OpenLLM-France/wikimedia huggingface dataset:
# Cauchy's convergence test

The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. This convergence criterion is named after Augustin-Louis Cauchy who published it in his textbook Cours d'Analyse 1821.

## Statement

A series $\sum _{i=0}^{\infty }a_{i}$ is convergent if and only if for every $\varepsilon >0$ there is a natural number $N$ such that
    $|a_{n+1}+a_{n+2}+\cdots +a_{n+p}|<\varepsilon$
holds for all $n>N$ and all $p\geq 1$.

## Explanation

$(x_{n}),$
$x_{n}$
$n$
The test works because the space $\mathbb {R}$ of real numbers and the space $\mathbb {C}$ of complex numbers (with the metric given by the absolute value) are both complete. From here, the series is convergent if and only if the partial sums
    $s_{n}:=\sum _{i=0}^{n}a_{i}$
are a Cauchy sequence.
Cauchy's convergence test can only be used in complete metric spaces (such as $\mathbb {R}$ and $\mathbb {C}$), which are spaces where all Cauchy sequences converge. This is because we need only show that its elements become arbitrarily close to each other after a finite progression in the sequence to prove the series converges.

## Proof

We can use the results about convergence of the sequence of partial sums of the infinite series and apply them to the convergence of the infinite series itself. The Cauchy Criterion test is one such application. For any real sequence $a_{k}$, the above results on convergence imply that the infinite series
    $\sum _{k=1}^{\infty }a_{k}$
converges if and only if for every $\varepsilon >0$ there is a number N, such that m ≥ n ≥ N imply
    $|s_{m}-s_{n}|=\left|\sum _{k=n+1}^{m}a_{k}\right|<\varepsilon .$$^{:188}$
Probably the most interesting part of this theorem is that the Cauchy condition implies the existence of the limit: this is indeed related to the completeness of the real line. The Cauchy criterion can be generalized to a variety of situations, which can all be loosely summarized as "a vanishing oscillation condition is equivalent to convergence".
This article incorporates material from Cauchy criterion for convergence on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
# Catá

The catá or guagua is a Cuban percussion instrument which originated in the eastern region of the island. It is classified as a directly struck idiophone, traditionally made out of a hollowed tree trunk, which the player hits with wooden sticks or mallets. The resulting sound is dry and penetrating, similar to that of the claves, although with a different pitch. Of Congolese origin, it is an essential instrument in tumba francesa, yuka and some rumba ensembles.

## Use

The catá is primarily used in the tumba francesa tradition from eastern Cuba, which originated in the early 19th century. Its role in tumba francesa is to provide the main rhythm in the form of a cinquillo pattern. In fact, in Saint Domingue (current Haiti), from where the tumba francesa was imported, the word catá (of Bantu origin), denoted this rhythm. The catá is considered a reconstruction of idiophones from the Congo region, brought by slaves to the Caribbean.
The catá has been incorporated into Cuban rumba, where it "locks" with the claves, establishing the clave rhythm. In the context of rumba, the term guagua is more common, as in guaguancó, or palitos, which refers to the sticks. Nonetheless, these have been replaced by the caja china (wood block) or the more durable jam block, made of plastic. The guagua is also used in yuka, one of the oldest genres of Afro-Cuban percussion.
Musicologists from Guantánamo, such as Ramón Gómez Blanco, hypothesize that the catá pattern was adapted by the marímbula players in changüí, highlighting the common Bantu roots of tumba francesa and changüí.
# Glasgow Cross

Glasgow Cross is at the hub of the ancient royal burgh and now city of Glasgow, Scotland, close to its first crossing over the River Clyde. It marks the notional boundary between the city centre and the East End
As a major junction at the gateway into the city centre, its five streets run: north up the High Street to Glasgow Cathedral, Cathedral Square and the Royal Infirmary; east along Gallowgate and London Road, close to St Andrew's Square; south on the Saltmarket to Glasgow Green and the Justiciary Buildings; and west along Trongate continuing as Argyle Street towards St Enoch Square and Buchanan Street.
Its most recognisable features are the Tolbooth Steeple, the surviving part of the 17th century Glasgow Tolbooth, and the mercat cross replica commissioned in 1929 by William George Black, and designed by architect Edith Hughes.
Linked to the Tolbooth stood the Tontine Hotel and its Assembly Rooms, designed from 1737 by architect Allan Dreghorn with adaptations in 1781 by architect William Hamilton of St Andrew's Square. The Tontine was the exchange centre of early mercantile business and the focal point of political and social gatherings. A number of artist paintings over the centuries depict Glasgow Cross, the Tolbooth and Tontine. In front of the Tontine was placed the equestrian statue of King William III, erected in 1734; now sited at Cathedral Square. After the Tolbooth Steeple, the nearby Tron Theatre, formerly the Tron Kirk, built in 1794 is one of the oldest buildings in the city.
The presently disused Glasgow Cross railway station sits beneath the junction.
* Glasgow Cross with Tolbooth Steeple and Mercat Cross.
* Tontine Buildings, Tolbooth, Steeple and King William equestrian statue at Glasgow Cross, 1868 photograph by Thomas Annan
* Mercat Cross and Mercat Building at Glasgow Cross
# Colobothea guatemalena

Colobothea guatemalena is a species of beetle in the family Cerambycidae. It was described by Henry Walter Bates in 1881.
# Edward Ford

Edward Ford may refer to:
* Edward Ford (surgeon) (1746–1809), British surgeon
* Edward Ford (courtier) (1910–2006), courtier in the Royal Household of King George VI and Queen Elizabeth II
* Edward Ford (soldier) (1605–1670), English soldier and inventor
* Edward Ford (physician) (1902–1986), Australian soldier, academic and physician
* Edward Onslow Ford (1852–1901), English sculptor
* Edward Ford (born 1914), brother of United States president Gerald Ford
* Edward Hastings Ford (1887–1970), vaudeville comedian who created the radio show Can You Top This?
* Edward E. Ford (1894–1963), American philanthropist and businessman serving on the board of directors of IBM
* Whitey Ford (Edward Charles Ford, 1928–2020), American baseball pitcher
# Forest of the Gods (film)

Forest of the Gods (Lithuanian: Dievų miškas) is a 2005 film, directed by Algimantas Puipa, based on the Balys Sruoga novel of the same name, published originally in 1957.

## Plot

This story is about one man — who is an artist and an intellectual — he was imprisoned by two brutal regimes, the Nazis and the Soviets. 'The Professor' is a man who lives by his own personal version of the Ten Commandments. After miraculously surviving imprisonment in a Nazi concentration camp through a bit of ironic fate, he writes a memoir of his life, which becomes the target of the Soviet censors.

## Reception

The film became the most profitable film released after Lithuania restored its independence.
The 98-year-old Vladislovas Telksnys, the only Lithuanian survivor of the Stutthof concentration camp in 2013, referred to the movie as "a piece of nonsense". In particular he referred to the scene depicting a Gestapo officer marching and a woman with an umbrella following behind. According to Telksnys, "there were no such things".
# Hugh McQuillan

Alvin Hugh McQuillan (September 15, 1895 – August 26, 1947) was an American professional baseball player. He played in Major League Baseball as a pitcher from 1918 to 1927. He played for the Boston Braves and New York Giants.
In 1561.2 innings pitched in 279 games over 10 seasons, McQuillan compiled an 88-94 won-loss record with a 3.83 Earned Run Average, allowing 1703 hits, 489 bases on balls and recording 446 strikeouts. He pitched 10 shutouts and recorded 17 saves. As a hitter, he posted a .195 batting average (103-for-527) with 45 runs, 2 home runs and 37 RBI.
# Wilson, Garrett County, Maryland

Wilson is an unincorporated community in Garrett County, Maryland, United States. Wilson is located on a CSX Transportation line 7.5 miles (12.1 km) east-northeast of Oakland.
# IBC (bus manufacturer)

IBC was an Australian bus chassis manufacturer based in Brisbane.

## History

IBC was founded in the 1963 by Ian & Bruce Campbell and manufactured bus and coach chassis powered by Caterpillar or General Motors engines. In 1980 it had a chassis bodied by Pressed Metal Corporation to the same style as being delivered to the Urban Transit Authority as a demonstrator. It ceased trading in October 1991.
# IBCA

IBCA may refer to:
* International Biennale of Contemporary Art 2005: A Second Sight (IBCA 2005)
* International Business Companies Act
* International Braille Chess Association, a chess organization for the visually impaired
* Inter Bank Credit Advice, (description needed)
* Israel, Britain and the Commonwealth Association
* Investment Banking Council of America
* Department of Interior Board of Contract Appeals
* International Brewing & Cider Awards
# Zahra

Zahra or Zehra may refer to:

## Buildings and institutions

* Alzahra University, female-only university in Tehran, Iran
* Az-Zahraa Islamic Academy, school in Richmond, British Columbia, Canada
* Al-Zahra Mosque, Sydney, Australia
* Behesht-e Zahra, cemetery in Tehran, Iran
* Ennejma Ezzahra ("Star of Zahra"), palace at Sidi Bou Said, northern Tunisia

## People

* Zahra (name), female given name and surname, also spelt Zehra, Zohra, and other variants
* Abd al-Zahra, male given name

## Places

* Zahra, Ardabil, village in Iran
* Zahra, Kuwait, an area in Kuwait
* Žehra, village and municipality in Slovakia

## Other uses

* Zahra, film by Mohammad Bakri (2007)
* Zahra Foundation Australia, anti-domestic violence organisation in Adelaide, South Australia
* Zahrah, title character of Nnedi Okorafor's children's novel Zahrah the Windseeker
# Zakrzewski

Zakrzewski (feminine: Zakrzewska, plural: Zakrzewscy) is a Polish surname. At the beginning of the 1990s there were approximately 26,210 people in Poland with this surname.
People named Zakrzewski:
* Alex Zakrzewski, American television director
* Andrzej Zakrzewski (1941–2000), Polish politician
* Arseni Zakrzewski (1783–1865; Arseniy Zakrevskiy), Russian politician
* Barbara Maria Zakrzewska-Nikiporczyk (born 1946), Polish composer and musicologist
* Bogdan Zakrzewski (1916–2011), Polish literary historian
* Dariusz Zakrzewski (born 1961), Polish cyclist
* Eulalia Zakrzewska-Rolińska (b. 1946), Polish sport shooter
* Henryk Zakrzewski (1897–1973), Polish politician
* Ignacy Wyssogota Zakrzewski (1745–1802), Polish nobleman and politician
* Jadwiga Zakrzewska (born 1950), Polish politician
* Jan Dołęga-Zakrzewski (1866–1936), Polish surveyor, activist and publicist
* Jan Andrzej Zakrzewski (1920–2007), Polish journalist, writer and translator
* Jan Zakrzewski (athlete) (born 1970), Polish athlete
* Janina Zakrzewska (1928–1995), Polish lawyer
* Janusz Andrzej Zakrzewski (1932–2008), Polish physicist
* Joasia Zakrzewski (born 1976), Scottish ultrarunner
* John Zakrzewski (born 1982), French pentathlete
* Karolina Zakrzewska, Polish model
* Kazimierz Zakrzewski (1900–1941), Polish historian and publicist
* Konstanty Zakrzewski (1876–1948), Polish physicist
* Ksawery Zakrzewski (1876–1915), Polish doctor and activist
* Łukasz Zakrzewski (born 1984), Polish sailor
* Marie Elizabeth Zakrzewska (1829–1902), German-born physician
* Mirosława Zakrzewska-Kotula (1932–1990), Polish volleyball, basketball, handball player and coach
* Pierre Zakrzewski (1966–2022), Irish photographer and journalist
* Roman Zakrzewski (1955–2014), Polish painter
* Ryszard Zakrzewski (lived in the 19th century), Polish traveler, topographer and officer
* Stanisław Zakrzewski (1873–1936), Polish historian
* Stanisław Zenon Zakrzewski (1890–1976), Polish sailing activist
* Tadeusz Paweł Zakrzewski (1883–1961), Polish Catholic priest and bishop
* Wincenty Zakrzewski (1844–1918), Polish historian
* Witold Zakrzewski (1903–1987), Polish sailing activist
* Włodzimierz Zakrzewski (1916–1992), Polish painter, graphician and poster artist
* Zbigniew Zakrzewski (economist) (1912–1992), Polish economist
* Zbigniew Zakrzewski (soccer player) (b. 1981), Polish football (soccer) player
* Zofia Zakrzewska (1916–1999), Polish scoutmaster
# Alpine speedwell

Alpine speedwell is a common name for several plants and may refer to:
* Veronica alpina, native to Europe, Asia, and North America
* Veronica wormskjoldii, native to North America
# Hôtel de Boadès

The Hôtel de Boadès is a listed hôtel particulier in Aix-en-Provence.

## Location

It is located at 8, place Jeanne d'Arc in the center of Aix-en-Provence.

## History

In 1935, Blanche d’Estienne de Saint Jean, an heiress to the Château du Grand-Saint-Jean, donated it the city of Aix-en-Provence and asked them to donate the proceeds to the Academy of Aix-en-Provence.
It is now home to city administration offices.

## Heritage significance

It has been listed as a historical building since 1947.
# Windhorst

Windhorst may refer to:

## People with the surname

* Brian Windhorst (born 1978), American sportswriter
* Fritz Windhorst (born 1935), American attorney and politician
* Lars Windhorst (born 1976), German entrepreneur
* Rogier Windhorst (born 1954), Dutch astronomer and professor
* Stephen J. Windhorst (born 1957), American judge
* Uwe Windhorst (born 1946), German scientist
# Winship-Smernes Building

The Winship-Smernes Building, at 948 Main St. in Napa, California, was built in 1888. It was designed by Napa architect Luther Turton in Italianate style. It was listed on the National Register of Historic Places in 1977.
It has also been known as the Hennessey Building.
The National Register nomination document from 1977 should be available online, but in 2019 only the accompanying photo is found.
# IBM 416

The IBM 416 was a tabulating machine released in 1941 and produced in Milan.
# Hämeen-Anttila

Hämeen-Anttila is a Finnish-language surname. Notable people with the surname include:
* Jaakko Hämeen-Anttila (born 1963), Finnish academic researcher
* Virpi Hämeen-Anttila (born 1958), Finnish writer
# Woman's Commonwealth

The Woman's Commonwealth (also Belton Sanctificationists and Sisters of Sanctification) was a women's land-based commune first established in Belton, Texas. It was founded in the late 1870s to early 1880s by Martha McWhirter and her women's bible study group on land that was inherited when the women's husbands died or quit the home.

## Members

Residents of the commune were women and their dependent children; many of the women fled abusive homes to join the community. At one point, there were between 42 and 50 women members on record, including at least one African American woman who is thought to have been a former slave.

## Ideology

The Sisters embraced first wave feminist ideologies, and sought spiritual, economic, and social equality for women. To that end, they practiced celibacy as a way to liberate women from the spiritual degradation of heterosexual intercourse, the oppressive needs of children and child rearing, and male violence. In the 1880s, the citizens of Belton blamed the Sanctificationists for rising separation and divorce rates, and of undermining the meaning of marriage through their practice of celibacy.

## History

The Sanctificationists were economically successful; they ran several boarding houses and two hotels, formed holding companies to manage their properties, and operated two farms to provide food for their multiple dining rooms. They started the first public library in Belton, the Woman's Wednesday Club Library, out of one of their boarding houses.
In 1899, the entire commune moved to Washington, DC where they opened boarding houses and a hotel, and participated in urban feminist organizations. In 1903, there were ten remaining members who purchased a farm in rural Maryland to provide food for their urban dining halls, and to provide a pastoral retreat for themselves in a rural landscape. McWhirter died in 1904, and the commune began a slow decline.
The last member of the commune died in 1983 at the age of 101.

## Impact

The George and Martha McWhirter House at 400 North Pearl St., Belton, Texas, is on the National Register of Historic Places listings in Bell County, Texas. At the address, there is a historical marker dedicated to the Sanctificationists. Jan Berliner Statman considers the Woman's Commonwealth to be one of the first women's shelters in the United States.
A brief article published in the lesbian separatist periodical, Austindyke (alternately spelled as Austin Dyke), in 1979 and then reprinted in Sisters United in 1980 described the Woman's Commonwealth as a forerunner of the lesbian land movement. It is unclear whether the Sanctificationists influenced the movement that flourished in the 1970s and 1980s.
# Altra

Altra may refer to:

## Places

* Altra College, a school in Amsterdam, Netherlands
* Altra, Nordland, an island in Alstahaug municipality in Nordland county, Norway

## Businesses

* Altra Industrial Motion, a power transmission products manufacturer
* Altra Running, an athletic footwear company

## Other

* Nissan Altra, a model of car
* L'Altra, an American band formed in 1999
* L'Altra (film), a 1947 Italian film
* Altra Running, an athletic shoe company
# Altran Praxis

Altran UK (formerly known as Altran Praxis, Praxis High Integrity Systems, Praxis Critical Systems, Altran Xype, Xype and Altran Technologies) is a division of parent company Altran. Altran Praxis was a British software house that specialised in critical systems. This role is continued under the banner of high-tech engineering consultancy services provided by the rest of the Altran group.
The division formerly known as Praxis (the critical systems specialists) is based in SouthGate, Bath, England, close to Bath Spa railway station, and also has offices in London, Loughborough, Paris, Sophia Antipolis, and Bangalore.
Altran UK as a whole has offices in Bath, Bristol, London, Loughborough, Manchester, Slough and Coventry.

## History

The company Praxis Systems Limited was founded by Martyn Thomas and David Bean in 1983: it was incorporated on 1 June 1983 and commenced business on 1 July 1983. On 28 June 1985 it became a Public limited company Praxis Systems plc. Until 1988, Praxis was owned almost entirely by its staff. In 1988 Praxis obtained venture capital finance in order to provide funds for future acquisitions and working capital for continued growth. On 27 November 1992 Praxis was acquired by Deloitte Consulting (then known as Touche Ross), an international firm of accountants and management consultants. The critical systems part of the company was acquired by the Altran Group in 1997. In 2004, Praxis Critical Systems and HIS Consulting merged to form Praxis High Integrity Systems. In January 2010, the company was merged with SC2 by Altran to form Altran Praxis.The company has since been rebranded to Altran along with Altran Xype and Altran Technologies. In December 2012, AdaCore along with Altran Praxis released SPARK Pro 11. In 2013, Altran acquired Sentaca, a specialty telecoms consultancy.
A distinguishing feature of the former Praxis office's is its extensive use of formal methods such as the Z notation and the SPARK toolset (acquired through the takeover of the developers Program Validation Limited in 1994) in its approach to improving the reliability of software engineering. A major project using Z has been an enhancement for the United Kingdom's National Air Traffic Services (NATS).
# Altpert

Altpert (died 790) was the Abbot of Farfa from the death of Ragambald in 786 until his own death a few years later. He was described by Gregory of Catino, writing some three centuries later, as having been born in Paris "of the Gauls" (Galliarum), presumably meaning that he was a Romance-speaking subject of the Carolingians. He increased the patronage of the abbey compared to his predecessor, but Farfa was still less successful in seeking out grants and donations than it had been under the local abbot Probatus. Altpert received a donation of lands at Rabenno from Duke Hildeprand of Spoleto, two other donations and one oblation.
# Altoviti family

Altoviti may refer to:
* Altoviti, prominent noble family of Florence, Italy
* Bindo Altoviti (1491 - 1557), banker and patron of the arts
* Portrait of Bindo Altoviti, painting by Raphael commissioned by Bindo Altoviti
* Madonna dell'Impanata, painting by Raphael commissioned by Bindo Altoviti
* Antonio Altoviti (1521 - 1573), Archbishop of Florence
* Giacomo Altoviti (1604 - 1693), Patriarch of Antiochia and Archbishop of Athenae
* Banking families
# Amazing Thailand

Amazing Thailand is a promotional slogan used by the Tourism Authority of Thailand (TAT) to promote tourism to the country. It was originally conceived as a two-year campaign to span the years 1998 and 1999, but was extended for several years and has since become a perennial slogan of the TAT.
The original Amazing Thailand campaign was conceived in response to the 1997 financial crisis which crippled the country's economy, in order to leverage the fall in value of the baht to promote tourism and bring in foreign spending. It featured materials with imagery conveying a striking, sensual aesthetic, and identified "nine facets of travel" in its promotion.
The campaign—which was planned to coincide with two major events: the 1998 Asian Games in Bangkok, and the 72th birthday anniversary of King Bhumibol Adulyadej in 1999—was well received, and was extended into the following years. Amazing Thailand was used as a primary promotional slogan until 2004, and was revived in 2007. It is now usually expanded upon with several taglines or variants on the wording. These include "Amazing Thailand Always Amazes You", introduced in 2011, "Amazing Thailand: It Begins with the People" in 2014, and "Amazing Thailand, Amazing New Chapters" in 2022.
# Amazing Things

Amazing Things may refer to:
* Amazing Things (Runrig album), released in 1993
* Amazing Things (Don Broco album), released in 2021
# Zbrodzice

Zbrodzice is a village in the administrative district of Gmina Busko-Zdrój, within Busko County, Świętokrzyskie Voivodeship, in south-central Poland. It lies approximately 4 kilometres (2 mi) north-east of Busko-Zdrój and 46 km (29 mi) south of the regional capital Kielce.
# Amboseli Elephant Research Project

The Amboseli Elephant Research Project is a long-term research project on the ethology of the African elephant, operated by the nonprofit Amboseli Trust for Elephants. The project studies the elephant's social behavior, age structure and population dynamics. It is the longest running study of elephant behavior in the wild, and has gathered data on life histories and association patterns for more than 2,000 individual elephants.
The research project was initiated in 1972 by Cynthia Moss and Harvey Croze in Amboseli National Park in the south of Kenya. Relatively few poachers have been active in Amboseli Park's approximately 390 km² area. This is especially due to the Maasai people, and the constant presence of tourists and researchers. Thus, Amboseli is one of the few regions in Africa where the age structure of elephants has remained undistorted. The area is monitored by game wardens and scientists throughout the year.
The subjects of the Amboseli Elephant Research Project, mostly notably the elephant matriarch Echo, have been described at length in documentaries on PBS and Animal Planet.
# Amblyseius kokufuensis

Amblyseius kokufuensis is a species of mite in the family Phytoseiidae.
# Amblyseius koreaensis

Amblyseius koreaensis is a species of mite in the family Phytoseiidae.