figure Jephthah was removed, although references to Iphigenia remained important. In Chapter 56, Thackeray originally confused Samuel – the boy whose mother Hannah had given him up when called to by God – with Eli, the old priest to whose care he was entrusted; this mistake was not corrected until the 1889 edition, after Thackeray's death.

The serials had been subtitled Pen and Pencil Sketches of English Society and both they and the early bound versions featured Thackeray's own illustrations. These sometimes provided symbolically-freighted images, such as one of the female characters being portrayed as a man-eating mermaid. In at least one case, a major plot point is provided through an image and its caption. Although the text makes it clear that other characters suspect Becky Sharp to have murdered her second husband, there is nothing definitive in the text itself. However, an image reveals her overhearing Jos pleading with Dobbin while clutching a small white object in her hand. The caption that this is Becky's second appearance in the character of Clytemnestra clarifies that she did indeed murder him for the insurance money, likely through laudanum or another poison.

"The final three illustrations of Vanity Fair are tableaux that insinuate visually what the narrator is unwilling to articulate: that Becky... has actually been substantially rewarded – by society – for her crimes." One of the Thackeray's plates for the 11th issue of Vanity Fair was suppressed from publication by threat of prosecution for libel, so great was the resemblance of its depiction of Lord Steyne to the Marquis of Hertford. Despite their relevance, most modern editions either do not reproduce all the illustrations or do so with poor detail.

 * [ Wikisource ] [ Archive.org ].
 * , reprinted 1925.
 * , without illustration.
 * , reprinted 1898.
 * , reprinted 1886.
 * , in four editions.
 * , reprinted 1995.
 * , reprinted 2008.
 * , reprinted 2003, 2004, & 2008.
 * , reprinted 1995.
 * , reprinted 2008.
 * , reprinted 2003, 2004, & 2008.
 * , reprinted 1995.
 * , reprinted 2008.
 * , reprinted 2003, 2004, & 2008.
 * , reprinted 1995.
 * , reprinted 2008.
 * , reprinted 2003, 2004, & 2008.
 * , reprinted 2008.
 * , reprinted 2003, 2004, & 2008.
 * , reprinted 2003, 2004, & 2008.
 * , reprinted 2003, 2004, & 2008.

Reception and criticism

Contemporaneous reception
The style is highly indebted to Henry Fielding. Thackeray meant the book to be not only entertaining but also instructive, an intention demonstrated through the book's narration and through Thackeray's private correspondence. A letter to his editor at Punch expressed his belief that "our profession... is as serious as the parson's own". He considered it his own coming-of-age as a writer and greatest work.

Critics hailed the work as a literary treasure before the last part of the serial was published. In her correspondence, Charlotte Brontë was effusive regarding his illustrations as well: "You will not easily find a second Thackeray. How he can render, with a few black lines and dots, shades of expression, so fine, so real; traits of character so minute, so subtle, so difficult to seize and fix, I cannot tell—I can only wonder and admire... If Truth were again a goddess, Thackeray should be her high priest."

The early reviewers took the debt to Bunyan as self-evident and compared Becky with Pilgrim and Thackeray with Faithful. Although they were superlative in their praise, some expressed disappointment at the unremittingly dark portrayal of human nature, fearing Thackeray had taken his dismal metaphor too far. In response to these critics, Thackeray explained that he saw people for the most part as "abominably foolish and selfish".

The unhappy ending was intended to inspire readers to look inward at their own shortcomings. Other critics took notice of or exception to the social subversion in the work; in his correspondence, Thackeray stated his criticism was not reserved to the upper class: "My object is to make every body engaged, engaged in the pursuit of Vanity Fair and I must carry my story through in this dreary minor key, with only occasional hints here and there of better things—of better things which it does not become me to preach".

Analysis
The novel is considered a classic of English literature, though some critics claim that it has structural problems; Thackeray sometimes lost track of the huge scope of his work, mixing up characters' names and minor plot details. The number of allusions and references it contains can make it difficult for modern readers to follow.

The subtitle, A Novel without a Hero, refers to the characters all being flawed to a greater or lesser degree; even the most sympathetic have weaknesses, for example Captain Dobbin, who is prone to vanity and melancholy. The human weaknesses Thackeray illustrates are mostly to do with greed, idleness, and snobbery, and the scheming, deceit and hypocrisy which mask them. None of the characters is wholly evil, although Becky's manipulative, amoral tendencies make her come pretty close. However, even Becky, who is amoral and cunning, is thrown on her own resources by poverty and its stigma. (She is the orphaned daughter of a poor artist and an opera dancer.) Thackeray's tendency to highlight faults in all of his characters displays his desire for a greater level of realism in his fiction compared to the rather unlikely or idealised people in many contemporary novels.

The novel is a satire of society as a whole, characterised by hypocrisy and opportunism, but it is not necessarily a reforming novel; there is no clear suggestion that social or political changes or greater piety and moral reformism could improve the nature of society. It thus paints a fairly bleak view of the human condition. This bleak portrait is continued with Thackeray's own role as an omniscient narrator, one of the writers best known for using the technique. He continually offers asides about his characters and compares them to actors and puppets, but his cheek goes even as far as his readers, accusing all who may be interested in such "Vanity Fairs" as being either "of a lazy, or a benevolent, or a sarcastic mood". As Lord David Cecil remarked, "Thackeray liked people, and for the most part he thought them well-intentioned. But he also saw very clearly that they were all in some degree weak and vain, self-absorbed and self-deceived." Amelia begins as a warm-hearted and friendly girl, though sentimental and naive, but by the story's end she is portrayed as vacuous and shallow. Dobbin appears first as loyal and magnanimous, if unaware of his own worth; by the end of the story he is presented as a tragic fool, a prisoner of his own sense of duty who knows he is wasting his gifts on Amelia but is unable to live without her. The novel's increasingly grim outlook can take readers aback, as characters whom the reader at first holds in sympathy are shown to be unworthy of such regard.

The work is often compared to the other great historical novel of the Napoleonic Wars, Tolstoy's War and Peace. While Tolstoy's work has a greater emphasis on the historical detail and the effect the war has upon his protagonists, Thackeray instead uses the conflict as a backdrop to the lives of his characters. The momentous events on the continent do not always have an equally important influence on the behaviours of Thackeray's characters. Rather their faults tend to compound over time. This is in contrast to the redemptive power the conflict has on the characters in War and Peace. For Thackeray, the Napoleonic Wars as a whole can be thought of as one more of the vanities expressed in the title.

A common critical topic is to address various objects in the book and the characters' relationships with them, such as Rebecca's diamonds or the piano Amelia values when she thinks it came from George and dismisses upon learning that Dobbin provided it. Marxist and similar schools of criticism that go farther and see Thackeray condemning consumerism and capitalism. However, while Thackeray is pointed in his criticism of the commodification of women in the marriage market, his variations on Ecclesiastes's "all is vanity" are often interpreted as personal rather than institutional. He also has broad sympathy with a measure of comfort and financial and physical "snugness". At one point, the narrator even makes a "robust defense of his lunch": "It is all vanity to be sure: but who will not own to liking a little of it? I should like to know what well-constituted mind, merely because it is transitory, dislikes roast-beef?"

Despite the clear implications of Thackeray's illustration on the topic, John Sutherland has argued against Becky having murdered Jos on the basis of Thackeray's criticism of the "Newgate novels" of Edward Bulwer-Lytton and other authors of Victorian crime fiction. Although what Thackeray principally objected to was glorification of a criminal's deeds, his intent may have been to entrap the Victorian reader with their own prejudices and make them think the worst of Becky Sharp even when they have no proof of her actions.

Adaptations
The book has inspired a number of adaptations:

Radio

 * Vanity Fair (7 January 1940), the CBS Radio series Campbell Playhouse, hosted by Orson Welles, broadcast a one-hour adaptation featuring Helen Hayes and Agnes Moorehead.
 * Vanity Fair (6 December 1947), the NBC Radio series Favorite Story, hosted by Ronald Colman, broadcast a half-hour adaptation with Joan Lorring as "Becky Sharp"
 * Vanity Fair (2004), BBC Radio 4 broadcast an adaptation of the novel by Stephen Wyatt, starring Emma Fielding as Becky, Stephen Fry as the Narrator, Katy Cavanagh as Amelia, David Calder, Philip Fox, Jon Glover, Geoffrey Whitehead as Mr. Osborne, Ian Masters as Mr. Sedley, Alice Hart as Maria Osborne, and Margaret Tyzack as Miss Crawley; this was subsequently re-broadcast on BBC Radio 4 Extra in 20 fifteen-minute episodes.
 * Vanity Fair (2019), BBC Radio 4 broadcast a three-part adaptation of the novel by Jim Poyser with additional material by Al Murray (Thackeray's actual descendant, who also stars as Thackeray), with Ellie White as Becky Sharp, Helen O'Hara as Amelia Sedley, Blake Ritson as Rawdon Crawley, Rupert Hill as George Osborne and Graeme Hawley as Dobbin.

Silent films

 * Vanity Fair (1911), directed by Charles Kent
 * Vanity Fair (1915), directed by Charles Brabin
 * Vanity Fair (1922), directed by W. Courtney Rowden
 * Vanity Fair (1923), directed by Hugo Ballin

Sound films

 * Vanity Fair (1932), directed by Chester M. Franklin and starring Myrna Loy, updating the story to make Becky Sharp a social-climbing governess
 * Becky Sharp (1935), starring Miriam Hopkins and Frances Dee, the first feature film shot in full-spectrum Technicolor
 * Vanity Fair (2004), directed by Mira Nair and starring Reese Witherspoon as Becky Sharp and Natasha Little, who had played Becky Sharp in the earlier television miniseries of Vanity Fair, as Lady Jane Sheepshanks

Television

 * Vanity Fair (1956-7), a BBC serial adapted by Constance Cox starring Joyce Redman
 * Vanity Fair (1967), a BBC miniseries adapted by Rex Tucker starring Susan Hampshire as Becky Sharp, for which she received an Emmy Award in 1973. This version was also broadcast in 1972 in the US on PBS television as part of Masterpiece Theatre.
 * Yarmarka tshcheslaviya (1976), a two-episode TV miniseries directed by Igor Ilyinsky and Mariette Myatt, staged by the Moscow State Academic Maly Theater of the USSR)
 * Vanity Fair (1987), a BBC miniseries starring Eve Matheson as Becky Sharp, Rebecca Saire as Amelia Sedley, James Saxon as Jos Sedley and Simon Dormandy as Dobbin.
 * Vanity Fair (1998), a BBC miniseries starring Natasha Little as Becky Sharp
 * Vanity Fair (2018), a seven-part ITV and Amazon Studios adaptation, starring Olivia Cooke as Becky Sharp, Tom Bateman as Captain Rawdon Crawley, and Michael Palin as Thackeray.

Theatre

 * Becky Sharp (1899), play written by Langdon Mitchell
 * Vanity Fair (1946), play written by Constance Cox
 * Vanity Fair (2017), play written by Kate Hamill
 * Vanity (2023), musical written and composed by Bernard J. Taylor

Fiction

 * Becky (2023), novel written by Sarah May

title: Vanity Fair (novel)


text:
Acetic acid bacteria

Acetic acid bacteria (AAB) are a group of Gram-negative bacteria which oxidize sugars or ethanol and produce acetic acid during fermentation. The acetic acid bacteria consist of 10 genera in the family Acetobacteraceae. Several species of acetic acid bacteria are used in industry for production of certain foods and chemicals.

Description
All acetic acid bacteria are rod-shaped and obligate aerobes. Acetic acid bacteria are airborne and are ubiquitous in nature. They are actively present in environments where ethanol is being formed as a product of the fermentation of sugars. They can be isolated from the nectar of flowers and from damaged fruit. Other good sources are fresh apple cider and unpasteurized beer that has not been filter sterilized. In these liquids, they grow as a surface film due to their aerobic nature and active motility. Fruit flies or vinegar eels are considered common vectors in the propagation of acetic acid bacteria.

The growth of Acetobacter in wine can be suppressed through effective sanitation, by complete exclusion of air from wine in storage, and by the use of moderate amounts of sulfur dioxide in the wine as a preservative.

Metabolism
Vinegar is produced when acetic acid bacteria act on alcoholic beverages such as wine. Specific oxidation reactions occur through oxidative fermentation, which creates vinegar as a byproduct. In the biotechnological industry, these bacteria's oxidation mechanism is exploited to produce a number of compounds such as l-ascorbic acid, dihydroxyacetone, gluconic acid, and cellulose. Besides food industry, some acetic acid bacteria are used as biocatalysts for the industrial production of compounds. They are used as the important biocatalysts for the development of eco-friendly fermentation processes as an alternative to the chemical synthesis. Some genera, such as Acetobacter, can oxidize ethanol to carbon dioxide and water using Krebs cycle enzymes. Other genera, such as Gluconobacter, do not oxidize ethanol, as they do not have a full set of Krebs cycle enzymes. As these bacteria produce acid, they are usually acid-tolerant, growing well below pH 5.0, although the pH optimum for growth is 5.4-6.3. Acetobacter xylinum is able to synthesize cellulose, something normally done only by plants.

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

title: Acetic acid bacteria


text:
Talk:Acetic acid bacteria

''Text from a flashcard I wrote. Update article as needed. maveric149'' Acetic acid bacteria

Gram reaction?

Microscopic appearance?

Colony characteristics?

Isolation? inoculum? media? conditions?

Gram -

rods

oxidize ethanol to acetic acid, used to make vinegar, CaCO3 in agar --> HCO3 if

acid is made = clearing

fermented OJ Yeast Extract Ethanol Agar 20 C Acetobacter can oxidize acetic acid, Gluconobacter cannot --

WikiProject Food and drink Tagging
This article talk page was automatically added with WikiProject Food and drink banner as it falls under Category:Food or one of its subcategories. If you find this addition an error, Kindly undo the changes and update the inappropriate categories if needed. The bot was instructed to tagg these articles upon consenus from WikiProject Food and drink. You can find the related request for tagging here. Maximum and careful attention was done to avoid any wrongly tagging any categories, but mistakes may happen... If you have concerns, please inform on the project talk page -- TinucherianBot (talk) 05:49, 4 July 2008 (UTC)

This article is stolen or may have been stolen from. http://www.economicexpert.com/a/Acetic:acid:bacteria.html
 * The page states in its footer that it takes content from this Wikipedia page, not the other way around. Yangosplat222 (talk) 18:34, 22 April 2013 (UTC)

Merge of Acetobacter
The Acetobacter page was recently merged into this one. I think it ought to have its own page as Acetobacter is a specific genus and thus a subset of all kinds of acetic acid bacteria. Discuss? Yangosplat222 (talk) 18:39, 22 April 2013 (UTC)
 * I think Acetobacteraceae and Acetobacter should have their own pages. I don't agree with the merging.--Miguelferig (talk) 18:01, 1 February 2014 (UTC)

Further reading section
I renamed the Academic references section to Further reading because that is more consistent with Wikipedia formatting; however, it's not exactly accurate, and ideally those sources should be moved into Acetic acid bacteria and cited in the body of the article. Yangosplat222 (talk) 18:47, 22 April 2013 (UTC)

Nomenclature for the bacteria that synthesize cellulose: Acetobacter xylinum?
The synthesis of cellulose by a bacteria is very interesting and does belong in the article. However, if I understand correctly, the current nomenclature is not Acetobacter xylinum. Instead, it's Acetobacter aceti subsp. xylinus, according to bacterio.net. My expertise isn't sufficient to determine the best way to present this in a Wikipedia article, so I will let someone else decide whether an edit is desirable. Oaklandguy (talk) 09:21, 10 December 2016 (UTC)

I agree, but I am pretty sure that cellulose production is not part of their oxidative metabolism. These are highly used in industry, maybe an industrial usage section could be added and cellulose production move there. — Preceding unsigned comment added by 140.228.217.193 (talk) 00:06, 27 January 2023 (UTC)

title: Talk:Acetic acid bacteria


text:
Talk:Monoid

Why?
* Associativity: for all a, b, c in M, (a∗b)∗c = a∗(b∗c) * Identity element: there exists an element e in M, such that for all a in M, a∗e = e∗a = a. One often sees the additional axiom * Closure: for all a, b in M, a∗b is in M though, strictly speaking, this is not necessary as it is implied by the notion of a binary operation.
 * Why? Doesn't Closure need to be defined for Associativity to be? --Carbonrodney 07:43, 16 November 2006 (UTC)

 * It's not saying that closure isn't needed, it's saying that we already have it, because we have a binary operation $$M\times M\to M$$. --Zundark

 * It seems it would be clearer and more consistent with the definitions of the Group and Category pages if the Closure property was surfaced as a top-level axiom. At the very least "binary operation" should be explicitly prefaced as "closed"- I had to reference https://en.wikipedia.org/wiki/Template:Group-like_structures in order to determine if Monoids were closed or not. --Domohawk

For me, the confusion is coming because of two different symbols × and •. I think we can write S × S → S as S • S → S and closure property will be implicit from definition --Mukesh Tiwari

 * S × S is the notation for Cartesian product, in other words, the set of pairs of elements of S. It is not intended to denote the same operation as the monoid operation •.  Deltahedron (talk) 19:42, 6 September 2014 (UTC)

Computer Examples
could you give some examples related to computer ?
 * Lists with the concatenation operation, and the empty list is a monoid — Preceding unsigned comment added by 187.191.13.47 (talk) 23:24, 16 April 2013 (UTC)

Uniqueness of identity element
Under what situation is the identity element guaranteed to be unique? My off-the-cuff guess is that a cancellative monoid has a unique identity. Is there more to it than that? (Thanks!)

The identity is unique in every monoid. If e and f are two identities, then e = ef = f, so they are equal. -- Fropuff 15:13, 2004 Jul 29 (UTC)

Fixed Identity under Mappings
Can someone show me an example of when a homomorphism would not preserve the identity (assuming that wasn't given as an axiom)?

In my graduate abstract book, it doesn't state that a homomorphism must preserve identity (only an isomorphism) and leaves it as an exercise to construct an example to illustrate. However, in a different class, I was asked to show that a ring isomorphism preserves multiplicative identities (when present, obviously). As far as I can tell, I didn't make use of the fact that my mapping was bijective (1-1 and onto). Since my rings are additive groups and multiplicative monoids, then there should be no difference, unless the distributive law somehow differentiates the two types of monoids. -- Ub3rm4th 13:05, 2005 Jan 25 (UTC-6)

 * That is very strange. The whole point of a homomorphism is that it preserves the essential properties of the algebraic structure.  If a monoid homomorphism doesn't preserve the identity, then it's just a semigroup homomorphism. --MarkSweep 19:24, 25 Jan 2005 (UTC)

 * For an example of a homomorphism not preserving the identity, consider a monoid involving a set with an identity element, e, and a non-identity element, say x, where x*x = x. If you define f to map all elements of its domain to this non-identity element, then f is a homomorphism because it satisfies f(ab) = f(a)f(b). The mapping f doesn't preserve the identity because it maps the identity element in its domain to x, the non-identity element. --Mike Fikes (talk) 03:31, 22 April 2008 (UTC)

Yep. Fairly standard terminology (although I'm sure you'll find somebody who disagrees!) is that a monoid homomorphism is a map between monoids which preserves the multiplication and the identity. Since monoids are also semigroups, there is also a notion of a "semigroup homomorphism of monoids", which as it turns out will preserve multiplication but not necessarily the identity. You can easily show that a homomorphic image of a monoid identity will act as a local identity for the image of the map, which is another way of saying that a surjective semigroup homomorphism always preserves an identity if present; hence the result for rings. Cambyses 05:37, 26 Jan 2005 (UTC)

 * Thank you very much. From my past experiences with wikipedia, I didn't expect answers so soon, so this is the first I've checked.  For some reason, I like the answer that it would have to be a "semigroup homomorphism of monoids".  My interpretation of homomorphisms was exactly that they preserve the structure of the system, thus I was deeply disturbed.  I don't think my book (Hungeford) differentiates between a monoid homomorphism and a semigroup homomorphism of monoids.  Much gratitude! -- Ub3rm4th 10:38, 07 Feb 2005 (UTC-6)

Uniqueness of inverses?
If an element in a monoid has an inverse is that inverse unique? Also why?

 * Yes, associtivity guarantees that inverses, if they exist, are unique. Suppose b and c are both inverses of a. Then
 * $$c = ce = c(ab) = (ca)b = eb = b$$
 * So b = c. -- Fropuff 00:24, 13 January 2006 (UTC)

Why magma in definition?
The term 'magma' is quite unnecessary in encyclopedic definition of monoid. Very few people use this word outside Bourbaki circles. The idea to insert an obscure term in a definition or an explanation - for students etc - is simply ridiculous.

Of course we need an article for magma, but it does not mean we should stick this word everywhere.

 * I tend to agree. I'll remove it for now. -- Fropuff 03:23, 28 March 2006 (UTC)

Recursively adding an identity?
The fourth example stated:

Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining ee = e and es = s = se for all s ∈ S. This can be done recursively (i.e. if S is monoid with identity e, one obtains a new monoid S ∪ {e′} with identity e′, and so on).

I removed the last sentence because by adjoining an identity e′ to a monoid with identity e simply gives e = e′ and the monoids are isomorphic.

 * No, that is false. Instead, given a monoid N with identity e (which is of course a semigroup), we can always embed N in a monoid M with identity e′ distinct from e; and if |N| is finite, this embedding cannot yield an isomorphism. (This is never the case if, e.g., we replace "monoid" with "group"). 71.198.111.245 20:05, 2 June 2007 (UTC)

If someone can think of a compelling reason to keep this "recursive" construction method in please say so. TooMuchMath 21:04, 10 April 2006 (UTC)

 * As far as regards the usefulness of the construction, I agree; except to demonstrate that monoid endomorphisms (which preserve the identity) and monoid homomorphisms aren't coincident. 71.198.111.245 20:05, 2 June 2007 (UTC)

Every monoid contains a group?
Is it true that "every monoid contains a group" as written in the article? For example, if Z+ forms a monoid over multiplication with identity one, what group is made with Z+? I assume that to form a group, that set would need to be augmented with inverses. Maybe the word "contains" is misleading me. I can see how every group contains a monoid, but not vice-versa. - Simian1k 15:24, 13 April 2006 (UTC)

 * I don't know why the article bothers to mention it, but it's certainly true: every monoid contains at least the trivial group {1}. --Zundark 17:42, 13 April 2006 (UTC)

If you consider all the units in a monoid as a set they form a submonoid (IE the set is closed under *) that is also a group (inverses are present). This is the largest group contained in the monoid.

 * We need to be a bit careful regarding what we mean by a "group contained in the monoid" here. If we mean "a subset of the monoid M which is a group w.r.t. the identity of M", then there is even a unique subset G of M which is maximal w.r.t. this property. On the other hand, consider the group C_7. As with any semigroup, it can be embedded in a monoid M = C_7 union {e} of order 8. The largest subset which is a group is of order 7; but the set of units has order 1. 71.198.111.245 20:05, 2 June 2007 (UTC)

For some monoids the group of units is trivial, however there are examples where this is not the case. Consider $$M = < x, y | x^5=1, y^5=y^2, [x,y]=1 > $$. This is the (monoid) direct product of two cyclic monoids. The submonoid $$$$ is a group isomorphic to Z/5Z and the submonoid $$$$ is not a group. The set of units of M is given by the submonoid $$$$, IE the only elements of M which are invertible are powers of x.

Thank you for clearing that up. --Simian1k 16:01, 14 April 2006 (UTC)

unify or clarify the following statements in the article
These appear to be two different ways of saying the same thing: 1) A monoid satisfies all the axioms of a group with the exception of having inverses. A monoid with inverses is the same thing as a group; 2)If a monoid has the cancellation property and is finite, then it is in fact a group. drefty.mac 08:15, 28 October 2006 (UTC)

 * They are not really the same thing. Cancellativity is (in general) a necessary but not a sufficient condition for the existence of inverses. So (1) does not immediately imply (2). And (2) is a statement only about finite monoids (it is false if you remove the hypothesis of finiteness) so it can't imply (1) in the general (possibly infinite) case. (Of course in a strict logical sense, any two statements which are provable imply each other, but you know what I mean.... :-). Best wishes, Cambyses 11:21, 23 November 2006 (UTC)

Addition operator
The article states that there is a preordering if and only if there is a z such that x+z=y. But the addition operator is not defined. What am I missing? —Preceding unsigned comment added by 82.235.223.112 (talk)

 * It's just the binary operation of the commutative monoid. I'll add a note to make this clearer. --Zundark 12:55, 8 May 2007 (UTC)

Add pointer to Magma Definition
One might want to add a pointer to the definition of Magma since it now exists in the Wikipedia. --Gdinolt 17:43, 21 May 2007 (UTC)

Generators / Submonoids
The article states:

 * Equivalently, a submonoid is a subset N such that N=N*, where the superscript * is the Kleene star. For any subset N of M, the monoid N* is the smallest monoid that contains N.

First, strictly speaking, in the article on Wikipedia the Kleene star forms sets of strings of symbols from sets of symbols. Strings of symbols are not themselves symbols without some sort of (generally not injective) mapping. Of course, the mapping here is pretty obvious from context - if we already know what's going on, which should not be the point of view of the article IMO. A better link than to Kleene star explaining this idea might be free monoid or free object and some sort of discussion of presentation of a monoid similar to the article on presentation of a group.

Secondly, define (M,*) on the set {1,x} as: 1*1 = 1, 1*x = x*1 = x; x*x = x. M is a monoid. Let N = {x}. The semigroup (N,*\N} meets the requirement of being a monoid of order 1. Is "the smallest monoid containing N" meant to be (N,*\N), or is it meant to be (M,*)? Equivalently, is {x} a submonoid of {1,x}? (Note that this confusion cannot arise with subgroups of a group).

All of my comments here seem to revolve around the question of whether there is a preferred identity element 1 which is determined by the fact that we are working in the context of a /particular/ monoid M. Since monoids often are encountered as the multiplicative monoid of a ring with identity 1, I would expect that we usually map the empty string in N* to this 1, and not some other element of M; and that a submonoid N of M must contain 1; and that a group G embedded in M is assumed to be a submonoid of M. But I could be wrong! 71.198.111.245 20:05, 2 June 2007 (UTC)

Actions
The sentence "This is the analogue in monoid theory of a (left) group action" seems a bit out of place in an article on monoids: what is "monoid theory" if not this article? Maybe it was meant to be "group theory"? Actually the article on group theory should refer to this article's treatment of actions, since a group is the same thing as a monoid whose left and right actions are all invertible; the fact that both left and right are invertible allows the element itself to have an inverse. --Vaughan Pratt (talk) 09:07, 24 December 2008 (UTC)

Definition of monoid
Rewrote the definition of monoid to link to binary operation instead of operation. It is not necessary to say how to pronounce a symbol such as "•" but I put one in anyway. I also left out the closure property, which is old fashioned and included in the definition of binary operation. However, I notice that it is also used in the definitions of group and semigroup. Is there some kind of editorial policy about this? SixWingedSeraph (talk) 03:17, 16 November 2009 (UTC)

 * Im sorry but I have changed your definition back to include closure as one of the axioms. I left in the link to binary operation but I removed text in parenthesis which explains that a binary operation implies closure, as I think that this is just a distraction and makes it more difficult to understand the definition. If you look at the articles on group, semigroup and ring you will see that all of them link to binary operation and at the same time also include the closure axiom in their definitions, even though the term binary operation implies closure. As another example, you can see that Wolfram MathWorld defines a monoid as a "set that is closed under an associative binary operation and has an identity element." And to be honest, the real reason that I was compelled to add back the closure property to this definition is because it completely threw me off. When I looked at your definition (and I admit I did not read it very closely) I noticed that closure property was missing and erroneously assumed that this must mean that the definition of monoid does NOT require closure, which I found to be very surprising and it took me a few minutes of searching to figure out that the closure property was simply missing from the definition of this article. So I humbly submit to you that adding the closure property might be old fashioned but is more user friendly and could prevent some possible confusion. -99.242.17.45 (talk)

 * Suggestion: Definition and later references should be changed from pair (M,•) to triple (M,•,e). This follows some kind of normalization rules for universal algebras (including heterogenous algebras): Axioms with $$\exist$$ should be avoided (if possible). As the identity element is unique, it is a constant and should be reffered to in the describing n-tuple (regarding it as a nullary operation). That is, any describing n-tuple does contain the underlying set(s), follwed by the operations (with decreasing n-ary). In our case, these ideas result in a triple (M,•,e). You may also refer to Monoid. Kind regards--Ernsts (talk) 20:27, 1 January 2018 (UTC)

find-first monoid, find-last monoid
I can not find any reference to those. I guess that a find-first monoid is a monoid where, if an element is not neutral, it is left-absorbing. I doubt that "idempotent monoid" and "find-first monoid" coincide. An idempotent monoid is a monoid whose binary operation is idempotent. Every find-first monoid is idempotent.

Consider the monoid with the following table of the binary operation: (In other words, this is the semigroup $$(\{0,1\},\lor)$$, turned by the free functor into the monoid.) The monoid is idempotent. 0 is not neutral and is not left-absorbing. The monoid is not find-first. --Beroal (talk) 12:54, 15 January 2011 (UTC)

Monoid congruence definition is lacking
Monoid congruence redirects here, but aside from its use in the section about presentations and the corresponding article on a presentation of a monoid, it is not mentioned. This is a problem, because no definition is given, so the redirect of monoid congruence to this article is really a dead end. Can someone who knows the definition of a monoid congruence please add the definition to this article? Furby100 (talk) 14:47, 26 April 2012 (UTC)
 * I guess it is a particular case of Congruence relation. I changed that redirection. --Beroal (talk) 15:50, 4 May 2012 (UTC)

The "unit element"
The current article says "A submonoid of a monoid M is a subset N of M containing the unit element", but I don't see a definition for "unit element" that preceeds this. I assume it means "identity element" in this context. Tashiro (talk) 01:19, 7 October 2012 (UTC)
 * Fixed. — Quondum 05:38, 4 September 2013 (UTC)

Definition of submonoid
I have changed the definition of a submonoid to match that of Jacobson, effectively reversing my earlier change that excluded the requirement that it include the identity of the enclosing monoid. This is in line with a change of semantics from a subset that is a monoid under the monoid's binary operation to a subset that preserves the defined structure of the monoid, with the identity element being regarded as part of the defined structure (as in category theory, where it is regarded as a nullary operation). This is compatible with the definition of a monoid homomorphism in this article, in the sense that the submonoids of a monoid are precisely the images of the monoid endomorphisms.

It may be noted that there are conflicting, but less notable, web definitions such as, and , which prompted my earlier edit. An article should give due weight to conflicting definitions. I leave it to others to determine whether this conflicting definition deserves more than the footnote that I included. — Quondum 11:42, 26 September 2013 (UTC)

Suggested tweaks to new illustration
I like the new illustration File:Exponentiation as monoid homomorphism.pdf added, but would like to suggest some tweaks to the diagram: — Quondum 23:14, 9 October 2013 (UTC)
 * Since we are dealing with the standard, known operations, the diagram should use the standard symbols, to wit: the monoid under multiplication should have its operation denoted ×, not *.
 * Since (N,×) is a monoid and is a suitable codomain for the indicated mapping, there is no benefit in excluding 0. Excluding zero risks creating the impression that 0 must be excluded for some reason, and we should not do so, so I suggest including it in the multiplication table.
 * It is sufficient to indicate the mapping on one axis only. I would suggest removing the arrows from the second axis, as the double mapping slows interpretation.
 * Thanks, Jochen, for updating it as I suggested. I think that works very well. — Quondum 18:45, 10 October 2013 (UTC)

Monoid vs. group
The only difference between monoid and group is that in a group each element is required to have an inverse. There is no "nontrivial theorem" needed to prove this; it is what the definitions currently on Wikipedia say. (The axioms are exactly the same, except for the existence of inverses.) Ebony Jackson (talk) 22:48, 7 December 2013 (UTC)

Please be direct with your language
Subtle coincidence does not make the cut for encylopedic entries, I am going to edit the statement on identity element so that it states "There exists an element e in S such that for every element a in S, the equation e • a = a • e   holds" as it makes no sense as written unless the typo was not as I will edit from and the correct statemeant is "There exists an element e in S such that for every element a in S, the equations e • a = a • e = a holes". -Dirtclustit (talk) 15:03, 10 May 2015 (UTC)

Monoid homomorphisms
In the section about monoid homomorphisms one can read "In contrast, a semigroup homomorphism between groups is always a group homomorphism, as it necessarily preserves the identity."

Can you please explain why this is always the case?--Suitangi (talk) 16:14, 24 July 2018 (UTC)

MapReduce
The whole section on MapReduce is written in vague terms. It's not clear what the monoid is. Also it's not clear whether it is an actual application in the sense that the monoid terminology helps one understand it, or whether it is just something that turns out to be a monoid. Unless a clearer description of the relevance can be given, I would suggest removing the section. Ebony Jackson (talk) 18:12, 2 January 2022 (UTC)

 * I suggest to make it a subsection of "Monoids in computer science", since "Reduce" is a synonym for "fold", as far as I know. The text should be copy-edited; it could follow some easy-to-grasp application example from "big data", which probably can be found in the MapReduce article. I suspect that the work of Richard Bird, Lambert Meertens etc. on algebraic methods in functional programming (Bird–Meertens formalism) is part of the theoretic foundation of MapReduce, without being recognized or acknowledged by most applied computer scientists. - Jochen Burghardt (talk) 20:07, 2 January 2022 (UTC)

Monoids in computer science
Is the operation "fold" simply taking a sequence to its product? What is the purpose of giving the more complicated displayed equation? Ebony Jackson (talk) 18:14, 2 January 2022 (UTC)

 * The first answer is "yes".
 * The second is something like this: Sequences in computer science are often built from the constructors nil:List(A) and cons:A×List(A)→List(A), which goes back to the Lisp programming language ("A" denotes the element type). Then it is natural to define a function, like fold:List(A)→A, recursively over these constructors ("structural recursion"). The "monoid multiplication", i.e. concatenation of two lists, needn't even be considered in this approach. It can, of course, be defined by recursion over nil and cons, too, and is called append in Lisp. - Jochen Burghardt (talk) 19:56, 2 January 2022 (UTC)
 * Thank you for the reply. Yes, it is pseudo-Lisp.  I think the binary operation being used here is not concatentation of elements of M*, but the binary operation on M.  The recursive definition of product of a finite sequence is already given earlier in the article, using less clumsy notation.  The section claims "any data structure can be 'folded' in a similar way, given a serialization of its elements", but this cannot be taken at face value - this certainly does not apply to every type listed at the data structure page.  I think that the section is trying to say something more than just that one can take the product of a finite sequence of elements of a monoid, since it speaks of binary trees (in terms that are too vague for me to understand).  It is also unclear what is meant by "many abstract data types can be endowed with a monoid structure" - what data types are we talking about, what is the underlying set, and what is the binary operation?  In the sentence "For instance, many iterative algorithms need to update some kind of running total at each iteration; this pattern may be elegantly expressed by a monoid operation", what does it mean to "express a pattern by a monoid operation"?  I don't want to delete the whole section, since certainly monoids do arise in computer science, but the present text is not doing justice to the topic, I feel. Ebony Jackson (talk) 22:33, 2 January 2022 (UTC)

Trace Monoids
So far as I am aware, trace monoids are always infinite. However, $$\{1, a, a^2\}$$ with $$a^3 = a^2$$ is a finite (partially) commutative monoid which is not a trace monoid. (I came to this article searching for a definition of an abstract trace monoid.) I propose changing "A monoid for which the operation is commutative for some, but not all elements is a trace monoid; trace monoids commonly occur in the theory of concurrent computation" to "One type of monoid for which the operation is commutative for some, but not necessarily all, generators is the trace monoid; trace monoids commonly occur in the theory of concurrent computation". Note that $x^{2} • x = x • x^{2}$ for all monoids, so saying 'element' is not good. --RichardW57m (talk) 16:08, 4 April 2022 (UTC)

title: Talk:Monoid


text:
Arthrobacter

Arthrobacter (from the Greek, "jointed small stick”) is a genus of bacteria that is commonly found in soil. All species in this genus are Gram-positive obligate aerobes that are rods during exponential growth and cocci in their stationary phase. Arthrobacter have a distinctive method of cell division called "snapping division" or reversion in which the outer bacterial cell wall ruptures at a joint.

Description
Arthrobacter can be grown on mineral salts pyridone broth, where colonies have a greenish metallic center on incubated at 20 C. Under the microscope, Arthrobacter appear as rods when rapidly dividing, and cocci when in stationary phase. Dividing cells may also appear as chevrons ("V" shapes). Other notable characteristics are that it can use pyridone as its sole carbon source, and that its cocci are resistant to desiccation and starvation.

Use in industry
Arthrobacter, like other bacterial genera including Brevibacterium, Microbacterium, and Corynebacterium are used for industrial production of L-glutamate. In industrial applications, Arthrobacter is often grown with low-cost sugar sources such as cane or beet molasses, starch hydrolysates from corn or cassava tubers, or tapioca. Along with sugar, ammonia and ammonium salts are added as a nitrogen source. The vitamins, minerals, and some other types of nutrients can be provided by adding corn steep liquour.

Other uses
Various Arthrobacter species have been investigated for other commercial applications. A. crystallopoietes and A. chlorophenolicus have been shown to reduce hexavalent chromium and 4-chlorophenol levels in contaminated soil, suggesting they may be useful for bioremediation. Similarly, Arthrobacter sp. strain R1 (American Type Culture Collection strain number 49987) has been shown to grow on a variety of aromatic compounds, including homocyclic compounds, such as hydroxybenzoates, as well as N-heterocycles, including pyridine and picoline.

Arthrobacter sp. H65-7 produces the enzyme inulase II that converts inulin into the medically relevant nutrient difructose anhydride.

The enzyme Alu obtained from Arthrobacter luteus is able to cleave Alu sequences which is frequently repeated in human DNA.

Species
Arthrobacter comprises the following species:

 * A. agilis (Ali-Cohen 1889) Koch et al. 1995

 * A. alkaliphilus Ding et al. 2009
 * A. alpinus Zhang et al. 2010

 * A. bambusae Park et al. 2014

 * A. bussei Flegler et al. 2020
 * "A. casei" Wenning et al. 2006
 * A. castelli Heyrman et al. 2005
 * A. celericrescens Yan et al. 2019
 * A. cheniae Yang et al. 2021

 * A. citreus Sacks 1954 (Approved Lists 1980)

 * "A. crusticola" Liu et al. 2020
 * "A. crygenae" Vasil'eva et al. 1998
 * A. cryoconiti Margesin et al. 2012

 * A. crystallopoietes Ensign and Rittenberg 1963 (Approved Lists 1980)

 * A. cupressi Zhang et al. 2012

 * A. deserti Hu et al. 2016
 * "A. dextranlyticum" Hatada et al. 2004
 * "A. dokdonellae" Koh et al. 2019

 * A. echini Lee et al. 2016

 * A. flavus Reddy et al. 2000
 * A. frigidicola Yang et al. 2021
 * A. gandavensis Storms et al. 2003

 * A. ginkgonis Cheng et al. 2017
 * "A. ginsengisoli" Siddiqi et al. 2014
 * A. glacialis Liu et al. 2019

 * A. globiformis corrig. (Conn 1928) Conn and Dimmick 1947 (Approved Lists 1980)
 * A. gyeryongensis Hoang et al. 2014
 * A. halodurans Chen et al. 2012

 * A. humicola Kageyama et al. 2008

 * "A. ipsi" Gonzalez-Dominici et al. 2021
 * A. jiangjiafuii Zhang et al. 2022

 * "A. keyseri" Eaton 2001
 * A. koreensis Lee et al. 2003
 * A. liuii Yu et al. 2015
 * A. livingstonensis Ganzert et al. 2011
 * A. luteolus Wauters et al. 2000
 * "A. luteus" Kaneko et al. 1969

 * A. methylotrophus Borodina et al. 2002
 * A. mobilis Ye et al. 2020
 * A. monumenti Heyrman et al. 2005

 * A. nanjingensis uang et al. 2015

 * "A. nitrophenolicus" Arora and Jain 2013
 * A. oryzae Kageyama et al. 2008

 * A. paludis Zhang et al. 2018
 * "A. paraffineus" Duvnjak et al. 1982
 * A. parietis Heyrman et al. 2005
 * A. pascens Lochhead and Burton 1953 (Approved Lists 1980)

 * "A. photogonimos" Phinney and Hoober 1992

 * A. pigmenti Heyrman et al. 2005
 * A. pityocampae İnce et al. 2014
 * A. pokkalii Krishnan et al. 2017

 * A. psychrochitiniphilus Wang et al. 2009
 * A. psychrolactophilus Loveland-Curtze et al. 2000

 * A. ramosus Jensen 1960 (Approved Lists 1980)
 * A. rhombi Osorio et al. 1999
 * A. roseus Reddy et al. 2002
 * A. ruber Liu et al. 2018
 * A. russicus Li et al. 2004

 * "A. saudimassiliensis" Papadioti et al. 2017

 * "A. sedimenti" Lin et al. 2020
 * "A. senegalensis" Ndiaye et al. 2019

 * A. silvisoli Yan et al. 2018
 * A. silviterrae Lee et al. 2017

 * A. stackebrandtii Tvrzová et al. 2005
 * A. subterraneus Chang et al. 2008

 * "A. sulfonylureivorans" Han et al. 2021

 * A. sunyaminii Zhang et al. 2022
 * A. tecti Heyrman et al. 2005
 * "A. terrae" Jiang et al. 2022

 * A. terricola Trinh and Kim 2021
 * A. tumbae Heyrman et al. 2005

 * A. ulcerisalmonis Kämpfer et al. 2020

 * "A. wenxiniae" Sun et al. 2022
 * A. woluwensis Funke et al. 1997
 * A. yangruifuii Ge et al. 2020
 * A. zhaoguopingii Ge et al. 2020

title: Arthrobacter


text:
Talk:Arthrobacter

Mav, I'm entirely aware that the blank slot in the table was intended for a future image. However, on my machine at least, it makes the table look very awkward. Given how long it will be before we have images for many things (and that it is entirely reasonable that we should not have images for everything), wouldn't it make more sense to leave the table in a form which looks better, and add the row when we add the image? -JG

 * IMO, no. Most writers have a hard enough time with HTML as it is so keeping the empty cell makes things that much easier for them. This is also important due to the fact that each table is potentially a template for many others. Hm. An HTML comment in the empty cell will even be better (indicating the exact place where the image should go). In my browser there is a thick blank line where the cell is but this doesn't happen for over 90% of the people reading this page (since it looks like there isn't a cell at all in IE). This, IMO, is a small price to pay for making things easier for the person who will eventually add the photo. And it might even be a good thing to have things a bit non-purty for some other people to act as a reminder that this article needs a micrograph. --mav

10% of our readership is hopefully more than the one person who will end up adding a picture. I'd imagine that if they can figure out how to add images, they can figure out how to insert them in the table, especially since they'll probably add more than one, and have a number of samples to work off of. If not, we have a number of people who don't mind helping. If you insist on having some sort of guide for the table tags already in place, maybe they could be commented out?

Arthrobacter Flashcard

1) Inoculum source

2) Enrichment strategy

3) Microscopic appearance

4) Gram reaction, respiration

5) Colony appearance

6) Other special properties

1) soil

2) mineral salts pyridone broth, 20ªC

3) log phase rods, stat. phase cocci

4) +, obligate aerobes

5) greenish metalic in center

6) snapping division (outer cell wall rupture), pyridone as C source, cocci resistant to desication & starvation, Induction (rods/cocci), Bacillary (motile rods), Reversion (rods break into cocci)

Life Cycle?
Is there any reason to leave the Life Cycle section in the article? It looks like someone wanted to make a flowchart or table out of it, but it just looks sloppy now. I'm removing the section, but here is what it consisted of:

"Induction phase (rods and cocci are mixed), Bacillary phase (motile rods predominate during exponential growth), Reversion phase (rods break into cocci) -> Induction..."

It may be interesting to make this into a sort of flow chart that could be applied to other bacteria pages. Opinions?

Vaihead (talk) 22:48, 11 December 2009 (UTC)

title: Talk:Arthrobacter


text:
Mineral salts pyridone broth

Mineral salts pyridine broth is a selective medium for bacteria that can metabolize pyridine (which is an unusual carbon source that a select few types of bacteria can use). This medium is used to isolate bacteria belonging to the genus Arthrobacter among other bacteria genera.

title: Mineral salts pyridone broth


text:
Talk:Bacillus

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 27 August 2019 and 11 December 2019. Further details are available on the course page. Student editor(s): Hlmartinez.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 15:11, 16 January 2022 (UTC)

Untitled
''Text from a flashcard I wrote. Update article as needed.'' maveric149 Bacillus Flashcard

1) Gram/Catalase rxn. (E pathway)?

2) Microscopic appearance?

3) Colony characteristics?

4) Isolation & Enrichment Strategy?

5) Representitive Species (notable attributes)?

1) +/+ (O2 as TEA –– fac. anaerobes)

2) Rods w/ lobes (oval endospores)

3) Lg., spreading w/ irregular edges

4) a) Soil (shake w/ water) b) MS agar (melted) low nutrient c) 20°C 5) B. cereus (food poisoner in milk) B. subtilis (obl. aerobe; spores survive heating ; ropiness in bread) B. coagulans (grows to pH 4.2 ; flat sour of cans)

 * Info is now in article. --mav

Gram-stained?
"A Gram stain allows one to distinguish between cocci (round) and bacilli (rod-shaped) bacteria, as well as between Gram-positive and Gram-negative bacteria (the former are stained purple, the latter red)."

Elaborate more on this to get it more accurate. Gram-staining might help to distinguish bacteria shapes, but it doesn't really have anything to do with shape does it? And "the former are stained purple, the latter red"? The Gram-negative bacterium isn't gram stained at all is it? It's completely unaffected? - Jerryseinfeld 23:59, 1 Oct 2004 (UTC)

 * Gram negative bacteria are stained (red) by a Gram stain. If you don't use a stain of some sort, you can't tell what shape the bacterium is, because you can't see it. The Gram-stain stains both Gram-negative and Gram-positive bacteria, but it stains them differentially.
 * But with an electron microscope you see the shape regardless of color don't you? - Jerryseinfeld 23:59, 1 Oct 2004 (UTC)
 * Well, you don't look through an electron microscope, so seeing here means what you see in looking at the photographic (or CRT) image produced by an electron microscope, and the sample has been treated in various ways prior to the microscopy to make the bacteria visible. - Nunh-huh 00:54, 2 Oct 2004 (UTC)

 * [1] the initial stain, crystal violet, stains both types, both Gram-positive and Gram-negative: if you stop after step one, both Gram-positive and Gram-negative bacteria are purple.
 * [2] Gram's iodine solution is added, fixing the crystal violet in the Gram-positive bacteria. If you look after this step, both Gram-positive and Gram-negative bacteria are still purple.
 * [3] The slide is then decolorized with an alcohol and actone mixture. If you look now, Gram-positive bacteria are purple, and Gram-negative are clear.
 * [4] Safranin is now applied: it is taken up by both Gram-positive and Gram-negative bacteria. The Gram-positive bacteria are already purple, and the safranin doesn't change the color much, but it does make the Gram-negative bacteria pink/red.

 * Both crystal violet and safranin are taken up by both Gram-negative and Gram-positive bacteria: the step/characteristic that allows their differentiation is the decolorization step, which removes the crystal violet from the gram-negative bacteria only (at least it does if it's done right: it's not an exact differentiation and there's some element of skill in the decolorizaiton step).

 * How does it work? Gram-positive cells have a much thicker outer layer of peptidoglycan than do Gram-negative. When the iodine is added to a crystal violet-stained cell, it combines to form a larger molecule that precipitates out within the cell. The decolorizing mixture causes dehydration of the multilayered peptidoglycan in the gram-positive call wall, thus decreasing the space between the molecules and causing the cell wall to trap the crystal violet-iodine complex within the cell. But in gram-negative bacteria, the decolorizing mixture acts as a lipid solvent and dissolves the outer membrane of the gram-negative cell wall. The thin layer of peptidoglycan is unable to retain the crystal violet-iodine complex and the cell is decolorized.

 * Too much info for here I think, though perhaps it can be added to Gram stain - Nunh-huh 22:25, 28 Sep 2004 (UTC)

You can make out cocci and bacilli through the light microscope without any staining. Gram-staining does help, but so do some other things, and I don't think it makes sense to discuss the techniques here. Josh

Isolation
Regarding this:

An easy way to isolate a Bacillus species is by placing non-sterile soil in a test tube with water, shake, place in melted mannitol salts agar, and incubate at room temperature for at least a day.

Its not that accurate, even if you dilution plate on to mannitol salts, you will get many different organisms growing. I know because I have done this, I got about 55 OTU's (operational taxonomic units) out of soil. So yep you will be some Bacillus, but lots of other species also. Onco p53 06:19, 18 Jan 2005 (UTC)

Question, does Bacillus species even grow in the high salt concentrations found on Mannitol Salts Plates? jvdimas

Paenbacillus
I noticed someone added Bacillus larvae here, but this has actually been reclassified as Paenbacillus larvae - it should now probably go under a separate entry for genus Paenbacillus, although I left it here for the moment. Any thoughts?
 * Change it to Paenibacillus. note the spelling. Onco p53 19:03, 17 Feb 2005 (UTC)

Bacillus sp.
I just read about something called "Bacillus sp," here:  There's no Wikipedia article. Should there be one? Badagnani 04:05, 25 June 2006 (UTC)
 * Bacillus sp. is bacillus species. It just means all bacteria that are of the genus bacillus, such as bacillus cereus or bacillus subtilis. So this page is about bacillus species itself. ClamsonJ 20:30, 15 August 2007 (UTC)ClamsonJ

Escherichia coli, gram negative bacillus
I realize the article is about the genus bacillus, nevertheless there should be an explanation somewhere in the article that the cell morphology term is different from the genus. Bacillus in morphology context does not automatically mean gram-positive, as E. Coli proves. -- —The preceding unsigned comment was added by Phange (talk • contribs).

It should be noted that the morphology of E. coli is not bacilli, but rather coccibacilli.

ipo0jkjjyuk??
Has there been any vandalism disrupting the article unnoticed by anyone? Quote from the text:

B. subtilis is the first bacterium for which the role of a ipo0jkjjyuk,mhn actin-like cytoskeleton...

It is obvious that the ipo0jkjjyuk doesn't belong there... is it? —Preceding unsigned comment added by 141.51.190.118 (talk) 13:35, 5 January 2008 (UTC)

Gram-confusion
I'm confused as to weather Bacillus thermoproteolyticus is gram-positive or gram-negative. This source says its negative while this source lists it as positive. Can anyone clear this confusion up for me? K.murphy (talk) 15:12, 12 June 2008 (UTC)

ANSWER: all Bacteria in the Family Bacillus are gram pos.... —Preceding unsigned comment added by 162.119.238.162 (talk) 06:43, 10 June 2009 (UTC)

obligate aerobe?
This page says Bacillus can be a facultative anaerobe. http://www.splammo.net/bact102/102bacillus.html —Preceding unsigned comment added by 129.7.239.171 (talk) 20:48, 27 February 2010 (UTC) rakimykeny —Preceding unsigned comment added by 69.211.96.188 (talk) 22:45, 21 March 2010 (UTC)

"Bacillus microorganisms were found to be an inherent part of the wild African moose's jejunial tract, which has proven to be a significant counterpart of the microbiological research field."

I removed this because it seems too preposterous for just a "citation needed". Please reinsert if you can find a source. Gigemag76 (talk) 14:06, 21 May 2010 (UTC)

Phylum
Bacillus is part of the Phylum: Firmicutes. The term division is used traditionally in botany. — Preceding unsigned comment added by 82.130.85.88 (talk) 10:01, 4 February 2014 (UTC)

Characteristics of Bacillus spp.
This section and the included table does not belong and appears to be self promotion. (https://en.wikipedia.org/wiki/Bacillus#Characteristics_of_Bacillus_spp.). Its a table talking about characteristics of some newly discovered bacillus species, it only represents the 9 species from the study and is not relevant to the whole characteristics of the genus. Bacillus spp. is the designation given to any new Bacillus species discovered before its given a proper species classification, meaning that it's not only temporarily representative of these 9 species but also misleadingly represents all other of the Bacillus species waiting for classification. Being misleading and appearing as self promotion it feels as though it should be removed. And personally, as an actual microbiologist its useless information crowding an otherwise useful page. ZeBeowulf (talk) 18:48, 18 August 2022 (UTC)

Bacillus
Apan 58.69.105.37 (talk) 10:33, 5 December 2022 (UTC)

title: Talk:Bacillus