ejaasaari/simplewiki-2025-04-01 huggingface dataset:
Gödel's incompleteness theorems is the name given to two theorems (true mathematical statements), proved by Kurt Gödel in 1931. They are theorems in mathematical logic. Mathematicians once thought that everything that is true has a mathematical proof. A system that has this property is called "complete"; one that does not is called "incomplete". Also, mathematical ideas should not have "contradictions". This means that they should not be true and false at the same time. A system that does not include contradictions is called "consistent". A system is a collection of theorems (logical consequences) based on axioms (basic assumptions). Axioms are statements that are accepted as true, and need no proof. Gödel said that "every non-trivial formal system (consistent and axiomatic system with theorems listable by following an algorithm) is incomplete and not provably consistent": Outline of Proof of Gödel’s Theorems The proof of Gödel’s theorems is based on forming and considering special self-referential statements. One way to prove the theorems is to consider the first theorem before considering the second theorem. There are three parts in this proof: A. Consider the first theorem and the truth of this first statement “This statement cannot be proved”: proving this first statement would be a contradiction because there would then be a proof for a statement that cannot be proved. For the sake of the consistency of the system, the first statement and hence the first theorem are therefore true but unprovable.  B. Recall from part A that if we were able to prove the first statement then our system would be inconsistent. Thus to prove the consistency of the system, we must prove that the first statement is not provable (ie: prove the contrapositive of the claim “if we were able to prove the first statement then our system would be inconsistent”). Because of self-reference in the first statement “this statement cannot be proved” (ie: proving the first statement is not provable is proving the first statement), therefore proof of the consistency of the system requires proof of the first statement.  C. Recall in part A that consistency
A cilium (plural "cilia") is an organelle found in eukaryotic cells. Cilia are slender protuberances that project from the much larger cell body. There are two types of cilia:  In eukaryotes, cilia and flagella together make up a group of organelles known as undulipodia. Eukaryotic cilia are structurally identical to eukaryotic flagella, although distinctions are sometimes made according to function and/or length. Motile cilia are found on protist ciliates like "Paramecium". They are how "Paramecium" moves around. They are also found on the epithelial cells of many internal organs of metazoans, such as the digestive system and the trachea of the lungs. Cilia in metazoa. Non-motile (or "primary") cilia usually occur one per cell; nearly all mammalian cells have a single non-motile "primary cilium". In addition, examples of specialized primary cilia can be found in human sensory organs such as the eye and the nose:  Status of cilia. Cilia are structurally almost identical with the much larger flagella. So much so that it has been proposed protists bearing either should be unified in the Phylum "Undulipodia". Previously, Margulis had proposed that the Ciliates alone should be placed in a Phylum "Ciliophora". Admittedly, the Protista is a collection of disparate single-celled forms, but while a more sophisticated taxonomy is in flux (changing), Protista is still a useful term. Cilia and flagella are cell organelles, specialised units which carry out well-defined functions, like mitochondria and plastids. It is fairly certain now that all or most of these organelles have their origin in once-independent prokaryotes (bacteria or archaea), and that the eukaryote cell is a 'community of micro-organisms' working together in 'a marriage of convenience'.
Thirty Seconds to Mars (commonly stylized as 30 Seconds to Mars) are an American rock band from Los Angeles, California, formed in 1998 by the band consists of brothers Jared Leto (lead vocals) and Shannon Leto (drummer). During the course of its existence, it has undergone various line-up changes with the Leto brothers being the only consistent members. History. Formation and first years (1998-2000). Created in 1998 by the actor Jared Leto and his brother Shannon, Thirty Seconds to Mars began as a small family project. Matt Wachter later joined the band as bassist and keyboard player. After working with two guitarists, Kevin Drake and Solon Bixler, the band auditioned Tomo Miličević to join the band. According to an interview from Virgin Records, the band's name;"Actually comes from a thesis that the band found online that was written by a former Harvard professor. And one of the subsections of the thesis was titled "Thirty Seconds to Mars" and he goes on to talk about the exponential growth of technology that relates to humans and saying that we are quite literally thirty seconds to mars. What it means to us is, we thought it best described our music, in short." Even if Jared Leto is a major Hollywood actor, he prefers not to use this information to "sell" the band and he refuses to play shows where they use his name to promote the band. Debut album (2001–2004). Thirty Seconds to Mars retreated to the isolation of Wyoming's countryside in 2001 to record their debut album, working with producers Bob Ezrin and Brian Virtue. They contacted Ezrin because they grew up listening to his work with Pink Floyd, Kiss and Alice Cooper and they felt he was the only one who could help them capture the size and scope of what they wanted to accomplish on their debut recording. The band chose an empty warehouse lot on 15,000 acres (6,100 hectares), striving for the precise location that would enhance their sound. Even before the album was released, Puddle of Mudd invited Thirty Seconds to Mars to open a six-week tour for them in the
Mino Reitano (December 7, 1944 – January 27, 2009) was an Italian singer and actor. Mino Reitano was born into a poor family at a very small city called Fiumara, in the province of Reggio Calabria. He studied for eight years at Reggio's conservatory, where he learned to play violin, piano and trumpet. Reitano died of colorectal cancer.
Closed-circuit television (CCTV) is the use of video cameras to send a signal to a certain place, on a small set of monitors. It is often used to watch for trouble.  CCTV is widely used for surveillance and security purposes in public and private spaces. It helps monitor activities, deter crime, and provide evidence in case of incidents.  Read More
Eugene "Mean Gene" Okerlund (December 19, 1942 – January 2, 2019) was an American pro wrestling commentator and announcer. He was most known for his time with both then-World Wrestling Federation (WWF), now World Wrestling Entertainment (WWE), and World Championship Wrestling (WCW). He was the host of WWE Vintage Collection. Okerlund died on January 2, 2019 at a hospital in Sarasota, Florida of complications from a fall at the age of 76.
The SQL slammer worm (also known as W32.SQLExp.Worm) was a highly damaging computer worm that spread on the internet in early 2003. How it worked. The SQL worm mainly attacked computers that had Microsoft SQL Server 2000 or Microsoft Desktop Engine 2000 on them. The worm also produces a Denial-of-Service attack on some websites and computers because it sends too much data. History. In June 2002, Microsoft released a patch that fixed the weakness that the SQL worm attacked. However, many people did not fix the weakness. In January 2003, the worm was released. Within ten minutes of its release, it had attacked and infected 75,000 internet servers. Bank of America was one of the largest companies affected by the worm. Many of its ATM's would not work for consumers. The damage got worse, and on January 25, 2003, the worm cause a global internet slowdown. The worm was reported to have interfered with 911 calls and was responsible for many canceled flights. Aftermath and damage. During its lifetime in 2003, the SQL worm caused about 1 billion U.S Dollars in damage.
A computer worm is a kind of malware that is able to copy itself, and spread. Unlike a computer virus, this is done without changing files on a computer, and without affecting the boot sector of media. Worms do not need human help to reproduce. Worms spread over networks, or on removable media like USB flash drives. They almost always need a helper program that is able to access the network, or that executes when a new medium is inserted.  In that way, a Worm could start a program to send electronic mail, and send itself on to all the addresses in the address book of the email application. A very famous worm that appeared in 2000 was called ILOVEYOU (or "Love Letter"), it sent a simple mail with the subject ILOVEYOU, and an attachment of a document that contained the worm code.  Worms usually do not cause direct damage to a system. But they consume memory and network bandwidth, slowing down the computer. This makes it almost impossible to work with. Other examples of Worms are CodeRed and Sircam.
Lee Keun-ho (, born: 11 April 1985) is a South Korean professional athlete. He is best known as an association football player. He was a member of the Korean national team. Career. Lee plays in forward position, and usually Wing-Forward (at the side). He was born on April 5th, 1985. He is now playing for Daegu FC. His height is 176 cm, and his weight is 71 kg. He graduated from Bu-pyeong High School. His nickname is 'Eagle'. He joined Incheon United in 2005, but he stayed in the second team despite his potential ability. However, after he moved to Dae-gu FC, he played at his best. After that, many people became interested in him, and he was able to join the Korean National Team. He got his first goal for the National Team in June 29th, 2007. That game was against Iraq. It was his first game for the National Team.  After that game, he perform a meritorious deed, also in his club team. On October 11th, 2008, he scored 2 goals in the game agains Uzbekistan. Because of this, it was much easier for the Korean National Team to get to the World Cup. Nowadays, he is one of the main players of the national team, and he is trying to move to a European club team.
Mungo Park was a Scottish explorer of Africa. He was born in Foulshiels near Selkirk on September 11, 1771 and died in 1806 in Yelwa, Nigeria. He was the first Westerner (person from the Western Hemisphere) to visit the higher parts of the Niger River. In January 1806, on his second journey to explore the River Nigeria, his boat was overwhelmed in a native attack and in an attempt to escape, he jumped into the river and got drowned, ending his life at the age of 35.
Royal Rumble (2009) was a wrestling pay-per-view (PPV) made by World Wrestling Entertainment (WWE). It took place in Detroit, Michigan at the Joe Louis Arena. The event was held on January 22, 2009. The event had the 22nd annual Royal Rumble match as the main event, which Randy Orton won. One of the matches was Jeff Hardy defending his WWE Championship against Edge. Another was John Cena defending his World Heavyweight Championship against John "Bradshaw" Layfield with his employee Shawn Michaels. A third match was Jack Swagger defending his ECW Championship against Matt Hardy. The last match was Beth Phoenix defending her WWE Women's Championship against Melina. 450,000 paid to see the event. This was down from 533,000 the year before. Background. The main match in the Rumble was the yearly Royal Rumble match. The match starts with two wrestlers with another wrestler coming to the ring every 90 seconds until all 30 have entered. The match ends when one wrestler remains in the ring. This is after all 29 other wrestlers have been eliminated by being thrown over the top ring rope and having both feet touch the floor. The winner was given a championship match for the WWE, World Heavyweight, or ECW Championship at WrestleMania XXV. The main rivalry from the Raw brand was John "Bradshaw" Layfield (JBL) challenging John Cena for the World Heavyweight Championship. JBL earned his championship match against Cena after winning a Fatal Four-Way elimination match on the December 29, 2008 episode of "Raw" by beating Chris Jericho, Randy Orton, and Shawn Michaels. Another rivalry from the Raw brand was Melina challenging Beth Phoenix for her WWE Women's Championship in a singles match Melina won the chance to face Phoenix on the December 29, 2008 episode of "Raw" by winning a battle royal. The main rivalry from the SmackDown brand going into the Royal Rumble was Jeff Hardy and Edge fighting over the WWE Championship. At WWE's last pay-per-view event, Armageddon, Hardy defeated Edge and Triple H in a Triple Threat match, a match
English Football League One (commonly known as EFL League One) is the third division of football in England. It was introduced in 2004, replacing the old Second Division. TV Coverage. Sky Sports currently shows matches on their channel, and all highlights are available on the Sky Sports website. In the US, some important matches are shown on ESPN, along with EFL Championship and EFL League Two matches.  2020-21 season. These are the teams of the 2020–21 season.
The English Football League Two is a football league which is the fourth division in England. It is the name of the English Third Division since the 2004-2005 season. 2020-21 clubs. The following 24 clubs are competing in League Two during the 2020–21 season.
Phillip John-William Cocu (born 29 October 1970) is a Dutch professional football manager and former midfielder who was most recently the manager of Vitesse. "Scores and results list the Netherlands goal tally first, score column indicates score after each Cocu goal." Honours. Player. PSV Barcelona Al Jazira Manager. PSV Individual
Uwe Bein (born 26 September 1960) is a former German football player. He has played for Germany national team. "Scores and results list Germany's goal tally first, score column indicates score after each Bein goal." Honours. Germany Individual
is a former Japanese football player. He played for the Japan national team. His twin brother Hisato Sato also played for the Japan national team. Biography. Sato was born in Kasukabe on March 12, 1982. He joined J1 League club JEF United Ichihara (later "JEF United Chiba") with twin brother Yuto Sato from their youth team in 2000. He debuted in 2000 and played many matches as defensive midfielder from 2002. In 2003, he completely became a regular player and JEF United finished at the 3rd place under new manager Ivica Osim. After that, JEF United won the champions in 2005 and 2006 J.League Cup. In 2008, Sato moved to Kyoto Sanga FC. He played as regular player in 2 seasons. In 2010, Sato re-joined JEF United Chiba which was relegated to J2 League from 2010 season. He played as regular player. However the club missed promotion for J1. He retired end of the 2019 season. In August 2006, when Sato played for JEF United Chiba, he was selected Japan national team under new manager Ivica Osim who is manager for JEF United until July 2006. On August 16, Sato debuted for Japan against Yemen. Statistics. 459||37||26||3||53||6||538||46 459||37||26||3||53||6||538||46 !Total||1||0
Joaquín Sánchez (born 21 July 1981) is a Spanish football player. He plays for Valencia. Club career statistics. 317||44||14||5||19||1||350||50 317||44||14||5||19||1||350||50 International career statistics. !Total||51||4
Carlos Alberto "Capita" Torres (17 July 1944 – 25 October 2016), also known as the "Captain of the Third", was a former Brazilian football player. He has played for Brazil national team. A technically talented defender with good ball skills and defensive ability, he is widely regarded as one of the best defenders of all time. He also stood out for his leadership and was an excellent penalty taker. In the 1970 FIFA World Cup Final, Carlos Alberto scored the fourth Brazilian goal that closed the 4-1 rout against Italy. His goal is considered one of the greatest goals in the history of the tournament. Considered one of the greatest players in history in his position, he was the captain of the Brazilian team that won the 1970 FIFA World Cup in Mexico, becoming known as the Capitão do Tri. As far as clubs go, Carlos Alberto has played for Fluminense, Botafogo, Flamengo, California Surf, Santos and New York Cosmos. He was Pelé 's teammate in the last two clubs. Club career. Carlos Alberto joined Fluminense at the age of 19. He quickly made a name for himself in the team, and this from his first season at the club, thanks to his defensive qualities and his vision of the game but also an ability to dribble but also to make his teammates play, rare qualities for defenders. at that time. In 1966, he left for the Santos club where he joined his teammate Pelé. In 1974, he returned to Fluminense and enabled the club to win two consecutive Rio championships. Three years later, in 1977, he moved to Flamengo, Fluminense's biggest rival. Despite his success in Brazil, Carlos Torres joined New York club Cosmos in 1977. He arrived on the day of the New York power outage and reunited with his former teammate and friend Pelé. He helped his club win back-to-back NASL titles in 1979 and 1980. After a year at the California Surf club, he returned to New York and won a third NASL 3 title with his club in 1982. During his five years
Alessandro Costacurta (born 24 April 1966) is an Italian football pundit, manager and a former professional defender, who mostly played as a centre back. Career statistics. Club. "*European competitions include the UEFA Champions League, UEFA Cup, and UEFA Super Cup" Honours. Player. AC Milan Italy Individual
Kazumasa Uesato (born 13 March 1986) is a Japanese football player. He plays for Consadole Sapporo. Club career statistics. 129||9||10||1||1||0||140||10 129||9||10||1||1||0||140||10
Tomohiko Ikeuchi (born 1 November 1977) is a former Japanese football player. Club career statistics. 163||21||16||1||13||0||1||0||192||22 163||21||16||1||13||0||1||0||192||22
is a former Japanese football player. He played for the Japan national team. Biography. Kaji was born in Minamiawaji on January 13, 1980. After graduating from Takigawa Daini High School, he joined J1 League club Cerezo Osaka in 1998. In 2000, he moved to J2 League club Oita Trinita. He played as regular right side back in 2 seasons. In 2002, he moved to J1 club FC Tokyo. The club won the champions in 2004 J.League Cup which is first major title in the club history. In 2006, he moved to Gamba Osaka. The club won the champions in the 2007 J.League Cup, 2008 and 2009 Emperor's Cup. In Asia, the club won the champions 2008 AFC Champions League and the 3rd place 2008 Club World Cup. He played 225 matches for the club in 9 seasons. In summer 2014. he moved to Major League Soccer club Chivas USA. However, the club was disbanded in 2014, he returned to Japan and joined J2 League club Fagiano Okayama in 2015. He retired end of 2017 season. Kaji was a member of the Japan U-20 national team for the 1999 World Youth Championship. He played 3 matches and Japan won the 2nd place. On October 8, 2003, Kaji debuted for the Japan national team against Tunisia. He became a regular player as right side back from 2004. In 2004, he was selected Japan for 2004 Asian Cup and Japan won the champions. He also played at 2006 World Cup and 2007 Asian Cup. However his opportunity to play decreased behind young player Atsuto Uchida in 2008. He played 64 games and scored 2 goals for Japan until 2008. Statistics. 499||7||43||3||32||1||31||0||605||11 15||0||colspan="2"|-||colspan="2"|-||colspan="2"|-||15||0 514||7||43||3||32||1||31||0||620||11 !Total||64||2
Susumu Katsumata (born 17 February 1956) is a Japanese former professional football player. He has played for Kofu.
is a former Japanese football player. He played for the Japan national team. Biography. Doi was born in Kumamoto on July 25, 1973. After graduating from Ozu High School, he joined Hitachi (later "Kashiwa Reysol") in 1992. He battles with Ryuji Kato for goalkeeper position from 1997. However his opportunity to play decreased behind newcomer Yuta Minami from 1998. He moved to FC Tokyo in 2000. At 2004 J.League Cup, the club won the champions and he was selected MVP award. He played all matches from 2000 until round 32/34 in 2006 season. However his opportunity to play decreased behind Hitoshi Shiota in 2007. He moved to Tokyo Verdy with teammate Takashi Fukunishi in 2008. Although Doi played all matches in 2008 season, Verdy was relegated to J2 League. From 2011, his opportunity to play decreased behind Takahiro Shibasaki for injury in May 2011. In July 2012, Doi took regular position from Shibasaki. He retired end of 2012 season. In June 2003, Doi was selected the Japan national team for 2003 Confederations Cup, but he did not play in the match. On February 7, 2004, he debuted for the Japan national team against Malaysia. He was a member of Japan for 2004 Asian Cup which Japan won the champions. He played 4 games for Japan until 2005. Although he was selected Japan for most matches including 2006 World Cup from 2003 to 2006, he could hardly play in the match behind Yoshikatsu Kawaguchi and Seigo Narazaki. Statistics. 453||0||19||0||53||0||525||0 453||0||19||0||53||0||525||0 !Total||4||0
Rinus Michels (9 February 1928 – 3 March 2005) was a Dutch football player and football manager. He played for Ajax and Netherlands national team. Honours. Player. Ajax Manager. Ajax Barcelona 1. FC Köln Netherlands Individual Orders
Pär Zetterberg (born 14 October 1970) is a former Swedish football player. He has played for Sweden national team. "Scores and results list Sweden's goal tally first, score column indicates score after each Zetterberg goal." Honours. Anderlecht Olympiacos Individual
Teddy Lucic (born 15 April 1973) is a Swedish football player. He plays for Elfsborg. Club career statistics. 371||30 9||0 17||1 11||0 408||31 International career statistics. !Total||86||0
The Boro-ichi is a market in Setagaya, Tokyo, Japan. There is also a traditional Boro-ichi festival or "matsuri" which happens during the market. The market started in 1578. These days the market happens every year on January 15 and 16, and on December 15 and 16. There are over 700 stalls. More than 200,000 people come to the market. Most of the things people sell in the market are old and cheap. They sell things like antiques, books, plants and food.
Solid Snake is a fictional character who appeared in Metal Gear games by Konami. Introduced in the 1987 video games Metal Gear, and Metal Gear Solid, created by series creator Hideo Kojima, Solid Snake is a combination of a spy, special operations agent, and mercenary who works for FOXHOUND. Solid Snake (aka David) is one of three clones made in a secret project to clone the world's greatest soldier. His childhood is a mystery, but he is known to have fought in the Gulf War, and maybe a few others before that. After the war ended, he joined the Secret Organization known as FOXHOUND. While he was a member of this group, he discovered the existence of a new war machine, called Metal Gear. It is a staple throughout the series, as the title suggests. He fights a new type of Metal Gear in every games. In the fourth release in the Metal Gear Solid series, Snake's codename is changed to "Old Snake" as a reference to his old age. In reality, he is not actually as old as he seems. A side effect of the cloning that created him, was an aging process that would speed up when he reached a certain age, around the time a normal human's body starts to weaken. It should be noted, that another side effect of the cloning, is that he cannot have children. Snake appeared in the Nintendo fighting games "Super Smash Bros. Brawl" and "Super Smash Bros. Ultimate".