hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Law of trichotomy
In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero.

More generally, a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of xRy, yRx and x = y holds.  Writing R as <, this is stated in formal logic as:

With this definition, the law of trichotomy states that < is a trichotomous relation on the set of real numbers.
In other words, if x and y are real numbers, then exactly one of the following must be true: x<y, x=y, y<x.

Set (mathematics)
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, geometric shapes, variables, or other sets.  A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.  Instead, sets serve as foundational objects whose behavior is described by axioms modeled on intuition about collections, and then essentially all other mathematical objects are rigorously defined in terms of sets.

Set theory studies possible axiom systems and their consequences.
Since the first half of the 20th century, ZFC (Zermelo–Fraenkel set theory with the axiom of choice) has been the axiom system most commonly used.
Horningsea Park, New South Wales
Horningsea Park is a suburb of Sydney, in the state of New South Wales, Australia. Horningsea Park is located 39 kilometres south-west of the Sydney central business district, in the local government area of the City of Liverpool and is part of the Greater Western Sydney region.

Vaiben Solomon
Vaiben Solomon (abt 1800 – 21 June 1860) was a Jewish-English convict who, with his brother Emanuel, was transported for larceny to New South Wales in 1818. Despite further brushes with the law, Solomon and his brother seized business opportunities and became prosperous Sydney merchants. The brothers were later joined by more of their siblings, and became patriarchs of a family line that would go onto make its mark on Australia business and politics, particularly in New South Wales and South Australia.
D'Orsi
D'Orsi is a surname of Italian origin. Notable people with the surname include:

Achille D'Orsi (1845–1929), Italian sculptor from Naples

Angelo d'Orsi (b. 1947), Italian historian

Domenico D'Orsi (1930–2010), Italian philosopher

Eugenio D'Orsi (b. 1958), Italian politician, president of the Province of Agrigento

Juan Zanassi, born Juan Francisco Zanassi D'Orsi (1947–2022), Argentine rower and journalist

Libero D'Orsi (1888–1977), Italian archaeologist

Lucy D'Orsi (born 1969), British police officer

Ugo D'Orsi (1897-1964), Brazilian-American animator

Umberto D'Orsi (1929–1976), Italian character actor and comedian

Fictional characters

Enrico D'Orsi, played by Jean-Louis Trintignant in the Italian film La terrazza (1980)

Commander D'Orsi, played by Omar Sy in the French film The Wolf's Call (2019)

Lucy D'Orsi
Lucy Clare D'Orsi, CVO, QPM (née Copson; born December 1969) is a British police officer. Since March 2021, she has served as chief constable of British Transport Police. She was deputy assistant commissioner in the Metropolitan Police Service, with responsibility for the Protection Command.
Koty, Pisz County
Koty (pronounced [ˈkɔtɨ], German: Kotten) was a village in the administrative district of Gmina Biała Piska, within Pisz County, Warmian-Masurian Voivodeship, in northern Poland. The town no longer exists, as the region was converted into a military training ground, the Poligon Orzysz. It lay about a kilometer southwest of Zdedy, and about 112 km (70 mi) east of the regional capital Olsztyn.

Historically belonging to the Masurian cultural region, Koty was established in the mid-15th Century, and its population was entirely Lutheran by the 20th Century. Its name is the Polish word for "cats."

During World War I, 52 soldiers were buried in the town's cemetery, Of them, 45 were German, 3 were Russian, and 4 were unidentified.

Zdedy
Zdedy [ˈzdɛdɨ] is a village in the administrative district of Gmina Ełk, within Ełk County, Warmian-Masurian Voivodeship, in northern Poland. It lies approximately 13 km (8 mi) south-west of Ełk and 112 km (70 mi) east of the regional capital Olsztyn.
Francis Ferran
Francis Patrick Ferran (died 10 June 1923) was an Irish Sinn Féin politician and medical practitioner. He was elected unopposed as a Sinn Féin Teachta Dála (TD) to the 2nd Dáil at the 1921 elections for the Sligo–Mayo East constituency. He opposed the Anglo-Irish Treaty and voted against it. He was elected as an anti-Treaty Sinn Féin TD at the 1922 general election but did not take his seat. He died while imprisoned by the pro-Treaty government during the Irish Civil War at the Curragh Camp in 1923.

1921 Northern Ireland and Southern Ireland general elections
General elections took place in Ireland on 24 May 1921 to elect members of the House of Commons of Northern Ireland and the House of Commons of Southern Ireland. These legislatures had been established by the Government of Ireland Act 1920, which granted Home Rule to a partitioned Ireland within the United Kingdom.

The Ulster Unionist Party (UUP) won a landslide majority in Northern Ireland. In the area designated as Southern Ireland, Sinn Féin candidates were elected unopposed in 124 of the 128 seats.

Only the Northern Ireland House of Commons actually sat as a functional body; the Sinn Féin candidates elected across Ireland boycotted both institutions, and instead assembled as the Second Dáil.
Alicia Frost
Alicia Frost (born 20 September 1980) is a former Australian rugby union player.

Frost was named in Australia's squad for the 2006 Rugby World Cup in Canada. She made her test debut for the Wallaroos against South Africa in their opening match. She started in their 18–14 victory over Ireland for seventh place.

In 2007, she was a member of the Wallaroos team that played against the Black Ferns for the O'Reilly Cup.

South Africa women's national rugby union team
The South Africa women's national rugby union team represents South Africa in women's international rugby union and is governed by the South African Rugby Union. They have appeared in five World Cups since their debut in the 2006 Women's Rugby World Cup.
Darwin Quintero
Carlos Darwin Quintero Villalba (born 19 September 1987) is a Colombian professional footballer who plays as an attacking midfielder for Categoría Primera A club Deportivo Pereira. Quintero is also known by his nickname of El Científico del Gol (The Goal Scientist).  He has played various roles throughout his career, spending time leading the line as a striker, playing out wide as a winger, and playing underneath another striker as a second striker and central attacking midfielder throughout his career.  His main attributes throughout his career have been his pace, creativity, and dribbling ability.

2011–12 Mexican Primera División season
The 2011–12 Primera División Profesional was the 65th professional top-flight football league season in Mexico. The season was split into two tournaments: the Torneo Apertura and the Torneo Clausura; each of identical format and  contested by the same eighteen teams.
Priory Records
Priory Records is a record company in the UK founded in 1980, and devoted mostly to church music and organ music.
Important projects have included the complete Psalms sung by cathedral choirs to Anglican chant, all of the Magnificat and Nunc dimittis settings by Herbert Howells, the "British Church Composer Series", the "Choral and Music from English Cathedrals", the "Music for Evensong" and, more recently, all the hymns in the complete New English Hymnal Series. There are also three discs of the Communion Service settings of Stanford and four further discs featuring settings of the Te Deum and Jubilate (by various composers).

Priory has made over 1000 recordings over the life of the company. Around 600 of these were commercial album releases, with the remaining 400 produced as private pressings.

Te Deum
The Te Deum (/teɪ ˈdeɪəm/ or /tiː ˈdiːəm/, Latin: [te ˈde.um]; from its incipit, Te Deum laudamus (Latin for 'Thee, God, we praise')) is a Latin Christian hymn traditionally ascribed to a date before AD 500, but perhaps with antecedents that place it much earlier. It is central to the Ambrosian hymnal, which spread throughout the Latin Church with other parts of the Ambrosian Rite of Milan in the 6th to 8th centuries. It is sometimes known as the Ambrosian Hymn, although authorship by Saint Ambrose is unlikely. The term Te Deum can also refer to a short religious service (of blessing or thanks) that is based upon the hymn.

It continues in use in many contexts by several denominations. In particular it is the core of a short church service of thanksgiving held, often at short notice, to celebrate good news such as a military victory, the signing of a peace treaty, or the birth of a royal child.
Ricardo Burillo
Ricardo Burillo Stholle (27 March 1891 – 21 July 1939) was a Spanish police and military officer who played an important role during the Spanish Civil War. As the police chief in Barcelona, he was responsible for the repression and dismantling of the POUM in 1937. Throughout the war, he became commander of several military units, such as the 9th Division, the III Army Corps and the Extremaduran Army.

In Franco's historiography, he has been identified as one of the top Republican leaders who was responsible for the murder of the right-wing politician José Calvo Sotelo, an accusation that Burillo always rejected.

POUM
The Workers' Party of Marxist Unification (Spanish: Partido Obrero de Unificación Marxista, POUM; Catalan: Partit Obrer d'Unificació Marxista, POUM) was a Spanish communist party formed during the Second Republic and mainly active around the Spanish Civil War. It was formed by the fusion of the Trotskyist Communist Left of Spain (Izquierda Comunista de España, ICE) and the Workers and Peasants' Bloc (BOC, affiliated with the Right Opposition) against the will of Leon Trotsky, with whom the former broke.
NASCAR Busch Series at Nazareth Speedway
Stock car races in the now-NASCAR Xfinity Series were held at Nazareth Speedway in Nazareth, Pennsylvania between 1988 to 2004, after the owners, International Speedway Corporation, closed the facility. The race was replaced with a race (currently known as Mission 200 at The Glen) at Watkins Glen, another ISC-owned track.

The race was originally held for 300 laps, but shortened to 200 laps in 1991. Tim Fedewa and Ron Hornaday Jr. are the only two drivers with multiple wins in this race, both winning the event twice.

After the closure of the track, the Xfinity Series would return to racing in Pennsylvania when Pocono Raceway held its inaugural Xfinity Series event, the Pocono Green 250 in 2016. It was won by Kyle Larson after it was shortened by rain showers after just 53 of the scheduled 100 laps. Elliott Sadler was the only former Nazareth winner to start that race.

Tim Fedewa
Timothy Troy Fedewa (pronounced "fee-doo-wuh"; born May 9, 1967) is an American professional racing driver and spotter. He works for Team Penske as the spotter for Ryan Blaney's No. 12 Ford Mustang Dark Horse in the NASCAR Cup Series.

As a driver, Fedewa previously competed in the NASCAR Busch Series (now Xfinity), NASCAR Craftsman Truck Series, American Speed Association and ARTGO. As a spotter, Fedewa previously worked for Stewart–Haas Racing as a spotter in the Cup Series for their No. 4 car driven by Kevin Harvick and in the Xfinity Series for their No. 98 car driven by Riley Herbst.
Yasu District, Shiga
Yasu (野洲郡, Yasu-gun) was a district located in Shiga Prefecture, Japan.

On October 1, 2004, the former town of Yasu absorbed the town of Chūzu, effectively turning Yasu District into Yasu City. Therefore, Yasu District was dissolved as a result of this merger.

As of 2003, the district had an estimated population of 49,155 and a density of 799.92 persons per km2. The total area was 61.45 km2.

Districts of Japan
In Japan, a district (郡, gun) is composed of one or more rural municipalities (towns or villages) within a prefecture. Districts have no governing function, and are only used for geographic or statistical purposes such as mailing addresses. Cities are not part of districts.

Historically, districts have at times functioned as an administrative unit.  From 1878 to 1921 district governments were roughly equivalent to a county of the United States, ranking below prefecture and above town or village, on the same level as a city. District governments were entirely abolished by 1926.
Addah
Addah is a village in southern Ivory Coast. It is in the sub-prefecture of Jacqueville, Jacqueville Department, Grands-Ponts Region, Lagunes District.

Addah was a commune until March 2012, when it became one of 1,126 communes nationwide that were abolished.

Grands-Ponts
Grands-Ponts Region (also originally known as Leboutou Region) is one of the 31 regions of Ivory Coast. Since its establishment in 2011, it has been one of three regions in Lagunes District. The seat of the region is Dabou and the region's population in the 2021 census was 450,007.

Grands-Ponts is currently divided into three departments: Dabou, Grand-Lahou, and Jacqueville.
Revelation Song
"Revelation Song" is a song written by Jennie Lee Riddle with lyrics adapted from Revelation 4 of the New Testament. The song first gained exposure on U.S. Christian radio through a Christ for the Nations Institute recording, "Glorious" in 2004, as well as on Gateway Worship's debut album, Living for You in 2006, and subsequently included on Kari Jobe's self-titled album. It was later released by Phillips, Craig and Dean as the first single off Fearless.

Christ for the Nations Institute
Christ for the Nations Institute (CFNI) is an interdenominational charismatic Bible college based in Dallas that serves as the educational cornerstone of Christ for the Nations, Inc. It was established in July 1970 by Gordon and Freda Lindsay.
Simone Rossi
Simone Rossi (born October 1968) is an Italian businessman, and the CEO of EDF Energy, having succeeded Vincent de Rivaz in November 2017.

Simone Rossi was born in October 1968. He has a degree in business administration from Bocconi University, Milan, and a degree in clarinet from Istituto Puccini, Gallarate.

Rossi has worked for EDF since 2004. Prior to his appointment as CEO, Rossi was head of EDF Group's international division since 2015, and previously EDF Energy's chief financial officer.

Rossi is married, with two daughters.

Gallarate
Gallarate (Italian: [ɡallaˈraːte]; Lombard: Galaraa) is a city and comune of Alto Milanese of Lombardy and of Milan metropolitan area, northern Italy, in the Province of Varese. It has a population of 52.886 people (Jan 2025)

It is the junction of railways to Varese, Laveno and Arona (for the Simplon). Some 10 kilometres (6 miles) to the west are the electric works of Vizzola, where 23,000 hp are derived from the river Ticino. Its territory is crossed by the river Arnetta and belongs to the Ticino Natural Park.

The city had a strong textile industry in the first part of the 19th century.

In common with other nearby cities, such as Casorate Sempione and Samarate, its name comes from Latin.
HMS Lance (G87)
HMS Lance was an L-class destroyer of the Royal Navy.  She entered service during World War II, and had a short but eventful career, serving in Home waters and the Mediterranean Sea. She was damaged in two consecutive air attacks at Malta in 1942. She was towed back to Britain, declared a constructive total loss and was scrapped. She had been adopted by the civil community of Bexley and Welling, Kent in November 1941.

Bexley
Bexley is an area of south-eastern Greater London, England and part of the London Borough of Bexley. It is sometimes known as Bexley Village or Old Bexley to differentiate the area from the wider borough. It is located 13 miles (21 km) east-southeast of Charing Cross and south of Bexleyheath.

Bexley was an ancient parish in the county of Kent. As part of the suburban growth of London in the 20th century, Bexley increased in population, becoming a municipal borough in 1935 and has formed part of Greater London since 1965.
1987 Brazilian Grand Prix
The 1987 Brazilian Grand Prix was a Formula One motor race held on 12 April 1987 at the Jacarepaguá Circuit in Rio de Janeiro. The race, contested over 61 laps, was the sixteenth Brazilian Grand Prix and the eighth to be held at Jacarepaguá, and the first race of the 1987 Formula One season.

The race was won by defending World Champion Alain Prost, driving a McLaren-TAG. Local hero Nelson Piquet was second in a Williams-Honda, while Prost's new teammate Stefan Johansson took third.

Ivan Capelli
Ivan Franco Capelli (born 24 May 1963) is an Italian broadcaster and former racing driver, who competed in Formula One from 1985 to 1993.

Born and raised in Milan, Capelli began competitive kart racing aged 15. He was widely successful across lower formulae, winning titles in Italian Formula 3, FIA European Formula 3 and International Formula 3000. After making his Formula One debut with Tyrrell at the 1985 European Grand Prix, he made sporadic appearances for Tyrell and AGS before signing for March full-time in 1987. He participated in 98 Grands Prix, achieving three podiums.

After exiting Formula One, Capelli competed in touring car racing until 2017, becoming a race-winner in the Italian GT Championship and the Trofeo Maserati. From 1998 to 2017, he was a commentator and pundit for Rai 1.
2022 Michigan gubernatorial election
The 2022 Michigan gubernatorial election took place on November 8, 2022, to elect the governor of Michigan. Incumbent Democratic Governor Gretchen Whitmer ran for election to a second term and faced former political commentator Tudor Dixon in the general election. Whitmer defeated Dixon by a margin of nearly 11 percentage points, a wider margin than polls indicated as well as a wider margin than Whitmer's first victory four years prior. Whitmer won independent voters by double-digit margins.

This was the first gubernatorial election in Michigan history in which both major party candidates for governor were women, and the first since 1990 in which the winner was from the same party as the incumbent president.

Jack Bergman
John Warren Bergman (born February 2, 1947) is an American politician and retired United States Marine Corps lieutenant general serving as the U.S. representative from Michigan's 1st congressional district since 2017. He is a member of the Republican Party.

He served as commanding general of the Marine Forces Reserve and the Marine Forces North. He also served as a naval aviator, flying rotary-winged aircraft such as the CH-46 and UH-1, as well as fixed-wing aircraft such as the T-28 and KC-130.
Ragam Thanam Pallavi
Ragam Tanam Pallavi (RTP) is a form of singing in Carnatic music which allows the musicians to improvise to a great extent. It is one of the most complete aspects of Indian classical music, demonstrating the entire gamut of talents and the depth of knowledge of the musician. It incorporates raga alapana, tanam, niraval, and kalpanaswara. In more elaborate ragam tanam pallavis, a tani avartanam may follow.

Mohanam
Mohanam is a raga in Carnatic music (musical scale of South Indian classical music). It is an audava rāga (or owdava rāga, meaning pentatonic scale). It is usually described as a janya rāga of Harikamboji (28th Melakartha Raga). However, alternate opinions suggest that Mechakalyani or even Shankarabharanam may be a more appropriate classification based on the lakshana of the raga.

The equivalent of Mohanam in Hindustani music is Bhoop (or Bhopali).

It is one of the most common pentatonic scales across the world and is very popular in East Asian and Southeast Asian music, including China and Japan.
Maschito
Maschito (Arbëreshë Albanian: Mashqiti; Lucano: Maschìte) is a town and comune of the province of Potenza, in the Basilicata region of southern Italy. Like other towns in the Vulture area, Maschito was repopulated by Albanian refugees after the occupation of Albania by the Ottoman Empire.

Neapolitan language
Neapolitan (autonym: ('o n)napulitano [(o n)napuliˈtɑːnə]; Italian: napoletano) is a Romance language of the Southern Italo-Romance group spoken in most of continental Southern Italy. It is named after the Kingdom of Naples, which once covered most of the area, and the city of Naples was its capital. On 14 October 2008, a law by the Region of Campania stated that Neapolitan was to be protected.

While the language group is native to much of continental Southern Italy or the former Kingdom of Naples, the terms Neapolitan, napulitano or napoletano may also instead refer more narrowly to the specific variety spoken natively in the city of Naples and the immediately surrounding Naples metropolitan area and Campania region. The present article mostly deals with this variety, which enjoys a certain degree of prestige and has historically wide written attestations.
John David Preston
John David Preston (born December 29, 1950) is an American politician and author from Kentucky who served in various elected and judicial offices. He was a member of the Kentucky Senate from 1994 to 1997, representing Kentucky's 25th Senate district, which at the time included Johnson, Lawrence, and Boyd counties.

Boyd County, Kentucky
Boyd County is a county located in the U.S. Commonwealth of Kentucky. As of the 2020 census, its population was 48,261. The county seat is Catlettsburg, and its largest city is Ashland. The county was formed in 1860. The county spans 160 square miles (410 km2), and is found at the northeastern edge of the state, near the Ohio River and Big Sandy River and situated in mountainous Appalachia. Boyd County is in the Huntington-Ashland, WV-KY-OH metropolitan statistical area.
Mościska, Pomeranian Voivodeship
Mościska [mɔɕˈt͡ɕiska] is a village in the administrative district of Gmina Lubichowo, within Starogard County, Pomeranian Voivodeship, in northern Poland. It is located within the ethnocultural region of Kociewie in the historic region of Pomerania.

Kociewie
Kociewie is an ethnocultural region in the eastern part of Tuchola Forest, in northern Poland, Pomerania, that is inhabited by the Kociewians. Its cultural capital is Starogard Gdański, the biggest town is Tczew, while other major towns include Świecie, and Pelplin. The region has about 250,000 inhabitants. It has well-developed industry and agriculture. Administratively, it is divided between the Pomeranian and Kuyavian-Pomeranian Voivodeships.

Kociewie is bordered by the Chełmno Land in the south, Powiśle in the east, Kashubia and Żuławy Wiślane in the north, and other parts of historic Pomerania in the west.
USS SC-1316
USS SC-1316 was a 110-foot submarine chaser in the United States Navy during World War II.

The vessel was constructed and launched in 1943 in Nyack, New York. SC-1316 later was converted to a fishing vessel and renamed Helen E.

Helen E. was operated out of Coos Bay, Oregon, before it was grounded at Horsfall Beach near its home port. Someone burned the vessel after crews were unable to salvage Helen E.

Submarine chaser
A submarine chaser or subchaser is a type of small naval vessel that is specifically intended for anti-submarine warfare. They encompass designs that are now largely obsolete, but which played an important role in the wars of the first half of the 20th century. Many of the American submarine chasers used in World War I found their way to Allied nations by way of Lend-Lease in World War II.