hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Completeness of the real numbers
Completeness is a property of the real numbers that, intuitively, implies that there are no "gaps" (in Dedekind's terminology) or "missing points" in the real number line.  This contrasts with the rational numbers, whose corresponding number line has a "gap" at each irrational value.  In the decimal number system, completeness is equivalent to the statement that any infinite string of decimal digits is actually a decimal representation for some real number.

Depending on the construction of the real numbers used, completeness may take the form of an axiom (the completeness axiom), or may be a theorem proven from the construction.  There are many equivalent forms of completeness, the most prominent being Dedekind completeness and Cauchy completeness (completeness as a metric space).

Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M.

Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g.  is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.
Republican Party of India (United)
The Republican Party of India (United), or RPI(U) is a coalition of many factions of the Republican Party of India (RPI). It was formed as an electoral alliance ahead of the 2009 Maharashtra Legislative Assembly election. The party was initially led by Rajendra Gavai, Jogendra Kawade, T.M. Kamble, and others but Gavai's faction later split from the united party. The group has since suffered internal strife similar to the disputes prior to the coalition's creation. Several parties still claim to be the real RPI.

The RPI(U) was part of the Republican Left Democratic Front coalition in Maharashtra ahead of the state's 2009 election.

2009 Maharashtra Legislative Assembly election
The 13th Assembly elections were held in Maharashtra, India on October 13, 2009. The ruling Democratic Front (Congress and Nationalist Congress Party (NCP)) contested the elections against the alliance of Shiv Sena and Bharatiya Janata Party (BJP) and Against the Third Front Known as Republican Left Democratic Front popularly known as RIDALOS.

Voters elected the 288 members of the Maharashtra Legislative Assembly in newly organized assembly constituencies after the delimitation approved in 2008. The results were declared on October 22, 2009.
United States Capitol Complex
The United States Capitol Complex is a group of twenty buildings, grounds, and facilities in Washington, D.C., that are used by the United States Congress, and federal courts. The buildings and grounds within the complex are managed and supervised by the Architect of the Capitol.

Federal judiciary of the United States
The federal judiciary of the United States is one of the three branches of the  U.S. federal government organized under the U.S. Constitution and laws of the federal government. The U.S. federal judiciary does not include any state court (which includes local courts), which are completely independent from the federal government. The U.S. federal judiciary consists primarily of the U.S. Supreme Court, the U.S. courts of appeals, and the U.S. district courts. It also includes a variety of other lesser federal tribunals.

Article III of the Constitution requires the establishment of a Supreme Court and permits the Congress to create other federal courts and place limitations on their jurisdiction. Article III states that federal judges are appointed by the president with the consent of the Senate to serve until they resign, are impeached and convicted, or die.
Stud farm
A stud farm or stud in animal husbandry is an establishment for selective breeding of livestock. The word "stud" comes from the Old English stod meaning "herd of horses, place where horses are kept for breeding". Historically, documentation of the breedings that occur on a stud farm leads to the development of a stud book.  Male animals made available for breeding to outside female animals are said to be "standing at stud", or at "stud service".

The word stud is often restricted to larger domesticated (especially farm) animals, such as cattle and horses.  A specialized vocabulary exists for the studs of other animals, such as kennel (dog), cattery (cat) and aviary (birds).

Breed registry
A breed registry, also known as a herdbook, studbook or register, in animal husbandry, the hobby of animal fancy, is an official list of animals within a specific breed whose parents are known. Animals are usually registered by their breeders while they are young. The terms studbook and register are also used to refer to lists of male animals "standing at stud", that is, those animals actively breeding, as opposed to every known specimen of that breed. Such registries usually issue certificates for each recorded animal, called a pedigree, pedigreed animal documentation, or most commonly, an animal's "papers". Registration papers may consist of a simple certificate or a listing of ancestors in the animal's background, sometimes with a chart showing the lineage.
Cory James
Cory Miguel James (born May 22, 1993) is an American former professional football player who was a linebacker in the National Football League (NFL). He played college football for the Colorado State Rams, and was selected by the Oakland Raiders in the sixth round of the 2016 NFL draft.

Colorado State Rams football
The Colorado State Rams football program represents Colorado State University and is a member of the NCAA Division I Football Bowl Subdivision and the Mountain West Conference. The Rams have long-standing rivalries with Colorado, Wyoming, and Air Force. The team is currently led by interim head coach and defensive coordinator Tyson Summers, who was named interim head coach after Jay Norvell was fired on October 19, 2025. UConn Huskies football head coach Jim Mora will serve has head coach at the start of the 2026 season.

The Rams have played their home games at Canvas Stadium since 2017. Previously, the team played 49 seasons (1968–2016) at Sonny Lubick Field at Hughes Stadium. The first game at Canvas Stadium (known as Colorado State Stadium for the 2017 season only) was played on August 26, 2017, when the Rams defeated the Oregon State Beavers 58–27.
2010 Limerick Senior Hurling Championship
The 2010 Limerick Senior Hurling Championship was the 116th staging of the Limerick Senior Hurling Championship since its establishment by the Limerick County Board.

Adare were the defending champions.

On 3 October 2010, Kilmallock won the championship after a 1–16 to 1–12 defeat of Emmets in the final. It was their ninth championship title overall and their first title since 1994.

1994 Limerick Senior Hurling Championship
The 1994 Limerick Senior Hurling Championship was the 100th staging of the Limerick Senior Hurling Championship since its establishment by the Limerick County Board in 1887. The championship ran from 17 June to 23 October 1994.

Patrickswell entered the championship as the defending champions, however, they were beaten by Kilmallock in the quarter-finals. Hospital-Herbertstown were relegated.

The final, a replay, was played on 23 October 1994 at the Gaelic Grounds in Limerick, between Kilmallock and Bruree, in what was their first ever meeting in the final. Kilmallock won the match by 1–12 to 0–12 to claim their eighth  championship title overall and a first title in two years.

Bruree's Séamus O'Connell was the championship's top scorer with 2–55.
Adejoro Adeogun
Adejoro Adeogun (born 23 June 1967) is a Nigerian politician. He was a member of the House of Representatives of Nigeria, representing Akoko South East/Akoko South West Federal Constituency of Ondo State in the 9th National Assembly. He was succeeded by Adegboyega Adefarati.

House of Representatives (Nigeria)
The House of Representatives (also called Green Chamber) is the lower chamber of Nigeria's bicameral National Assembly. The Senate is the upper chamber.

The Green Chamber has 360 members who are elected in single-member constituencies using the plurality (or first-past-the-post) system, most recently in 2023. Members serve four-year terms. The presiding officer of the house is the Speaker, currently Tajudden Abbas (as of May 2024).
Manish Asiza
Manish Asija (born 20 October 1964) is an Indian politician and a member of the 18th Uttar Pradesh Assembly and also 17th Uttar Pradesh Assembly and Sixteenth Legislative Assembly of Uttar Pradesh in India. He represents the Firozabad constituency of Uttar Pradesh and is a member of the Bharatiya Janata Party political party. He has also previously served as the mayor of Firozabad twice.

Firozabad Assembly constituency
Firozabad Assembly constituency (Hindustani pronunciation: [fɪɾoːzaːbaːd̪]) is one of the 403 constituencies of the Uttar Pradesh Legislative Assembly, India. It is a part of the Firozabad  district and one of the five assembly constituencies in the Firozabad Lok Sabha constituency. First election in this assembly constituency was held in 1957 after the "DPACO (1956)" (delimitation order) was passed in 1956. After the "Delimitation of Parliamentary and Assembly Constituencies Order" was passed in 2008, the constituency was assigned identification number 97.
Øksendal Municipality
Øksendal is a former municipality in Møre og Romsdal county, Norway. The 226-square-kilometre (87 sq mi) municipality existed from 1854 until its dissolution in 1960. It had one of the smallest municipal populations in Norway. It was located in the northwestern part of the present-day Sunndal Municipality, along the Sunndalsfjorden. It included the coastal area along the fjord as well as the whole Øksendalen valley. The administrative centre of the municipality was the village of Øksendalsøra, where Øksendal Church is also located.

Prior to its dissolution in 1960, the 225.7-square-kilometre (87.1 sq mi) municipality was the 354th largest by area out of the 743 municipalities in Norway. Øksendal Municipality was the 734th most populous municipality in Norway with a population of about 486. The municipality's population density was 2.2 inhabitants per square kilometre (5.7/sq mi) and its population had decreased by 10% over the previous 5-year period.

Sunndalsfjorden
Sunndalsfjorden (sometimes Sunndalsfjord in English) is a fjord in Sunndal Municipality in Møre og Romsdal county, Norway. The 17-kilometre (11 mi) long Sunndalsfjorden comprises the southern end of the main Tingvollfjorden. It begins at the Ballsneset peninsula, at the municipal boundary of Sunndal and extends south to the village of Sunndalsøra. Other villages along the fjord include Jordalsgrenda and Øksendalsøra. The main inflow of the fjord is the river Driva which flows into the fjord at Sunndalsøra. Norwegian National Road 70 runs along the northeastern part of the fjord near Sunndalsøra.
Heaven and Earth (1990 film)
Heaven and Earth (天と地と, Ten to Chi to) is a 1990 Japanese epic jidaigeki film directed by Haruki Kadokawa. The film stars Takaaki Enoki, Tsugawa Masahiko, Asano Atsuko, Zaizen Naomi and Nomura Hironobu. It was released in Japan in June 1990, and an English version was released in North America in 1991.

Ken Watanabe was originally cast in the role of Kenshin but had to pull out due to his severe illness.

Atsuko Asano
Atsuko Asano (浅野 温子, Asano Atsuko, born March 4, 1961 in Adachi, Tokyo) is a Japanese actress. Upon marrying Tsutomu Uozumi, a reputed copywriter and lyricist in 1983, her “koseki” name (name in Japanese family registry) became Atsuko Uozumi.  She gave birth to a son in 1984.
Function pointer
A function pointer, also called a subroutine pointer or procedure pointer, is a pointer referencing executable code, rather than data. Dereferencing the function pointer yields the referenced function, which can be invoked and passed arguments just as in a normal function call. Such an invocation is also known as an "indirect" call, because the function is being invoked indirectly through a variable instead of directly through a fixed identifier or address.

Function pointers allow different code to be executed at runtime. They can also be passed to a function to enable callbacks.

Function pointers are supported by third-generation programming languages (such as PL/I, COBOL, Fortran, dBASE dBL, and C) and object-oriented programming languages (such as C++, C#, and D).

Third-generation programming language
A third-generation programming language (3GL) is a high-level computer programming language that tends to be more machine-independent and programmer-friendly than the machine code of the first generation and assembly languages of the second generation, while having a less specific focus to the fourth and fifth generations. Examples of common and historical third-generation programming languages are ALGOL, BASIC, C, COBOL, Fortran, Java, and Pascal.
Superstar (ski course)
Superstar is a World Cup ski piste in the northeast United States at Killington, Vermont.

Located on Skye Peak mountain of the Killington Ski Resort, the course is open to the public as a black diamond trail. It has hosted eleven women's World Cup events (45th of all-time), the sixth most in the U.S. The race course debuted in November 2016, succeeding Aspen, Colorado, as the early season U.S. host for women's technical events (slalom and giant slalom).

Giant slalom course has maximum incline at 62%, average incline at 39% and minimum incline at 24%.

Slalom course has maximum incline at 58%, average incline at 41% and minimum incline at 19%.

FIS Alpine Ski World Cup
The FIS Alpine Ski World Cup is the top international circuit of alpine skiing competitions, launched in 1966 by a group of ski racing friends and experts that included French journalist Serge Lang and the alpine ski team directors from France (Honore Bonnet) and the USA (Bob Beattie). It was soon backed by International Ski Federation president Marc Hodler during the FIS Alpine World Ski Championships 1966 at Portillo, Chile, and became an official FIS event in the spring of 1967 after the FIS Congress at Beirut, Lebanon.

The inaugural World Cup race was held on 5 January 1967 in Berchtesgaden, West Germany, a slalom won by Heinrich Messner of Austria. Jean-Claude Killy of France and Nancy Greene of Canada were the overall winners for the first two seasons.
Uí Fiachrach
The Uí Fiachrach (Irish pronunciation: [iː ˈfʲiəxɾˠəx]) were a royal dynasty who originated in, and whose descendants later ruled, the coicead or fifth of Connacht (a western province of Ireland) at different times from the mid-first millennium onwards. They claimed descent from Fiachrae, an older half-brother of Niall Noigiallach or Niall of the Nine Hostages. Fiachrae and his two full brothers, Brion and Ailill, were the collective ancestors of the Connachta dynasty that eventually became the new name of the province. Their mother was Mongfind.

Niall of the Nine Hostages
Niall Noígíallach (pronounced [ˈn̠ʲiːa̯l̪ n̪oːi̯ˈɣʲiːa̯l̪əx]; Old Irish "having nine hostages"), or Niall of the Nine Hostages, was a legendary, and possibly historical, Irish king. He was reputedly a High King of Ireland, and the progenitor of the Uí Néill dynasties who dominated Ireland from the 6th to the 10th centuries. Although Irish annalistic and chronicle sources place his reign in the late 4th and early 5th centuries, modern scholars date him about half a century later.: 70
Edgars Rinkēvičs
Edgars Rinkēvičs (born 21 September 1973) is a Latvian public official and politician serving as the 11th and current president of Latvia since July 2023. He previously served as the minister of foreign affairs of Latvia from 2011 to 2023, and head of the Chancery of the President of Latvia as state secretary of the Ministry of Defence, as well as a deputy of the Saeima. Upon taking office as president, Rinkēvičs became the first openly gay head of state in a European Union country.

Prior to becoming president, Rinkēvičs had represented Latvian Way, Reform Party, and the Unity party since May 2014. He left Unity after being elected president as it is customarily expected in Latvia for presidents to maintain political neutrality.

Reform Party (Latvia)
The Reform Party (Latvian: Reformu partija), formerly known as Zatlers' Reform Party (Latvian: Zatlera Reformu partija, ZRP) until April 2012, was a centre-right political party in Latvia founded by former President Valdis Zatlers on 23 July 2011. It won 22 seats in the Saeima in the 2011 election.
Doctor Who season 24
The twenty-fourth season of British science fiction television series Doctor Who began on 7 September 1987 with Sylvester McCoy's first story Time and the Rani, and ended with Dragonfire. John Nathan-Turner produced the series, with Andrew Cartmel script editing.

Doctor Who season 23
The twenty-third season of British science fiction television series Doctor Who, known collectively as The Trial of a Time Lord, aired in weekly episodes from 6 September to 6 December 1986. It contained four adventures: The Mysterious Planet, Mindwarp, Terror of the Vervoids and The Ultimate Foe; the season also marked the final regular appearance of Colin Baker as the Sixth Doctor.

The idea for the serial stemmed from several production changes to Doctor Who, such as reduced screen time for the season and an instruction from BBC1 controller Michael Grade that the series needed to contain less violence and more humour. Several problems occurred during production, including the death of scriptwriter Robert Holmes and the resignation of script editor Eric Saward. When it ended, Baker was dismissed from the role, according to some sources on the orders of Grade, although he has denied this. John Nathan-Turner produced the series.
North Eastern US Aleph Institute
Aleph Institute (North East US) is a Jewish humanitarian organization based in Pittsburgh, Pennsylvania. They provide various religious and humanitarian services for Jewish inmates in prisons and jail across the North Eastern US, as well as for their families. They also provide social services for the local Jewish community, including supporting food security.

Aleph Institute
The Aleph Institute is an American non-profit organization affiliated with the Chabad-Lubavitch  movement that provides support services to the approximately 85,000 Jews in the U.S. prison system and Jewish members of the U.S. military located in the United States and deployed abroad.
Adoration of the Three Kings from České Budějovice
This late Gothic relief with a scene showing the Adoration of the Three Kings came from the defunct hospital Church of St Wenceslaus in České Budějovice. It was carved between 1500 and 1510, most likely in the workshop of the Monogrammist AI who is often identified with Master Alexander (Alexandr Schniczer). The relief is on show at the permanent collection of the Aleš South Bohemian Gallery in Hluboká nad Vltavou.

České Budějovice
České Budějovice (Czech: [ˈtʃɛskɛː ˈbuɟɛjovɪtsɛ] ⓘ; German: Budweis) is a city in the South Bohemian Region of the Czech Republic. It has about 97,000 inhabitants. The city is located in the valley of the Vltava River, at its confluence with the Malše.

České Budějovice is the largest city in the region and its political and commercial capital, the seat of the Diocese of České Budějovice and the University of South Bohemia. It is famous for the Budweiser Budvar Brewery. The historic city centre is well preserved and is protected as an urban monument reservation.
1930 United States Senate election in Montana
The 1930 United States Senate election in Montana took place on November 4, 1930. Incumbent United States Senator Thomas J. Walsh, who was first elected to the Senate in 1912, and re-elected in 1918 and 1924, ran for re-election. He won the Democratic primary unopposed, and faced Montana Supreme Court Associate Justice Albert J. Galen, the Republican nominee, and several independent opponents in the general election. Ultimately, Walsh defeated his opponents in a landslide and won his fourth and final term in the Senate.

Montana Supreme Court
The Montana Supreme Court is the highest court of the state court system in the U.S. state of Montana.  It is established and its powers defined by Article VII of the 1972 Montana Constitution.  It is primarily an appellate court which reviews civil and criminal decisions of Montana's trial courts of general jurisdiction and certain specialized legislative courts, only having original jurisdiction in a limited number of actions.  The court's chief justice and six associate justices are elected by non-partisan, popular elections.  The Montana Supreme Court meets in the Joseph P. Mazurek Building in Helena, Montana, the state's capital, an international style building completed in 1982 and named in the honor of former Montana attorney general, Joseph P. Mazurek.
Nguyễn Văn Quyết
Nguyễn Văn Quyết (born 1 July 1991) is a Vietnamese professional footballer who plays as a winger or attacking midfielder for V.League 1 club Hà Nội.

Nguyễn Văn Quyết started his career with Thể Công before moving to V.League 1 side Hanoi FC in 2011, where he established himself as one of the best player in the league. He won thirteen trophies at Hanoi, including five V.League 1 titles, three National Cups and five Super Cups.

A youth international for Vietnam from under-19 to under-23 level, Văn Quyết made his senior debut in 2011. He has represented his nation at five editions of the ASEAN Championship, as well as the 2018 Asian Games. He retired from international football in 2024.

Vietnamese National Football Cup
Vietnamese National Football Cup (Vietnamese: Giải Bóng đá Cúp Quốc Gia Việt Nam), officially stylized as the National Cup (Vietnamese: Cúp Quốc gia), is a Vietnamese football competition. It is one of the most important club competitions in Vietnam.

The Vietnamese Cup was first held in 1992. Cảng Sài Gòn was the first cup winner.
1894 South Carolina gubernatorial election
The 1894 South Carolina gubernatorial election was held on November 6, 1894 to select the governor of the state of South Carolina. John Gary Evans was nominated by the Democrats and became the 85th governor of South Carolina.

Governor of South Carolina
The governor of South Carolina is the head of government of South Carolina. The governor is the ex officio commander-in-chief of the National Guard when not called into federal service. The governor's responsibilities include making yearly "State of the State" addresses to the South Carolina General Assembly, submitting an executive budget, and ensuring that state laws are enforced.

The 117th and current governor of South Carolina is Henry McMaster, who is serving his second elected term. He assumed the office on January 24, 2017, after Nikki Haley resigned to become the United States ambassador to the United Nations. He won election to full terms in 2018 and 2022. McMaster is also the state’s longest serving governor.
Mongolia at the 2014 Winter Paralympics
Mongolia sent a delegation to compete at the 2014 Winter Paralympics in Sochi, Russia, from 7–16 March 2014. This was Mongolia's third time participating in a Winter Paralympic Games. The delegation consisted of a single cross-country skier, Batmönkhiin Ganbold.  His best performance in any event was 14th in the men's standing 20 kilometer freestyle, he finished 31st in the 10 km event, and did not advance from the qualification round of the 1 km sprint.

Cross-country skiing at the 2014 Winter Paralympics – Men's 20 km Free
The men's 20 kilometres competition of the 2014 Winter Paralympics was held at Laura Biathlon & Ski Complex near Krasnaya Polyana, Sochi. The sitting 15 km competition took place on 9 March 2014 and the standing and visually impaired competition took place on 10 March 2014.