pszemraj/simple_wikipedia huggingface dataset:
Venn diagram

A Venn diagram is a diagram that shows the logical relation between sets. They were popularised by John Venn in the 1880s, and are now widely used. They are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses closed curves drawn on a plane to represent sets. Very often, these curves are circles or ellipses.
Similar ideas had been proposed before Venn. Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler (Letters to a German Princess) in 1768, for instance, came up with similar ideas. The idea was popularised by Venn in Symbolic Logic, Chapter V "Diagrammatic Representation", 1881.
Example
The following example uses two sets, A and B, represented here as coloured circles. The orange circle, set A, represents all living creatures that are two-legged. The blue circle, set B, represents the living creatures that can fly. Each separate type of creature can be imagined as a point somewhere in the diagram. Living creatures that can both fly and have two legs--for example, parrots--are then in both sets, and hence correspond to points in the area where the blue and orange circles overlap. That area contains all such (and only) such living creatures.
Humans and penguins are bipedal, and hence are in the orange circle, but since they cannot fly, they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes have six legs, and fly, so the point for mosquitoes is in the part of the blue circle that does not overlap with the orange one. Creatures that are not two-legged and cannot fly (for example, whales and spiders) would all be represented by points outside both circles.
The combined area of sets A and B is called the union of A and B, denoted by . The union in this case contains all living creatures that are either two-legged, or that can fly (or both).
The area in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by . For example, the intersection of the two sets is not empty, because there are points that represent creatures that are in both the orange and blue circles.
Venn diagrams of common operations on sets
In the illustrations below the left circle shows set and the right circle shows set . Results of operations are shown as colored areas.
Related pages
Exclusive disjunction
Inclusive disjunction
References
Set theory
Sautéing

Sauteing is a method of cooking food. It uses a small amount of fat in a shallow pan. The heat must be quite high. Ingredients are often cut into pieces or sliced thinly. It makes things cook faster.
Food that is sauteed is browned, but it keeps the same texture, moisture and flavor. If meat, or fish is sauteed, the saute is sometimes finished by using the pan's remains to make a sauce.
Sauteing is different from pan-frying. People sometimes confuse the two. In pan-frying larger pieces of food (for example, chops or steaks) are cooked quickly. Sauteing is also different from searing. Searing only browns the surface of the food. Olive oil or clarified butter are commonly used for sauteing. Most others fats will work too. Regular butter will produce more flavor. However it burns at a lower temperature and more quickly than other fats. This is because of the milk solids in it. Therefore clarified butter is better for sauteing.
Cooking methods
Foussais-Payré

Foussais-Payre is a commune. It is found in the region Pays de la Loire in the Vendee department in the west of France.
Communes in Vendee
Federal republic

A federal republic is a federation of states, with a republican form of central government. It differs from a unitary state in that in a federal republic, the authorities of the state governments cannot be taken back by the central government.
A republic is a country belonging to the people, whereas a federation is a form of government where by regional divisions are not branches of the central government. Thus, a federal republic has power divisions and regional governments fall under the power domain of the national government.
Many countries have a federal republic government; for example, the Republic of Austria, the Federal Republic of Brazil, the Federal Democratic Republic of Ethiopia, the Federal Republic of Germany, the Republic of India, the United Mexican States, the Swiss Confederation, the Federal Republic of Nigeria, the Islamic Republic of Pakistan, the Bolivarian Republic of Venezuela, and the United States of America. As this list shows, some of these countries use "Federal Republic" in their name, and some do not. Federal Republics usually have presidents.
There can be more than one type of Federal republic. For example, the United States is a Constitutional Democratic Federal Republic. Ethiopia also has a Federal Republic government
History of the American Federal republic
The American Federal republican system has grown over the past 225 years.
References
Republics
Monticello, Utah

Monticello ( ) is a city located in San Juan County, Utah, United States and is the county seat. It is the second most populous city in San Juan County, with a population of 1,824 at the 2020 census. It was made a city in 1910.
References
County seats in Utah
Cities in Utah
Bellagio

Bellagio is a small town on the shores of Lake Como in northern Italy. The southern part of Lake Como is split into two branches by a peninsula. The peninsula is shaped like a triangle. Bellagio is on the northern tip of the peninsula. In 2017 about 3,700 people lived in Bellagio. The Ancient Romans called the town Bilacus.
Twin towns
Bellagio is twinned with:
References
Other websites
Towns in Italy
Settlements in Lombardy
Autonomist Movement

The Autonomist Movement was a Chilean political movement. It was a founding member of the Broad Front on 21 January 2017. One year later, the movement became part of the party Social Convergence alongside Libertarian Left, Socialism and Liberty and New Democracy.
References
Political parties in Chile
Temple of King Kangsa Narayan

The Temple of King Kangsa Narayan () is a Hindu temple in northern Bangladesh. It is in Rajshahi's Tahirpur, where legend says that the Durga Puja of the Hindu community was performed for the first time in the Indian subcontinent.
References
Hindu temples in Bangladesh
Thermalito, California

Thermalito is a census-designated place (CDP) in Butte County, California.
References
Census-designated places in California
Settlements in Butte County, California
Pop Smoke

Bashar Barakah Jackson (July 20, 1999 - February 19, 2020), known professionally as Pop Smoke, was an American rapper. He was eventually signed to Victor Victor Worldwide and Republic Records. In April 2019, he released the song "Welcome to the Party". The song was the lead single of his first mixtape Meet the Woo, which was released in July 2019. "Welcome to the Party" was made into two remixes featuring Nicki Minaj and Skepta in August 2019. Pop Smoke also worked with Lil Tjay, Calboy and Travis Scott.
Life
Bashar Barakah Jackson was born in Brooklyn, New York. He attended middle school there and got expelled in 8th grade. He was the son of a Jamaican mother and a Panamanian father.
Murder
On February 19, 2020, Pop Smoke was shot three times by a male teenager during a home invasion in Los Angeles, California. He was taken to Cedars-Sinai Medical Center where he died later that day. He was 20.
Discography
Studio albums
Shoot for the Stars, Aim for the Moon (2020)
Faith (2021)
Mixtapes
Meet the Woo (2019)
Meet the Woo 2 (2020)
Singles
"Welcome to the Party"
"War"
"Christopher Walking"
"Dior"
"Shake the Room"
"Make It Rain"
"The Woo"
"Mood Swings"
"For the Night"
"What You Know Bout Love"
"Hello"
"AP"
"Mr. Jones"
"Demeanor"
"Woo Baby"
"Bad Boys"
Awards and nominations
{| class="wikitable sortable plainrowheaders" style="width: auto;"
|-
! scope="col" | Year
! scope="col" | Award
! scope="col" | Nominated work
! scope="col" | Category
! scope="col" | Result
! scope="col" class="unsortable"|
|-
| 2020
| BET Awards
| Himself
| Best New Artist
|
|
|-
| rowspan="2"|2020
| rowspan="2"|MTV Video Music Awards
| Himself
| Push Best New Artist
|
| rowspan="2"|
|-
| "The Woo" (featuring 50 Cent and Roddy Ricch)
| Song of Summer
|
|-
| 2020
| BET Hip Hop Awards
| Himself
| Best New Hip-Hop Artist
|
|
|-
| 2021
| ARIA Music Awards
| Pop Smoke - Shoot for the Stars, Aim for the Moon
| ARIA Award for Best International Artist
|
| style="text-align:center;"|
|-
| 2021
| Grammy Awards
| "Dior"
| Best Rap Performance
|
|
|-
| rowspan="10"|2021
| rowspan="10"|Billboard Music Awards
| Himself
| Top Artist
|
| rowspan="10"|
|-
| Himself
| Top New Artist
|
|-
| Himself
| Top Male Artist
|
|-
| Himself
| Top Billboard 200 Artist
|
|-
| Himself
| Top Hot 100 Artist
|
|-
| Himself
| Top Streaming Songs Artist
|
|-
| Himself
| Top Rap Artist
|
|-
| Himself
| Top Rap Male Artist
|
|-
| Shoot for the Stars, Aim for the Moon
| Top Billboard 200 Album
|
|-
| Shoot for the Stars, Aim for the Moon
| Top Rap Album
|
|-
Filmography
References
1999 births
2020 deaths
Rappers from New York (state)
Murdered African-American people
Murdered musicians
Murders by firearm in California
Musicians from Brooklyn
2020 crimes
African-American rappers
American songwriters
Gangsta rappers
Rappers from Los Angeles
People murdered in California
Pseudonyms
Unsolved murders in the United States
Old Schwamb Mill

The Old Schwamb Mill is the oldest continuously operating mill site in the United States. There has been a mill operating at this site since c.1650. The current mill is a 19th-century woodworking factory. The mill was built in 1861, and purchased by brothers Charles and Frederick Schwamb in 1864 for the manufacture of picture frames. It remained within the family's ownership and continued to operate, more or less unchanged in both equipment and processes, until 1969. Two wings were added during this time, however: one by 1881, and the other between that date and 1898. The mill still contains operational equipment and four preserved power systems.
References
Historic American Engineering Record (HAER) MASS, 9-ARL, 4-, Old Schwamb Mill, Stuart Campbell (historian) and Richard K. Anderson, Jr., (photographer), Library of Congress online collection. http://hdl.loc.gov/loc.pnp/hhh.ma1024
1861 architecture
Adoram Keisi

Adoram Keisi (; born June 17, 1972) is a retired Israeli professional football (soccer) player. Keisi was playing as a Left Back (defender), and he was known as a great header and as a winner that scores crucial goals when needed (such as the equalizer to Hapoel Tel Aviv or the goal that he scored against Sturm Graz, a goal that gave Maccabi Haifa F.C. the way to the UEFA Champions League group table.
Honours
Israeli Premier League - 5 Times, 2000-01, 2001-02, 2003-2004, 2004-05 and 2005-06
Israeli State Cup - 1 Time, 1997-98
Toto Cup - 2 Times, 2002-03 and 2005-06
References
Advrm kyysy at Maccabi Haifa FC
1972 births
Living people
Israeli footballers
Jewish Israeli sportspeople
Peter Renaday

Pierre Laurent Renoudet (born June 9, 1935), better known as Peter Renaday, is an American actor and voice actor. He was born in New Iberia, Louisiana.
Renaday was known for his roles in The Batman Superman Movie: World's Finest, The Lion King II: Simba's Pride, Antz (1998), The Odd Couple II (1998), Mulan (1998), The Prince of Egypt (1998), Ringmaster (1998), Scooby-Doo! and the Witch's Ghost (1999), The Road to El Dorado (2000), Shrek (2001), Madagascar (2005) and The Princess and the Frog (2009).
References
Other websites
Peter Renaday at Behind the Voice Actors
1935 births
Living people
American voice actors
American radio actors
American stage actors
American movie actors
American television actors
Actors from Louisiana
Satoru Noda

is a former Japanese football player.
Biography
Noda was born in Muroran on March 19, 1969. After graduating from Kokushikan University, he joined Japan Soccer League club Nissan Motors (later Yokohama Marinos) in 1991. In 1992, he became a regular player as defensive midfielder. The club won the champions in the 1991, 1992 Emperor's Cup and 1995 J1 League. In Asia, the club won the champions 1991-92 and 1992-93 Asian Cup Winners' Cup. In 1999, he moved to Avispa Fukuoka. Although he played as regular player, the club was relegated to J2 League in 2002. In 2002, his opportunity to play decreased and he moved to Regional Leagues club Volca Kagoshima in 2003. He retired end of 2004 season.
In 1988, when Noda was a Kokushikan University student, he was selected the Japan national "B team" for 1988 Asian Cup. At this competition, he played 1 game. However Japan Football Association don't count as Japan national team match because this Japan team was "B team" not "top team". In 1989, Noda selected Japan national futsal team for 1989 Futsal World Championship in Netherlands.
Statistics
|-
|1990/91||rowspan="2"|Nissan Motors||rowspan="2"|JSL Division 1||1||0||||||0||0||1||0
|-
|1991/92||2||0||||||0||0||2||0
|-
|1992||rowspan="7"|Yokohama Marinos||rowspan="7"|J1 League||colspan="2"|-||1||0||9||0||10||0
|-
|1993||23||1||0||0||5||0||28||1
|-
|1994||41||2||4||0||3||0||48||2
|-
|1995||50||2||2||0||colspan="2"|-||52||2
|-
|1996||28||4||1||0||9||0||38||4
|-
|1997||25||1||2||0||5||0||32||1
|-
|1998||27||0||0||0||4||0||31||0
|-
|1999||rowspan="4"|Avispa Fukuoka||rowspan="3"|J1 League||27||2||2||0||3||0||32||2
|-
|2000||29||2||1||0||3||0||33||2
|-
|2001||28||0||1||0||4||0||33||0
|-
|2002||J2 League||16||0||0||0||colspan="2"|-||16||0
297||14||14||0||45||0||356||14
297||14||14||0||45||0||356||14
|}
References
Other websites
1969 births
Living people
Footballers from Hokkaido Prefecture
J1 League players
J2 League players
Japan Soccer League players
Yokohama F. Marinos players
Avispa Fukuoka players
1988 AFC Asian Cup players
Futurama (video game)

Futurama is an 3D platformer based on the TV series of the same name.
2003 video games
Neumarkt-Sankt Veit

Neumarkt-Sankt Veit (until 1934 the town was called Neumarkt an der Rott) is a town in Muhldorf, in Bavaria, Germany. It is on the river Rott, 10 kilometers north of Muhldorf, and 33 kilometers southeast of Landshut.
Twin towns and cities
Neumarkt-Sankt Veit is twinned with:
Caneva, Italy, since 2002
References
Other websites
Verwaltungsgemeinschaft Neumarkt-Sankt Veit
Muhldorf (district)
2018 Strasbourg shooting

On 11 December 2018 a terrorist attack happened in Strasbourg, France. Five people were shot dead and several others were injured. The suspect, a 29 years old man who was known to the security services and thought of as an extremist was wounded in an exchange of fire with a soldier, is at large.
The incident occurred near Place Kleber, where Christkindelsmarik, a Christmas market, was being held.
References
2018 crimes in Europe
2018 mass shootings
2010s crimes in France
2010s mass shootings in Europe
2010s murders in Europe
December 2018 events
Islamic terrorist incidents in Europe
Islamic terrorist incidents in the 2010s
Mass murder in 2018
Mass murder in Europe
Murders by firearm in France
Strasbourg
Terrorist incidents in 2018
Terrorist incidents in Europe in the 2010s
Terrorist incidents in France
2018 in France
Bruzella

Bruzella was a municipality of the district Mendrisio in the canton of Ticino in Switzerland. On 25 October 2009 the former municipalities of Bruzella, Cabbio, Caneggio, Morbio Superiore, Muggio and Sagno merged into the new municipality of Breggia.
References
Other websites
Former municipalities of Ticino
The Bingo Long Traveling All-Stars & Motor Kings

The Bingo Long Traveling All-Stars & Motor Kings is a 1976 American road comedy movie directed by first time director John Badham and was loosely based on the 1973 novel of the same name by William Brashler. It stars Richard Pryor, James Earl Jones, Billy Dee Williams, Stan Shaw, Tony Burton, Jophery Brown, Ted Ross and was distributed by Universal Pictures.
Other websites
1976 comedy movies
1970s road movies
American road movies
American comedy movies
Movies based on books
Movies directed by John Badham
Universal Pictures movies
Movies set in the 1930s
Rainbow body

The rainbow body in Buddhism is a body that is made of light, not flesh. The term is mostly used in the part of Tibetan Buddhism called Dzogchen.
According to Dzogchen, the rainbow body is a sign of complete mastery of the Dzogchen view. Tenzin Wangyal Rinpoche states: "The realized Dzogchen practitioner, no longer deluded by apparent substantiality or dualism such as mind and matter, releases the energy of the elements that compose the physical body at the time of death".
Padmasambhava, who was the founder of Buddhism in Tibet, is often shown with the rainbow body on paintings known as thangkas.
Notes
References
Blackman, Sushila (Compiled and edited) (1997). Graceful Exits: How Great Beings Die: Death Stories Of Tibetan, Hindu & Zen Masters. New York, USA: Weatherhill, Inc.
Namkhai Norbu Rinpoche (Edited by John Shane) (1988). The Crystal and the Way of Light.. Routledge & Kegan Paul.
Namkhai Norbu Rinpoche (1999). The Crystal and The Way of Light: Sutra, Tantra and Dzogchen. Snow Lion Publications.
Reynolds, John Myrdhin (1996). The Golden Letters. (1st ed edition). Snow Lion Publications.
Sogyal Rinpoche; Harvey, Andrew (Editor) & Gaffney, Patrick (Editor)(1993). Tibetan Book of Living and Dying. (Rev and Updated ed.). HarperSanFrancisco.
Tenzin Wangyal Rinpoche (2002). Healing with Form, Energy, and Light. Ithaca, New York: Snow Lion Publications.
Other websites
Images of Rainbow Body
Buddhism
Verdun-en-Lauragais

Verdun-en-Lauragais is a commune of 273 people (2017). It is in the region Occitanie in the Aude department in the south of France.
Communes in Aude
Brădești, Dolj

Bradesti, Dolj is a commune in Dolj County, Romania.
References
Communes in Dolj County
Basque Country

Basque Country may refer to:
Basque Country (greater region) (Euskal Herria in Basque, or Pais Vasco in Spanish, Pays Basque in French), the approximate cultural area of the Basque people, culture and language
Basque Country (autonomous community) (Euskal Autonomia Erkidegoa in Basque; Comunidad Autonoma Vasca, Euskadi, Pais Vasco or Vascongadas in Spanish), an autonomous community of Spain (shown in pink on the map)
Northern Basque Country or French Basque Country (Ipar Euskal Herria or Iparralde in Basque; Pays Basque or Pays Basque Nord in French), the three (historic) northern provinces in France (shown in yellow on the map)
Southern Basque Country (Hego Euskal Herria or Hegoalde in Basque), the Basque provinces in Spain i.e. the autonomous Basque community plus Navarre (shown in pink and green on the map)
Related pages
Basque
Sumbawa Regency

Sumbawa Regency is a regency () of the Indonesian Province of West Nusa Tenggara.
Regencies_of_West_Nusa_Tenggara
Gravitropism

Gravitropism (also known as Geotropism) is a turning or growth movement by a plant, fungus, or animal in response to gravity. It is a general feature of all higher and many lower plants and also in other organisms. Charles Darwin was one of the first people to say that roots grow downward and stems grow upward in response to gravity.
Plant physiology
Outi Ojala

Outi Marjatta Ojala (28 June 1946 - 16 May 2017) was a Finnish politician of the Left Alliance. She served as a member of the Parliament of Finland from 1991 to 1996 and from 1999 to 2007, and as a Member of the European Parliament from 1996 to 1999. She was President of the Nordic Council in 2002.
References
Other websites
1946 births
2017 deaths
Finnish politicians
Antonio Veciana

Antonio Veciana Blanch (October 18, 1928 - June 18, 2020) was a Cuban exile. He was recruited by the Central Intelligence Agency (CIA) to kill Fidel Castro. He was the founder and a leader of the anti-Castro group Alpha 66.
Veciana was briefly employed as treasurer by Maurice Ferre's 2004 campaign for mayor of Miami-Dade. He resigned after a few days, as he did not meet the state requirement of being a registered voter.
Veciana died in Miami on June 18, 2020 at the age of 91.
References
1928 births
2020 deaths
Spies
American political activists
Cuban military people
Acromegaly

Acromegaly is a medical condition that happens when the anterior (rear) pituitary gland makes too much growth hormone (GH), after a person has passed puberty. If this happens before puberty it causes a condition known as gigantism. A number of medical conditions may cause the pituitary gland to make too much growth hormone, but the most common cause is a tumor on the pituitary gland called a pituitary adenoma'
Acromegaly is most commonly diagnosed in middle aged adults, and can result in severe disfigurement, serious complicating conditions, and early death if not treated. Acromegaly is hard to diagnose when it is just beginning. It is usually not found until 10-12 years after it starts. This is when it causes changes in the way a person looks, especially their face.
Signs and symptoms
Headaches
Vision problems
Hirsutism (in women): the growth of hair on the face.
Frontal bossing: the bone underneath the forehead becomes bigger than normal.
Prognathism: part of the face sticks out more than normal usually the lower jaw.
Fatigue: the person is often tired.
High blood pressure
Skin tags: Small wart-like growth on the skin which is not cancerous.
Hyperhidrosis: when a person sweats too much.
Bromhidrosis: Body odor
Hepatomegaly
Enlargement of hands and feet
Cardiomyopathy
Colonic cancer
References
Growth disorders
Neuroendocrinology
Spiritual (music)

Spirituals (or Negro spirituals) are the songs which were sung by the black slaves in the United States in the 18th and 19th centuries. The words to many Negro spirituals have Christian themes. This is because Black slaves in the United States turned to religion, as a way to cope with the pain of slavery. Negro spirituals combine traditional West African musical style with the style of Christian hymns from Europe.
Related pages
Gospel music
African-American history
Christian music
Folk music
Slavery
Songs by genre
IK Start

IK Start is a Norwegian football club. It was founded on 19 September 1905.
Current squad
As of 1 September 2009.
Out on loan
References
Other websites
Official IK Start Norwegian football club homepage (in Norwegian)
Norwegian football clubs
1905 establishments in Europe
20th-century establishments in Norway
Peter Cronjé

Peter Arnold Cronje (21 September 1949 - 4 September 2020) was a South African rugby union player. He was born in Johannesburg. From 1971 to 1974, he played for the national rugby team. From 1970 to 1976, he played for the Golden Lions.
Cronje died on 4 September 2020, aged 70.
References
1949 births
2020 deaths
South African rugby union players
Sportspeople from Johannesburg
Tim Mulherin

Timothy Sean Mulherin (24 August 1957 - 7 September 2020) was an Australian politician. He was a member of the Labor Party. He was the MP for Mackay in the Legislative Assembly of Queensland from 1995 to 2015. He also served as Deputy Leader of the Opposition from 2012 to 2015.
Mulherin was born in Mackay. He was married and had three children. He died of cancer on 7 September 2020 at the age of 63.
References
1957 births
2020 deaths
Australian Labor Party politicians
Cancer deaths in Queensland
Politicians from Queensland
Terence Stamp

Terence Henry Stamp (born 22 July 1938) is a British movie, voice, television, and stage actor who has appeared in over 100 movies such as; The Adventures of Priscilla, Queen of the Desert, Superman II, Get Smart,The Haunted Mansion, Star Wars Episode I: The Phantom Menace, Valkyrie, Yes Man, and Wanted. Stamp has been awarded a Golden Globe Award, Silver Bear Award, and a Satellite Award. He has acted in over 100 films.
Stamp was born in Stepney, London. In the 1960s he and supermodel girlfriend Jean Shrimpton were one of the most photographed couples of the day. Another of his famous girlfriends was Julie Christie. Later, Stamp became a follower of Bhagwan Shree Rajneesh, and lived for a while at the latter's ashram (~estate) in Poona.
At 64, Stamp married 29 year old Elizabeth O'Rourke in 2002. The couple divorced in 2008.
References
Other websites
Terence Stamp website
1938 births
Living people
Actors from London
English movie actors
English stage actors
English television actors
English voice actors
Golden Globe Award winning actors
People from the London Borough of Tower Hamlets
Idron

Idron is a commune of the Pyrenees-Atlantiques departement in the southwestern part of France.
Idron
Dominoes

Dominoes is a game played with small tiles called dominoes. A domino is a rectangular tile with a line in the middle that separates it into two sides. Each side has a number of black spots. The number of spots is different on each domino. Some dominoes have a side that is blank. The games possible with these objects resemble card games.
Other websites
Games
Games
Julian Lennon

Julian Charles John Lennon (b. 8 April 1963) is an English musician, photographer and philanthropist. He is the child of musician John Lennon and Cynthia Lennon, John's first wife. He was named after Julia Lennon, John Lennon's mother. She died in 1958, five years before Julian was born.
Julian was born shortly before Beatlemania started. This meant that John could not spend a lot of time with Julian. In 1968, John filed for divorce from Cynthia. He was leaving her to be with Yoko Ono. The divorce left Julian upset. After it, he could no longer spend time with his father. Beatles member Paul McCartney wrote Julian the song Hey Jude. Julian has spoken a lot about his father neglecting him. He stated:
1963 births
Living people
English musicians
English photographers
English philanthropists
The Beatles
Bayfield County, Wisconsin

Bayfield County is a county in the U.S. state of Wisconsin. In 2020, 16,220 people lived in the county. The county seat is Washburn.
References
1850 establishments in Wisconsin
Wisconsin counties
Brent, Alabama

Brent is a city in Bibb County, Alabama, United States. At the 2020 census, the population was 2,972.
References
Cities in Alabama
Mathematical proof

A mathematical proof is a way to show that a mathematical theorem is true. To prove a theorem is to show that theorem holds in all cases (where it claims to hold). To prove a statement, one can either use axioms, or theorems which have already been shown to be true. Many techniques for proving a statements exist, and these include proof by induction, proof by contraction and proof by cases.
Proof by induction
One type of proof is called proof by induction. This is usually used to prove that a theorem holds for all numbers (or all numbers from some point onwards). There are 4 steps in a proof by induction.
1. State that the proof will be by induction, and state which variable will be used in the induction step.
2. Prove that the statement is true for some beginning case.
3. Assume that for some value n = n0, the statement is true and has all of the properties listed in the statement. This is called the induction step.
4. Show that the statement is true for the next value, n0+1.
Once that is shown, it would mean that for any value of n that is picked, the next one is true. Since it is true for some beginning case (usually n=1), it's true for the next one (n=2). And since it is true for 2, it must be true for 3. And since it is true for 3, it must be true for 4, etc. Induction shows that it is always true, precisely because it is true for whatever comes after any given number.
An example of proof by induction is as follows:
Prove that for all natural numbers n, 2(1+2+3+....+n-1+n)=n(n+1).
Proof: First, the statement can be written as "For all natural numbers n, 2=n(n+1)."
By induction on n,
First, for n=1, 2=2(1)=1(1+1), so this is true.
Next, assume that for some n=n0 the statement is true. That is, 2 = n0(n0+1).
Then for n=n0+1, 2 can be rewritten 2(n0+1) + 2.
Since 2 = n0(n0+1), 2n0+1 + 2 = 2(n0+1) + 2n0(n0+1).
So 2(n0+1) + 2n0(n0+1)= 2(n0+1)(n0 + 2), which completes the proof.
Proof by contradiction
Proof by contradiction is a way of proving a mathematical theorem by showing that if the statement were false, then there would be a logical contradiction involved. That is, if one of the results of the theorem is assumed to be false, then there would be some inconsistency with the logic.
When proving a theorem by way of contradiction, it is important to note that in the beginning of the proof. This is usually abbreviated BWOC. When the contradiction appears in the proof, there is usually a symbol involved.
Related pages
Constructive proof
Direct proof
Mathematical logic
Quadratic equation, which can be solved using a kind of proof called "completing the square"
Reductio ad absurdum
References
Mathematics
The Illustrated World of Mortal Engines

The Illustrated World of Mortal Engines is a reference book written by Philip Reeve in 2018.
It is currently the last ever Reeve wrote.
2018 books
Cyprus cat

The Cyprus cat is a breed of cat. These cats are thought to have first come from ancient Egypt or Palestine. They were brought to the island of Cyprus by St. Helen. These are now common domestic cats that live in homes or outside. Many of these cats still live all over Cyprus. But, a large number are now feral. This means they are not tame and they run wild.
History
A researcher, J.-D. Vigne and his group, might have discovered the oldest domestic cat, in Cyprus. In 2004, archaeologists working at a Neolithic site in southern Cyprus dug up carefully buried bones of a cat. It had been placed next to human bones and artifacts. "Examination showed that a small pit or grave had been deliberately dug out, and the body of the cat was placed in it, then rapidly covered." The cat skeleton is about 4,000 years older than any known Egyptian drawings or writings.
Cyprus cats were probably living in a Byzantine monastery in the fourth century. In legends, it is said that St. Helen brought hundreds of cats to get rid of poisonous snakes that were taking over the monastery. The monastery had two bells. One rang to call the cats for their food. The second one rang to send the cats out to the meadows to hunt snakes. Now, the monastery has very few cats that live there.
Behavior
Cyprus cats are strong, athletic and full of energy. They live both in the cool mountains and in hotter areas near the sea coasts. They can adapt to any climate or living space.
References
Cat breeds
Robert Del Naja

Robert Del Naja (pron. ; born 21 January 1966, in Bristol, England), also known as 3D, is an English artist and musician. Originally famous as a graffiti artist and a member of the Bristol group known as "The Wild Bunch", Del Naja went on to become a founding member of the band Massive Attack where he is active to this day. However he has also admitted that he got his own way by "being stubborn, throwing tantrums -- the usual fucking childish behaviour."
References
1966 births
Living people
English artists
English singers
Entertainers from Bristol
Massive Attack
Trip hop musicians
Noordoostpolder

Noordoostpolder is a municipality of Flevoland, the Netherlands, and a former municipality of Overijssel. In 2016 about 47,000 people were living in Noordoostpolder.
Other websites
Noordoostpolder website
Municipalities of Flevoland
Former municipalities of Overijssel
ESTCube-1

ESTCube-1 was the first satellite from Estonia. It was made as part of the Estonian Student Satellite Program, and was launched on 7 May 2013 on a Vega rocket. The satellite is a project in which university and high-school students took part. The CubeSat standard for nanosatellites was followed while it was built, resulting in a 10x10x11.35 cm cube, with a volume of 1 liter and a mass of 1.048 kg.
ESTCube-1 was put into orbit by Arianespace, using a Vega rocket which took off from ELA-1 at Kourou at 02:06:31 UTC on 7 May 2013 at a height of 670 kilometres.
References
Satellites
Estonia
Émerson Luiz Firmino

Emerson Luiz Firmino (born July 28, 1973) is a former Brazilian football player.
Club career statistics
|-
|1995||Bellmare Hiratsuka||J. League 1||2||0||0||0||2||0
2||0||0||0||2||0
2||0||0||0||2||0
1973 births
Living people
Brazilian footballers
Frank O'Hara

Francis Russell "Frank" O'Hara (March 27, 1926 - July 25, 1966) was an American poet, art critic, and curator.
O'Hara was born in Baltimore, Maryland and grew up in Grafton, Massachusetts. He studied piano at the New England Conservatory in Boston from 1941 to 1944. During the last years of World War II, he served in the U.S. Navy in the South Pacific and Japan on a destroyer. After the war he attended Harvard University. At first, he studied music but then changed to English to become a writer. His roommate at Harvard was the artist Edward Gorey. He also became friends there with the poet John Ashbery.
O'Hara lived in New York City from 1951 until his death in 1966. In time, he and his poet-friends came to be known as The New York Poets. This group included Ashbery, James Schuyler, Barbara Guest, and Kenneth Koch. He also got to know many young New York artists, such as Larry Rivers, Jane Freilicher, Fairfield Porter, Joan Mitchell, Alex Katz, Jasper Johns, and Jackson Pollock.
O'Hara worked at the Museum of Modern Art. He put together exhibitions of art. He wrote catalogs and essays for those art shows. He made plans for the shows to travel to other cities.
He was not well-known as a poet until some of his poems were printed in The New American Poetry in 1960. This was a collection of many younger poets who were writing in original ways.
He published two important books of poetry in his lifetime, Meditations in an Emergency (1956) and Lunch Poems (1964). He wrote different kinds of poems. Some are very short and others are very long. Some use language in difficult ways. Others are very direct and sound like ordinary talking about the ordinary things he does in the city.
O'Hara's early death in 1966 was caused by a motor accident on the beach at Fire Island, New York.
Books
A City Winter and Other Poems (1952)
Oranges: 12 pastorals (1969)
Meditations in an Emergency (1957)
Second Avenue (1960)
Odes (1960)
Lunch Poems (1964)
In Memory of My Feelings (1967)
The Collected Poems of Frank O'Hara (1971)
References
1926 births
1966 deaths
American poets
LGBT poets
LGBT writers
American writers
Officer candidate school

Officer candidate schools or Officer Cadet Schools (OCS) are military institutions which train civilians and enlisted personnel to be officers in the armed forces of a country. Different countries and services run their Officer Candidate schools differently. Most schools are for less than one year. An OCS is different from a service academies which include academic instruction leading to a Bachelor degree. Another difference is that an OCS is taught almost exclusively by the military.
References
Other websites
Officer Candidate Schools
Educational institutions
Military organizations
Tau Ceti

Tau Ceti (t Cet, t Ceti) is a star in the constellation Cetus. It can be seen with the unaided eye as a third-magnitude star.
It has a spectrum similar to the Sun, but is only 78% of the Sun's mass. It is just under 12 light-years from the Solar System, a relatively nearby star. It is the closest solitary G-class star. The star appears stable, and is "metal-deficient" because (like the Sun) it is mostly made of hydrogen and helium.
There is more than ten times as much dust surrounding Tau Ceti as in the Solar System. There are probably five planets orbiting Tau Ceti, two in the habitable zone. Because of its debris disk, any planet orbiting Tau Ceti would get far more impact events than Earth. Despite this, its Sun-like characteristics have led to widespread interest in the star. Tau Ceti is consistently listed as a target for the Search for Extra-Terrestrial Intelligence (SETI), and it appears in some science fiction literature.
Searching
Project Ozma searched for intelligent life (SETI) by examining selected stars for artificial radio signals. It was run by the astronomer Frank Drake, who selected Tau Ceti and Epsilon Eridani as the first targets. Both are near the Solar System and are similar to the Sun. No artificial signals were found after 200 hours of observations. Subsequent radio searches of this star system have also turned up negative.
Planets?
On December 19, 2012, evidence was presented for a system of five planets orbiting Tau Ceti. The planets' estimated minimum masses are between two and six times the Earth's mass. Their orbital periods range from 14 to 640 days. One of them, Tau Ceti e, appears to orbit about half as far from Tau Ceti as Earth does from the Sun. With Tau Ceti's luminosity of 52% that of the Sun and a distance from the star of 0.552 AU, the planet would receive 1.71 times as much stellar radiation as Earth does. This is slightly less than Venus, which gets 1.91 times Earth's. Some research places it within the star's habitable zone.
The habitable zone for a star is where liquid water could be present on an Earth-like planet. For Tau Ceti, this is at a radius of 0.55-1.16 AU, where 1 AU is the average distance from the Earth to the Sun.
References in Science Fiction
The Expanse (TV): Destination of the Nauvoo, on a 100 year voyage. The ship is 500m cylinder, 2000m long. It would require a continuous acceleration of 0.05 m/s for 50 years, and an equal deceleration at the halfway point.
The Foundation book series by Isaac Asimov: The home star of the planet Aurora, first planet to be colonized by humans.
References
Stars
Veterans Day

Veterans Day is the American holiday when people who had served in the military during war-time are remembered and thanked. It is both a federal and a state holiday. The holiday is celebrated on the same day as Armistice Day or Remembrance Day in other countries. These holidays are all November 11. This is the day seen as the end of World War I. The first World War ended on November 11, 1918.
The holiday was first created as Armistice Day in 1919 by President Woodrow Wilson. Thirty states made it a state holiday that year. It was made a holiday for the entire country in 1938. In June 1, 1954, the name was changed to Veterans Day.
Other websites
Official Website United States Department of Veterans Affairs
Robin Dutt

Robin Dutt (born 24 January 1965) is a German football coach, executive and former player. He is the manager of Austrian club Wolfsberger AC.
Player career
As player he played for different amateur clubs in Germany.
Manager
As manager of SC Freiburg he reached the promotion to the Bundesliga.
Managerial statistics
1965 births
German footballers
German football managers
Living people
Wolfsberger AC managers
SC Freiburg managers
References
J. Geils

John Warren "J." Geils Jr. (February 20, 1946 - April 11, 2017) was an American guitarist. He was a member of the rock group The J. Geils Band.
Early life
Geils was born in New York City and grew up in Far Hills, New Jersey. In 1964, he went to Northeastern University and was a trumpeter in the marching band. When he was drawn to folk musicians in Boston, he left Northeastern for Worcester Polytechnic Institute, where he studied mechanical engineering.
The J. Geils Band
The J. Geils Band was influenced by soul music and rhythm and blues, but it moved toward pop and rock by the time the album Love Stinks (EMI, 1980) came out. Their next album, Freeze Frame, produced the song "Centerfold", which sat at number one for six weeks. Tension and conflict arose among band members, and Peter Wolf left to pursue a solo career. The band broke up in 1985.
Death
Geils was found dead at age 71 in his Groton, Massachusetts on April 11, 2017.
Discography
Jay Geils Plays Jazz! (Stony Plain, 2005)
Jay Geils, Gerry Beaudoin and the Kings of Strings, featuring Aaron Weinstein (Arbors, 2006)
Toe Tappin' Jazz (North Star, 2009)
As Bluestime
Bluestime (Rounder, 1994)
Little Car Blues (Rounder, 1996)
As New Guitar Summit
New Guitar Summit (2004)
New Guitar Summit: Live at the Stoneham Theatre (2004)
References
Other websites
1946 births
2017 deaths
American rock guitarists
American rock singers
American singer-songwriters
American jazz musicians
American blues musicians
Singers from New York City
Writers from New York City
Musicians from New York City
Singers from New Jersey
Musicians from New Jersey
Writers from New Jersey
Singers from Massachusetts
Writers from Massachusetts
Musicians from Massachusetts
Agnosia microta

Agnosia microta is a species of moth. It is in the family Sphingidae. It was described by George Hampson in 1907. It is from India.
References
Smerinthini
Wampsville, New York

Wampsville is a village found inside the Town of Lenox in Madison County, New York. About 543 people lived here as of the 2010 census. It is the county seat of Madison County.
References
Villages in New York (state)
County seats in New York (state)
Black finless porpoise

The Indian finless porpoise (Neophocaena phocaenoides phocaenoides), a finless porpoise, is one of seven porpoise species. Throughout their range, these porpoises stay in shallow waters, up to 50 m (160 ft) deep. They live close to the shore, in waters with soft or sandy seabeds, or in estuaries and mangrove swamps, such the Indus River delta.
Mammals of Pakistan
Toothed whales
Packwood, Iowa

Packwood is a city in Iowa in the United States.
Cities in Iowa
Eisuke Nakanishi

is a former Japanese football player. He played for the Japan national team.
Biography
Nakanishi was born in Suzuka on June 23, 1973. After graduating from Yokkaichi Chuo Technical High School, he joined J1 League club JEF United Ichihara in 1992. Although he mainly played as defender, he played many position including midfielder and forward in mid 1990s. The club won the 2nd place at 1998 J.League Cup and 3rd place at 2001 and 2003 J1 League. He moved to Yokohama F. Marinos in 2004. The club won the champions at 2004 J1 League. He retired end of 2006 season.
In September 1997, Nakanishi was selected the Japan national team for 1998 World Cup qualification. At this qualification, on September 7, he debuted against Uzbekistan. At 1998 World Cup, he played in the first two games as left back of three defense with Masami Ihara and Yutaka Akita. However he received a yellow card in both games, he was suspended in the third game. He played 14 games for Japan until 2002.
Statistics
|-
|1992||rowspan="12"|JEF United Ichihara||rowspan="12"|J1 League||colspan="2"|-||3||0||7||0||colspan="2"|-||10||0
|-
|1993||32||2||1||0||6||3||colspan="2"|-||39||5
|-
|1994||22||1||1||0||2||0||colspan="2"|-||25||1
|-
|1995||31||5||1||0||colspan="2"|-||colspan="2"|-||32||5
|-
|1996||20||5||0||0||10||1||colspan="2"|-||30||6
|-
|1997||18||4||1||1||6||1||colspan="2"|-||25||6
|-
|1998||22||2||1||0||2||0||colspan="2"|-||25||2
|-
|1999||26||9||1||1||1||0||colspan="2"|-||28||10
|-
|2000||27||3||3||0||1||0||colspan="2"|-||31||3
|-
|2001||29||3||3||2||4||0||colspan="2"|-||36||5
|-
|2002||24||0||2||0||4||0||colspan="2"|-||30||0
|-
|2003||22||0||0||0||2||1||colspan="2"|-||24||1
|-
|2004||rowspan="3"|Yokohama F. Marinos||rowspan="3"|J1 League||20||0||0||0||6||0||3||0||29||0
|-
|2005||13||0||2||0||1||0||3||0||19||0
|-
|2006||3||0||0||0||3||0||colspan="2"|-||6||0
309||34||19||4||55||6||6||0||389||44
309||34||19||4||55||6||6||0||389||44
|}
|-
|1997||5||0
|-
|1998||6||0
|-
|1999||1||0
|-
|2000||1||0
|-
|2001||0||0
|-
|2002||1||0
|-
!Total||14||0
|}
References
Other websites
1973 births
Living people
Footballers from Mie Prefecture
Japan international footballers
J1 League players
JEF United Chiba players
Yokohama F. Marinos players
1998 FIFA World Cup players
Granville County, North Carolina

Granville County is a county in the U.S. state of North Carolina. As of 2000, 48,498 people lived there. Its county seat is Oxford.
History
The county was made in 1746 from Edgecombe County.
In 1752 parts of Granville County, Bladen County, and Johnston County were combined to form Orange County. In 1764 the eastern part of Granville County became Bute County. And in 1881 parts of Granville County, Franklin County, and Warren County were combined to form Vance County.
Government
Granville County is part of the Kerr-Tar Regional Council of Governments.
Bordoring Counties
The counties border, or connect to, Granville County:
Mecklenburg County, Virginia - north
Vance County, North Carolina - east
Franklin County, North Carolina - southeast
Wake County, North Carolina - south
Durham County, North Carolina - southwest
Person County, North Carolina - west
Halifax County, Virginia - north-northwest
Cities and towns
These cities and towns are in Granville County:
Butner
Creedmoor
Oxford
Stem
Stovall
Other websites
Granville County government official website
Granville County Chamber of Commerce
Granville County Historical Society/Museums
North Carolina counties
1746 establishments
1740s establishments in the Thirteen Colonies
18th-century establishments in North Carolina
Ellie

Ellie is a female given name. Pet form of Ellen (or more commonly Elanor) which itself is of Hebrew origin and comes from the Hebrew element 'el' meaning 'god' or 'light', so the name means 'god is my light' or 'god is my candle. Ellie is a popular name in the United Kingdom, where it was the 67th most used baby names in England and Wales for 2020. However Ellie is more popular in the United States where it was ranked the 29th most popular girl's name in 2020.
People
Ellie Goulding, English singer
Ellie Leach, British actress
Ellie Gall, Australian actress
Ellie Kemper, American actress and comedian
References
Given names
Tann, Bavaria

Tann is a municipality in Rottal-Inn in Bavaria, Germany. It has about 4,000 residents and is 15 km from the corner of Austria away.
References
Other websites
Catholic Parish Tann
Rottal-Inn
Carmen Silvera

Carmen Silvera (3 June 1922 - 3 August 2002) was a Canadian-born British comic actress. She played Camilla Hope in the soap opera Compact. She also played Mrs. Van Schuyler in Lillie in 1978.
Silvera was born in Toronto, Canada. She died from lung cancer at age 80 in England.
English television actors
1922 births
2002 deaths
The Mansion of Happiness

The Mansion of Happiness is a 19th-century board game for children. It was designed by clergyman's daughter and children's author Anne Abbott. The game was published by W. & S. B. Ives in 1843. Parker Brothers republished the game in 1894. The firm claimed the game was the first board game published in America, but this claim is disputed. It was however the first mass-produced board game in America.
The game is didacticit is both entertaining and instructive. The theme of the game is Christian virtue. Players race about a track of 66 spaces. "The Mansion of Happiness" (Heaven, the center space) is their goal. Landing on a space marked with a vice (such as dishonesty) will send the player back several spaces and away from the goal. Spaces marked with virtues (such as honesty) send players forward and closer to the goal. The winner is the player who reaches the center space first.
Like many Christian-themed games of the middle 19th-century, The Mansion of Happiness lost some of its popularity in the last decades of the 19th century. It was then that games with secular and materialistic themes such as Milton Bradley's The Checkered Game of Life rose in demand. In literature, The Mansion of Happiness is mentioned in the boys' book Shifting for Himself; or, Gilbert Greyson's Fortunes (1876) by Horatio Alger, Jr. In this story, the title hero plays the game with friends Laura and Fred Vivian to while away the evening hours. In 2012 the game board was available on-line in a color reprint of the original.
Notes
References
Board games
Sierra Madre del Sur

The Sierra Madre del Sur (Spanish for "Southern part of the Mother Range") is a mountain range. It is in Mexico, Honduras, and Guatemala.
The Sierra Madre del Sur is about 620 miles long (1000 km) and runs northwest-southeast along the south coast of Mexico. It touches the Trans-Mexican Volcanic Belt. Its highest mountain is 12,149 feet (3703 meters) above sea level.
There are pine-oak forests and cloud forests in the Sierra Madre del Sur. Many animals and plants live there. Scientists call this biodiversity.
References
Mountains of North America
Geography of Mexico