OpenLLM-France/wikimedia huggingface dataset:
# List of axioms

This is a list of axioms as that term is understood in mathematics. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.

## ZF (the Zermelo–Fraenkel axioms without the axiom of choice)

Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology.
* Axiom of extensionality
* Axiom of empty set
* Axiom of pairing
* Axiom of union
* Axiom of infinity
* Axiom schema of replacement
* Axiom of power set
* Axiom of regularity
* Axiom schema of specification
See also Zermelo set theory.

## Axiom of choice

With the Zermelo–Fraenkel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable.

### Equivalents of AC

* Hausdorff maximality theorem
* Well-ordering theorem
* Zorn's lemma

### Stronger than AC

* Axiom of global choice

### Weaker than AC

* Axiom of countable choice
* Axiom of dependent choice
* Boolean prime ideal theorem
* Axiom of uniformization

### Alternates incompatible with AC

* Axiom of real determinacy

## Other axioms of mathematical logic

* Von Neumann–Bernays–Gödel axioms
* Continuum hypothesis and its generalization
* Freiling's axiom of symmetry
* Axiom of determinacy
* Axiom of projective determinacy
* Martin's axiom
* Axiom of constructibility
* Rank-into-rank
* Kripke–Platek axioms
* Diamond principle

## Geometry

* Parallel postulate
* Birkhoff's axioms (4 axioms)
* Hilbert's axioms (20 axioms)
* Tarski's axioms (10 axioms and 1 schema)

## Other axioms

* Axiom of Archimedes (real number)
* Axiom of countability (topology)
* Dirac–von Neumann axioms
* Fundamental axiom of analysis (real analysis)
* Gluing axiom (sheaf theory)
* Haag–Kastler axioms (quantum field theory)
* Huzita's axioms (origami)
* Kuratowski closure axioms (topology)
* Peano's axioms (natural numbers)
* Probability axioms
* Separation axiom (topology)
* Wightman axioms (quantum field theory)
* Action axiom (praxeology)
* Mathematics portal
# Nick De Luca

Nick De Luca (born 1 February 1984) is a Scottish former professional rugby union player who played as a centre.

## Early years

De Luca was born in Dumfries and grew up in Lockerbie.

## Club rugby

De Luca's position of choice is as a Centre. He can also operate at Full back and Wing. In his early career he caught the eye with his notable 'outside breaks', opening up defences and creating chances. His creative play has been noted for deceptive strength, slick handling and quick foot work.
At club level De Luca began as an apprentice with Edinburgh in 2005 before joining Border Reivers for the 2006–07 season. Following the region's dissolution in 2007 he returned to Edinburgh. De Luca's debut season was marked by memorable try against Toulouse in the Heineken Cup where he stood up the famed Yannick Jauzion to touch down, and he also contributed a spellbinding effort during the dramatic win at Ospreys later on that year. He was named in the Pro12 Dream team at the end of the 2007–08 season.

## International

De Luca was a member of the Scotland A squads for the 2006 and 2007 Churchill Cup tournaments in Canada and England respectively. A former Scotland Sevens internationalist, De Luca is the joint all-time leading try scorer for the Scotland under-21 team. He shares this honour with Ben Cairns.
Having already represented Scotland at all age-grade levels as well as 'A' level, De Luca was called up to the Scotland squad for the 2008 Six Nations Championship. He made his debut for Scotland against France in the first game of the 2008 Six Nations Championship. De Luca held on to his position for the following game against Wales. He had a difficult introduction to international rugby as he struggled throughout the 2008 RBS 6 Nations as part of an under-used and ineffective Scottish backline from which he has done well to recover.
De Luca was part of the Scotland team that recorded a historic series victory in Argentina in June 2010, starting at outside centre in the first test victory in Tucuman.
His first international try was on 19 March 2011 in the 2011 Six Nations Championship match against Italy at Murrayfield, the first Scotland try at the stadium since November 2009.
De Luca started for Scotland in the 2011 Rugby World Cup games against Georgia and Argentina. He displaced Joe Ansbro who had started in the first game for Scotland against Romania. In the next game, a decider against England, De Luca joined the game as a second-half substitute for the injured Max Evans.

## Personal life

De Luca is married to Alissa, and together they have two daughters.
Dumfries-born De Luca applauded the heroics of his local football team Queen of the South in reaching the 2008 Scottish Cup Final against the odds after recording a shock 4–3 semi-final win over Aberdeen. De Luca said: "Although I'm not a big football fan, it was really pleasing to see Queen of the South reach the Scottish Cup Final: that type of result is what sport is all about."
# The Christmas Mystery

The Christmas Mystery (Norwegian: Julemysteriet) is a 1992 Norwegian novel for children by Jostein Gaarder. The story has one chapter for each day of Advent.

## Story

Using the device of a "Story within a story", a young boy, Joachim, reads a story hidden behind each window in an advent calendar that he bought on November 30; every day, he finds small piece of paper from the doors of the calendar that tells the story of Elisabet Hansen, who chases a toy lamb that has come to life from an Oslo department store. The story within the advent calendar follows Elisabet as, with the angel Ephiriel and an increasing host of other characters, she crosses Europe whilst also travelling backwards in time towards Bethlehem to see the Christ-child. They meet other pilgrims which join the journey, including the shepherds Joshua and Jacob, the three wise kings, and several sheep.
As Joachim opens more doors on the calendar, he and his family try to find out about the mysterious flower seller, John, who appears to have made the calendar, and about Elisabet Hansen, a girl who disappeared in Norway many years earlier. Adding to the mystery is a photograph taken in Rome of a young woman - on the back of the photograph John has written 'Elisabet' - is she the same Elisabet?
# Bill May (Washington politician)

William J. S. May (April 6, 1902 – June 1, 1989) was an American politician in the state of Washington. He served in the Washington House of Representatives from 1961 to 1981.
# Pond Cove

Pond Cove is a small settlement in Newfoundland and Labrador, Canada. It is located south of Anchor Point.
# Mantis (genus)

The genus Mantis is in the family Mantidae, of the mantis order Mantodea.
Some of its species have the common name "praying mantis".

## Species

Mantis is a small genus of mantises, which includes 9 species (others are synonyms):
* Mantis beieri Roy, 1999 – Democratic Republic of the Congo
* Mantis callifera Wood-Mason, 1882
* Mantis carinata Cosmovici, 1888
* Mantis dilaticollis Gistel, 1856
* Mantis emortualis Saussure, 1869
* Mantis griveaudi Paulian, 1958
* Mantis insignis Beier, 1954 – Angola, Guinea, Congo
* Mantis macroalata Lindt, 1973 – Tajikistan
* Mantis macrocephala Lindt, 1974 – Tajikistan
* Mantis octospilota Westwood, 1889 — "eight-spotted mantis", or "blackbarrel mantid", Australia
* Mantis pia Serville, 1839
* Mantis religiosa (Linnaeus, 1758) — European mantis, or "praying mantis"Brown adult female Mantis religiosa
* Mantis splendida de Haan, 1842
* Mantis tricolor Linne, 1767
# Sifton Pass

Sifton Pass, 1,012 metres (3,320 feet), is a mountain pass in the Rocky Mountain Trench in the Northern Interior of British Columbia, Canada, forming the divide between the Fox and Kechika Rivers, and therefore between the drainage basins of the Finlay (the north fork of the Peace) and Liard Rivers. It also forms a division point between the Muskwa Ranges of the Northern Rockies to its east, and the Cassiar Mountains to its west.
It forms the prominence col for Thudaka Peak, many miles distant and the main height of land in the Interior Mountains between the Trench and the Boundary Ranges of the Coast Mountains. The resulting prominence for Thudaka is 1763 m, with the line parent for that peak being Mount Lloyd George, one of the highest in the Muskwa Ranges.
It was named for Clifford Sifton,$^{:243}$
# Barney Jackson

Harold N. "Barney" Jackson (March 18, 1904 – March 17, 1971) was an American politician in the state of Washington. He served in the Washington House of Representatives and Washington State Senate.
# Oliver Grüner

Oliver Grüner (born 12 March 1966) is a German rower. He competed in the men's quadruple sculls event at the 1988 Summer Olympics.
# Pukarani (La Paz)

Pukarani (Aymara pukara fortress, -ni a suffix, "the one with a fortress", also spelled Pucarani) is a mountain in the Bolivian Andes which reaches a height of approximately 3,720 m (12,200 ft). It is located in the La Paz Department, Loayza Province, Malla Municipality. Pukarani lies northwest of Chuqi Tira. The Malla Jawira flows along its south-western slopes.
# Johannes Müller (politician)

Johannes Müller (1880–1964) was a German politician and from 17 May 1927 until 28 March 1933 as mayor of Marburg. He later became a member of the Christian Democratic Union of Germany.
# Jacob Romeis

Jacob Romeis (December 1, 1835 – March 8, 1904) was an American businessman and politician who served two terms as a U.S. Representative from Ohio from 1885 to 1889.

## Biography

Born in Weisenbach, Bavaria in the German Confederation, Romeis attended the village schools. He immigrated in 1847 to the United States with his parents, who settled in Erie County, New York, and attended the public and select schools of Buffalo, New York. He engaged in the shipping business and railroading. He moved to Toledo, Ohio, in 1856.
Romeis was elected to the board of aldermen of the city of Toledo in 1874. He was reelected in 1876 and served as president of the board in 1877. He served as mayor of Toledo from 1879 to 1885.
Romeis was elected as a Republican to the Forty-ninth and Fiftieth Congresses (March 4, 1885 - March 3, 1889). He was an unsuccessful candidate for reelection in 1888 to the Fifty-first Congress. He later engaged in fruit growing near Toledo.
He died in Toledo, Ohio on March 8, 1904. He was interred in Woodlawn Cemetery.
# Andris Ambainis

Andris Ambainis (born 18 January 1975) is a Latvian computer scientist active in the fields of quantum information theory and quantum computing.

## Education and career

Ambainis has held past positions at the Institute for Advanced Study at Princeton, New Jersey and the Institute for Quantum Computing at the University of Waterloo. He is currently a professor in the Faculty of Computing at the University of Latvia.
He received a Bachelors (1996), Masters (1997), and Doctorate (1997) in Computer Science from the University of Latvia, as well as a PhD (2001) from the University of California, Berkeley.

## Contributions

Ambainis has contributed extensively to quantum information processing and foundations of quantum mechanics, mostly through his work on quantum walks and lower bounds for quantum query complexity.

## Recognition

In 1991 he received a perfect score and gold medal at the International Mathematical Olympiad. He won an Alfred P. Sloan Fellowship in 2008. Ambainis was an invited speaker at the 2018 International Congress of Mathematicians, speaking on mathematical aspects of computer science.
# Victor Skinner

Victor Garfield Skinner (May 12, 1882 – May 21, 1960) was an American politician in the state of Washington. He served in the Washington House of Representatives from 1933 to 1939. he was also the Sergeants at Arms of the House of Representatives from 1949 to 1953.
# Oliver Seack

Oliver Seack (born 28 July 1962) is a West German sprint canoer who competed in the early to mid-1980s. He won four medals at the ICF Canoe Sprint World Championships with a silver (K-1 500 m: 1985) and three bronzes (K-2 500 m: 1982, K-4 1000 m: 1981, 1982).
Seack also competed at the 1984 Summer Olympics in Los Angeles, finishing fifth in the K-2 1000 m and seventh in the K-2 500 m events.
# Spencer Lovejoy

Spencer Lovejoy (born 14 May 1998 in Connecticut) is an American professional squash player.
As of October 2021, he was ranked number 69 in the world. He has competed in multiple PSA professional tournaments and earned his first PSA title at the Mississauga Open in 2019.
Lovejoy graduated from Hopkins School in New Haven in 2016, and proceeded to play for the Yale Bulldogs men's squash team playing in the #1 seat all 4 years of his college career. He was a four-time First-Team All-American, winner of the Skillman Award for Sportsmanship in 2020, and named team captain his senior year.
# Leon Tarasewicz

Leon Tarasewicz (born 14 March 1957 in Waliły) is a Polish painter of Belarusian origin, professor of fine arts, academic teacher at the Academy of Fine Arts in Warsaw.

## Biography

Tarasewicz was born into a working-class family. A graduate of the Art High School in Supraśl, and then the Faculty of Painting of the Academy of Fine Arts in Warsaw in the studio of Tadeusz Dominik (he received his diploma in 1984). From 1996, he ran a guest painting studio at the same university. He became a lecturer in painting space at the Faculty of Media Art and Scenography of the Academy of Fine Arts in Warsaw. In 2011, the President of Poland, Bronisław Komorowski, awarded him the title of professor of fine arts.
He cooperates with Foksal Gallery in Warsaw, Galeria Monopol, Galeria Arsenal in Białystok, Galeria Krynki in Krynki, Galeria Ego in Poznań, and Galeria Biała in Lublin[6]. In 2008, he became the ambassador of the European Year of Intercultural Dialogue.
He emphasizes his Belarusian roots and promotes the culture of this minority in Poland.
Leon Tarasewicz's painting reflects the beauty and colors of nature in a unique way and refers to the complex history of the Polish borderland.
The most extensive bibliography of publications devoted to him (and filmography) is contained in the catalog of the exhibition at Ujazdowski Castle in 2003.
In 2005, at the ceremony during the season-opening concert in the building of the Podlaska Opera and Orchestra in Białystok, he was awarded the Gloria Artis Medal for Merit to Culture by the Minister of Culture, Waldemar Dąbrowski. In 2011, he was awarded the Knight's Cross of the Order of Polonia Restituta. He also received the Paszport Polityki award (2000), the Award of Jan Cybis (1998) and the Zofia and Jerzy Nowosielski Foundation Award. In 2007, Tarasewicz received the Grand Prize of the Cultural Foundation for 2006 for consistently challenging both the traditional understanding of painting and all conventions of understanding art. In 2014, he received the Honorary Pearl of the Polish Economy (in the culture category), awarded by the editorial office of Polish Market. In 2022, he was awarded an honorary doctorate from the University of Białystok.
# Logan H. Roots

Logan Holt Roots (March 26, 1841 – May 30, 1893) was an American politician who served as the U.S. representative for Arkansas's 1st congressional district from 1868 to 1871. He was a member of the Republican Party. He is the namesake of Fort Logan H. Roots.

## Early life and education

Roots was born in Perry County, Illinois. He completed preparatory studies and graduated in 1862 from Illinois State Normal University. He assisted in recruiting the 81st Illinois Infantry, in which he served until the close of the Civil War. Commissioned a first lieutenant, by the time of his discharge in 1865, he was breveted a lieutenant colonel. After the war, Roots settled in Arkansas to engage in planting and business.

## Political career

Upon the readmission of Arkansas to the Union, Roots served as an internal revenue collector for the first district of Arkansas. Roots was elected as a Republican to the Fortieth Congress and reelected to the Forty-first Congress and served from June 22, 1868, to March 3, 1871. He was an unsuccessful candidate for reelection in 1870 to the Forty-second Congress. After his time as a U.S. Representative, Roots was appointed marshal for the U.S. District Court for the Western District of Arkansas. Political scandal led to his removal the following year.

## Later life

In 1891, Roots was named the first president of the Arkansas Bankers Association. He served as president of the First National Bank of Little Rock until his death. He died at his home in Little Rock on May 30, 1893, and is interred there at Oakland Cemetery.
# Barney & Clyde

Barney & Clyde is a daily newspaper comic strip created by Washington Post columnist Gene Weingarten, his son Dan Weingarten, and cartoonist David Clark. Originally syndicated by The Washington Post Writers Group, it debuted on June 7, 2010. Barney & Clyde appears in The Washington Post, The Miami Herald, The Detroit Free Press and many other newspapers.

## History

On Father's Day 2010, Gene Weingarten wrote about how their collaboration began.
In 2011, Florida resident Horace LaBadie began suggesting scripts to the creators. In time, he became a frequent contributor to the strip.
In 2022, The Washington Post Writers Group announced it was winding down its comic strip business; Barney & Clyde eventually was picked up for syndication by Counterpoint Media.

## Characters

Barney & Clyde is about the friendship between a billionaire and a homeless man.
Title characters:
* J. Barnard (Barney) Pillsbury -- owner and CEO of multinational drug company Pillsbury Pharmaceuticals.
* Clyde Finster -- a homeless man. Clyde cares for a rabbit named Adolf (in honor of Adolf of Osnabrück, the patron saint of alms and charity for the poor). When panhandling, Clyde refers to Adolf by his stage name, Fluffykins McNeedsahug.
Barney's family:
* Lucretia Pillsbury -- Barney's second (and current) wife.
* Cynthia Pillsbury -- Barney's 11-year-old daughter from his first marriage.
* Eb Pillsbury -- Barney's father, who has memory issues. He has a robotic dog, Webster.
Additional characters (alphabetical):
* Charles -- Barney and Lucretia's chauffeur.
* Consuela -- Barney and Lucretia's housekeeper.
* Dabney Mountbatten IV -- Clyde's homeless friend.
* Duane Butkis -- an assistant to Barney at his pharmaceutical company.
* Horace -- a street denizen who tells arcane jokes other characters do not understand.
* Ms. Foxx -- an assistant to Barney at his pharmaceutical company.
* Ms. Lanham -- Cynthia's teacher.
* Rachel Jones -- principal at Cynthia's school.
# Lavelle Hawkins

Lavelle Lamar Hawkins (born July 12, 1986) is an American former professional football wide receiver. He was selected by the Tennessee Titans in the fourth round of the 2008 NFL draft. He played college football at California.

## Early life

He played high school football at Edison High School in Stockton, California. He originally committed to LSU. As a freshman in 2004, he transferred after one game to City College in San Francisco. As a sophomore, he transferred to California.

## Professional career
### Tennessee Titans

The Tennessee Titans selected Hawkins with the 126th overall pick in the fourth round of the 2008 NFL draft. He is notable for being the player the Titans selected with the pick they acquired in the Pacman Jones trade, as well as being the only wide receiver the Titans selected in the 2008 NFL Draft.
During five seasons with the Titans, Hawkins caught 71 receptions for 771 yards. His most productive season was in 2011 when he played in all 16 games and caught 47 passes for 470 yards and one touchdown.

### New England Patriots

Hawkins was signed by the New England Patriots to a 2-year deal on May 9, 2013. On July 31, 2013, Hawkins was released.

### San Francisco 49ers

On August 2, 2013, Hawkins signed with the San Francisco 49ers. Despite a productive preseason, he was released during the final round of roster cuts on August 31, 2013.

### San Diego Chargers

On October 1, 2013, Hawkins signed with the San Diego Chargers. Hawkins appeared in four games as a kick returner.

### Tampa Bay Buccaneers

On April 7, 2014, Hawkins signed with the Tampa Bay Buccaneers. Hawkins was released by the Buccaneers on August 20, 2014.

### BC Lions

On March 24, 2015, Hawkins signed with the BC Lions, reuniting with his former university coach Jeff Tedford. He left the team during training camp on June 6, 2016, to become a firefighter.

## Coaching career

Hawkins is currently the wide receivers coach/director of football operations at his alma mater, Edison High School in Stockton, California.

## Personal

Hawkins is a cousin of former New Orleans Saints running back Lynell Hamilton.
# Sugar Rush (album)

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
| The Daily News | Favourable |
Sugar Rush is the second studio album by the experimental rock band The Humans, consisting of Toyah Willcox, Bill Rieflin and Chris Wong. It was first released in the USA on 27 September 2011 via The End Records, and then worldwide on 2 October via Willcox's Vertical Species label.

## Background

Robert Fripp of King Crimson (and privately Toyah's husband) plays guitar on the album's every track. Igor Abuladze joined The Humans on their 2011 US and UK tour in support of the album. Promotional music video for "Sea of Size" had been released in October 2010. Live at Scala London EP was made available as a free download via The Humans' official website, with a download link listed in the UK CD album's liner notes.
In 2020, Sugar Rush was re-issued by Demon Music Group in vinyl and digital formats, credited to Toyah & The Humans.

## Track listing

All songs written by Toyah Willcox, Bill Rieflin and Chris Wong, except 8 (Willcox).
* "Titanium Girl" – 3:14
* "Love in a Different Way" – 4:35
* "Sea of Size" – 3:03
* "Pebble" – 3:51
* "Small Town Psychopath" – 4:53
* "Sweet Agitation" – 4:08
* "Playing in the Dark" – 3:27
* "Snow at 10:23" – 4:27
* "Sugar Rush" – 2:15
* "This Reasoning" – 4:53
* "Fragment Pool" – 3:52
* "Put a Woman on the Moon" – 2:14
    Bonus track
* "Small Town Psychopath" (Version) – 4:37

## Personnel

* Toyah Willcox: vocals
* Bill Rieflin: bass guitar, percussion, keyboards, production
* Chris Wong: bass guitar, guitar
* Robert Fripp: guitar
# Hal Wolf

Hal Wolf (January 31, 1926 – January 8, 1992) was an American politician. He served as a Republican member for the 22nd district of the Washington House of Representatives.

## Life and career

Wolf was born in Tacoma, Washington. He attended Yelm High School and the University of Puget Sound. He served in the United States Navy during World War II.
In 1965, Wolf was elected to represent the 22nd district of the Washington House of Representatives. He served until 1973, when he was succeeded by Del Bausch.
He was father to 3 children Diana Wolf Harold E Wolf (also known as Hap) and Mark Warren Wolf He was a wonderful teacher and father to all three of them and he was also my grandfather Joshua Harold Wolf
Wolf died in January 1992 of cancer, at the age of 65.
# Oliver Westerbeek

Oliver Westerbeek (born 8 February 1966) is a German former professional footballer who played as a defender or midfielder.

## Personal

Westerbeek works since 1999 as player agent for Rogon.