title: No-hitter

text: There have been three postseason no-hitters in MLB history: two solo and one combined. On October 8, 1956, Don Larsen of the New York Yankees threw a perfect game in Game 5 of that year's World Series against the Brooklyn Dodgers. Nine years earlier, the Yankees' Bill Bevens had come within one out of a no-hitter against the Brooklyn Dodgers in Game 4 of the 1947 World Series, only to lose the game on a pinch-hit double by Cookie Lavagetto. (There have been other one-hitters in the World Series, with the lone hit coming earlier in the game than in Bevens' effort.) On October 6, 2010, Roy Halladay of the Philadelphia Phillies, in the first postseason appearance of his career, threw the second no-hitter in postseason history, in Game 1 of the Phillies' NLDS against the Cincinnati Reds. On November 2, 2022, Cristian Javier, Bryan Abreu, Rafael Montero, and Ryan Pressly of the Houston Astros combined to no-hit the Phillies in Game 4 of that year's World Series.


title: No-hitter

text: Twenty-five MLB rookies have pitched a no-hitter since 1901. Four pitchers have thrown a no-hitter in their first major league start; two others have done it in their second major league starts.


title: No-hitter

text: Bumpus Jones of the Cincinnati Reds threw a no-hitter on October 15, 1892, in his first major league game. Jones pitched only eight games in the big leagues, finishing with a career win–loss record of 2–4 and a career earned run average of 7.99.


title: No-hitter

text: Ted Breitenstein pitched a no-hitter in his first major league start on October 4, 1891; however, it was not his first major league game. He later threw a second no-hitter on April 22, 1898.


title: No-hitter

text: On May 6, 1953, Bobo Holloman pitched a no-hitter for the St. Louis Browns in his first major league start (also not his first major league game). This game would prove to be one of only three major league wins that Holloman achieved, against seven losses, all in 1953. Bill Veeck, then-owner of the Browns, in his autobiography described the 27 outs of Holloman's no-hitter as consisting of hard-hit ground balls, screaming line drives, and deep fly balls.


title: No-hitter

text: On August 14, 2021, Tyler Gilbert of the Arizona Diamondbacks pitched a no-hitter against the San Diego Padres in his first major league start and fourth appearance. His first major league game came just 11 days before his no-hitter.


title: No-hitter

text: At the other end of the spectrum, there are nine 300-game winners—Grover Cleveland Alexander, Kid Nichols, Lefty Grove, Early Wynn, Steve Carlton, Don Sutton, Greg Maddux, Roger Clemens and Tom Glavine—who failed to pitch a no-hitter.


title: No-hitter

text: On August 11, 1991, Wilson Álvarez of the Chicago White Sox pitched a no-hitter in his second career major league start. During Alvarez's first career start, he had allowed three runs on a pair of home runs and did not retire a single batter. Unlike Jones and Holloman, Alvarez went on to win 102 games over a 16-year career.


title: No-hitter

text: Clay Buchholz pitched a no-hitter for the Boston Red Sox in his second major league start on September 1, 2007, at Fenway Park. The game ended in a 10–0 victory for the Red Sox over the Baltimore Orioles.


title: No-hitter

text: Charlie Robertson of the Chicago White Sox pitched a perfect game against the Detroit Tigers on April 30, 1922, in his fourth career start and fifth career appearance.


title: No-hitter

text: Unlike a perfect game, in which no batters reach base, in regular no-hitters batters can reach base in other ways, such as a walk, an error, or a hit batsman, thus it is possible for the team pitching the no-hitter to lose. On April 23, 1964, Ken Johnson of the Houston Colt .45s became the only pitcher to lose a complete game no-hitter in nine innings when he was beaten, 1–0, by the Cincinnati Reds. The winning run was scored by Pete Rose in the top of the ninth inning via an error, groundout, and another error.


title: No-hitter

text: On April 30, 1967, Steve Barber and Stu Miller of the Baltimore Orioles pitched a combined no-hitter, but lost 2–1 to the Detroit Tigers.


title: No-hitter

text: On July 1, 1990, Andy Hawkins of the New York Yankees pitched an eight-inning no-hitter (the Yankees were the away team) against the Chicago White Sox and lost the game 4–0 after an eighth inning which saw three errors. The four runs that the White Sox scored are the most by any team in a game in which they had no hits. Because Hawkins only threw eight innings, this game is not recognized as an official no-hitter by Major League Baseball; however, it was considered a no-hitter at the time it was pitched. In the year after the game, the rules regarding no-hitters, (and rules regarding other statistics), were changed and applied retroactively in order to "clean up the record book". The Hawkins "no-hitter" failed on one main provision of the new standards. To be classified a valid no-hitter, the pitcher or pitching staff must hold the opposing team hitless for the entire game "and" face opposing batters in at least nine full innings, meaning the only way a team can pitch a losing no-hitter on the road is if the game goes to extra innings and the home team manages to win the game on a walk-off without the benefit of a hit.


title: No-hitter

text: On April 12, 1992, Matt Young of the Boston Red Sox faced the Cleveland Indians in the first game of a doubleheader. Young allowed no hits but gave up two runs on seven walks and an error by shortstop Luis Rivera, en route to the second unofficial no-hitter by a losing pitcher on the road.


title: No-hitter

text: Jered Weaver and José Arredondo of the Los Angeles Angels also combined for eight innings of no-hit baseball in a 1–0 road loss to the Los Angeles Dodgers on June 28, 2008, after Matt Kemp reached on an error, stole second, advanced to third on another error, and scored on a sacrifice fly. However, since the Angels only pitched eight innings, this game is once again not recognized as an official no-hitter.


title: No-hitter

text: On May 15, 2022, Cincinnati Reds pitchers Hunter Greene and Art Warren also combined to pitch an eight inning no-hit loss against the Pittsburgh Pirates. The only run of the game was scored when Pirates shortstop Rodolfo Castro scored on a groundout. The game is again not recognized as an official no-hitter, due to only 8 innings of no-hit play.


title: No-hitter

text: A game shortened by previous agreement or that cannot continue due to weather or darkness may be considered a completed official game, as long as at least five innings have been completed. Until 1991, any such game in which a pitcher held the opposing team without hits was considered an official no-hitter; however under the current rule, a no-hitter must last for at least nine innings to count. There are thirty-seven such shortened no-hitters. As the rule was applied retroactively, there are thirty-five games in which a no-hitter was shortened by previous agreement, weather, or darkness, with lengths ranging from 5 to 8 innings, that are no longer considered no-hitters.


title: No-hitter

text: There are four shortened no-hitters that were ended early as part of a previous agreement for travel purposes.


title: No-hitter

text: In 2020 and 2021, MLB used 7-inning doubleheaders, and on April 25, 2021, Madison Bumgarner threw the fifth shortened no-hitter in baseball history not shortened by weather or darkness. On July 7, 2021, Collin McHugh, Josh Fleming, Diego Castillo, Matt Wisler, and Pete Fairbanks of the Tampa Bay Rays threw a combined 7-inning no-hitter. No-hitters recorded in 7-inning doubleheaders do not count as official no-hitters unless the game lasts at least nine innings and the no-hitter is preserved through the end of the game.


title: No-hitter

text: If the home team leads after the top of the ninth, they do not bat in the bottom of the ninth, thus the visiting team only pitches eight innings. Since it is possible to score runs without getting hits, a visiting team can complete a full game without allowing a hit but not be credited with an official no-hitter. This has happened five times in MLB history. Silver King (1890), Andy Hawkins (1990), and Matt Young (1992) pitched complete games without allowing a hit, but pitched only eight innings as the losing pitcher from the visiting team, and thus are not credited with a no-hitter. In 2008, Jered Weaver and José Arredondo combined to throw eight no hit innings, and in 2022, Hunter Greene and Art Warren also combined to throw eight no-hit innings, while losing the game 1–0.


title: No-hitter

text: A game that is a no-hitter through nine innings may be broken up in extra innings. Under current rules, such a game (whether won or lost) is not considered an official no-hitter because the pitching staff did not keep the opposing team hitless for the entire course of the game.


title: No-hitter

text: On May 2, 1917, a game between the Chicago Cubs and the Cincinnati Reds reached the end of nine innings in a hitless scoreless tie, the only time in baseball history that "neither" team has had a hit in regulation. Both Hippo Vaughn of the Cubs and Fred Toney of the Reds continued pitching into the tenth inning. Vaughn lost his no-hitter in the top of the tenth, as the Reds got two hits and scored the winning run. Toney retired the side in the bottom of the tenth and recorded a ten-inning no-hitter. This game was long considered a "double no-hitter", but Vaughn is no longer credited with a no-hitter under the current rules.


title: No-hitter

text: Of the thirteen potential no-hitters that have been lost in extra innings, two were perfect games until the inning when the first hit was surrendered. On May 26, 1959, Harvey Haddix of the Pittsburgh Pirates pitched a remarkable twelve perfect innings against the Milwaukee Braves before losing the perfect game on an error and then the no-hitter and the game in the thirteenth inning. On June 3, 1995, Pedro Martínez of the Montreal Expos pitched nine perfect innings against the San Diego Padres before giving up a hit in the tenth and exiting the game, which the Expos then won, 1–0.


title: No-hitter

text: On August 23, 2017, in a game between the Los Angeles Dodgers and the Pittsburgh Pirates, Dodgers pitcher Rich Hill pitched nine no-hit innings, only to lose his no-hit bid (and the game) on a walk-off homer by Josh Harrison in the 10th inning. This was another potential perfect game; the perfect game was broken up by a ninth-inning error, the first time that had happened in MLB history.


title: No-hitter

text: On April 23, 2022, the Tampa Bay Rays threw a combined no-hitter against the Red Sox that was broken up in the tenth inning. J. P. Feyereisen, Javy Guerra, Jeffrey Springs, Jason Adam, Ryan Thompson, and Andrew Kittredge threw nine hitless frames before Matt Wisler surrendered a triple to Boston's Bobby Dalbec, which scored the extra-innings runner on second base. The Rays would go on to walk-off the game in the bottom of the inning with a Kevin Kiermaier home run; Wisler was credited with the win.


title: No-hitter

text: All 30 active teams in Major League Baseball have pitched a no-hitter. The last active MLB team to throw its first no-hitter was the San Diego Padres, when pitcher Joe Musgrove struck out ten batters and held the Texas Rangers hitless at Globe Life Field on April 9, 2021, 52 years after the team's debut in 1969. The closest attempt by a single pitcher prior to 2021 was against the Philadelphia Phillies on July 18, 1972: Steve Arlin came within one out of a no-hitter before Denny Doyle broke up his bid with a single. On July 9, 2011, five Padres pitchers combined for innings of no-hit pitching against the Los Angeles Dodgers before Juan Uribe hit a double, which was followed by a Dioner Navarro single that allowed the Dodgers to score to win the game, 1–0.


title: No-hitter

text: The Cleveland Guardians have the longest active no-hitter drought; the last such game thrown by the team was Len Barker's perfect game on May 15, 1981.


title: No-hitter

text: The New York Mets, who began play in 1962, went without a no-hitter until Johan Santana pitched one on the night of June 1, 2012, against the St. Louis Cardinals at home at Citi Field. The 8–0 victory closed out their era as the oldest franchise without a no-hitter and ended a drought that lasted 8,019 regular-season and 74 post-season games. As of the start of the 2021 season, Mets pitchers have thrown 39 one-hitters.


title: No-hitter

text: The longest no-hitter drought in MLB history was suffered by the Philadelphia Phillies between May 1, 1906, and June 21, 1964, a span of 8,945 games.


title: No-hitter

text: The Washington Nationals achieved their first no-hitter on September 28, 2014. The franchise has four previous no-hitters in its history as the Montreal Expos, including a perfect game by Dennis Martínez.


title: No-hitter

text: Six current NL teams—the Braves, Dodgers, Giants, Phillies, Cubs and Reds—all pitched their first no-hitters before the advent of the American League in 1901. Among the early National League teams still playing, the last to get their first no-hitter was the St. Louis Cardinals, when Jesse Haines pitched one on July 17, 1924. Of the original American League teams, the last team to get their first no-hitter was the New York Yankees, when George Mogridge pitched one on April 24, 1917. There are a number of short-lived Major League franchises from the nineteenth century that folded without ever recording a no-hitter.


title: No-hitter

text: All modern-era MLB teams have experienced at least two no-hitters pitched against them. The record for the longest period of time without being no-hit is held by the Chicago Cubs, who succeeded in getting at least one hit in every game following Sandy Koufax's perfect game against them on September 9, 1965, until they were no-hit by Cole Hamels of the Philadelphia Phillies on July 25, 2015, a period of (7951 games, including 31 postseason games). Koufax's perfect game, together with Bob Hundley's one-hitter, is the only major league game in which the two teams combined for only one hit.


title: No-hitter

text: The second-longest streak without having an official no-hitter pitched against them is held by the New York Yankees, who had a gap of between nine-inning no-hitters from September 21, 1958, to June 10, 2003. However, during this time, the Yankees failed to collect a hit in a rain-shortened official game on July 12, 1990, after .


title: No-hitter

text: Including games of less than nine innings, the St. Louis Cardinals have the second-longest streak between games when they did not collect a hit: May 12, 1919, to May 14, 1960, a period of . Among AL teams, the Kansas City Royals hold the longest such streak: May 15, 1973 to May 19, 2008, a period of .


title: No-hitter

text: The longest current streak is held by the Oakland Athletics, last held hitless on July 13, 1991 ( ago) via a combined no-hitter by four Baltimore Orioles pitchers.


title: No-hitter

text: Forbes Field, home of the Pittsburgh Pirates from the middle of the 1909 season until the middle of the 1970 season, is the only long-term major league ballpark where a no-hitter was never thrown during its existence. There are three recently built fields where no-hitters have not yet been thrown, Busch Stadium, Truist Park, and Target Field. Four parks presently in existence for a decade or more have only seen one no-hitter each: Coors Field, the hitter-friendly home of the Colorado Rockies (Hideo Nomo on September 17, 1996); the Orioles' current home, Oriole Park at Camden Yards, known for being hitter friendly (Nomo on April 4, 2001); PNC Park, the current home of the Pirates, which like Forbes Field is known for being hitter-friendly (Homer Bailey on September 28, 2012); and Petco Park, home of the San Diego Padres, which initially was known as a pitcher's park but was modified with shorter fences in 2013 (Tim Lincecum on July 13, 2013).


title: No-hitter

text: American Family Field, home of the Milwaukee Brewers, has hosted two no-hitters, but only one involved its home team. Both no-hitters were thrown by the Chicago Cubs—Alec Mills threw a no-hitter on September 13, 2020, against the Brewers; and Carlos Zambrano pitched one on September 14, 2008, against the "home" Houston Astros in a game displaced by Hurricane Ike.


title: No-hitter

text: There have been 66 no-hitters in Nippon Professional Baseball history. As noted above, unlike Major League Baseball, the Japanese league does not count combined or not shutout no-hitters.


title: No-hitter

text: Ongoing research by baseball historians has revealed the existence of 34 no-hitters thrown in Negro league baseball; the research has had to clarify differences between play from teams and barnstorming, and one of the no-hitters was done at a Benefit All-Star Game. In 2020, Major League Baseball announced the addition of the seven "Negro Major Leagues" that played from 1920 to 1948 as major leagues, which recognized statistics from over 3,400 players that played in those seasons, which will only increase the need for further research and verification over no-hitters.


title: No-hitter

text: This presumes that 22 to 24 no-hitters from that said era (22 regular season, one postseason, one All-Star game) could be recognized by official record books such as Elias in future years. There are also six games that were prematurely cut from the intended length of nine innings that were called due to weather that ranged from 1926 to 1945, one of which includes Luther Farrell and his seven-inning no-hitter in Game 5 of the 1927 Colored World Series.


title: No-hitter

text: Four pitchers threw two no-hitters: Bill Gatewood, Phil Cockrell, Jesse Winters, and Satchel Paige; Dick Redding, nicknamed "Cannonball", was reported to have thrown as many as 30 no-hitters in his career, but the disparity in finding enough box scores to verify such claim still proves too great for researchers (incidentally, Paige had estimated he threw 55 no-hitters in a long career of league games and barnstorming). At any rate, his no-hitter for the Lincoln Giants against the Cuban Stars is generally considered the first no-hitter documented between two African American teams considered to have played at the highest level. Leon Day threw a no-hitter on May 5, 1946, to open the season for the Newark Eagles against the Philadelphia Stars, which is believed to be the second no-hitter thrown by a pitcher on Opening Day.


title: No-hitter

text: Eleven were done in the 1910s, while fourteen were verified to have been done in the 1920s, six in the 1930s, and three in the 1940s. Likely the most famous no-hitter thrown by a player in the Negro leagues was Red Grier, who pitched a no-hitter in Game 3 of the 1926 Colored World Series on October 3, 1926, doing so for the Bacharach Giants against the Chicago American Giants. It was the first no-hitter thrown in a major league postseason game, and no one would throw another in the playoffs until Don Larsen 30 years later.


title: No-hitter

text: In December 2020, Major League Baseball announced that it was classifying the seven "Negro Major Leagues" as major leagues, recognizing statistics and approximately 3,400 players who played from 1920 to 1948.


title: No-hitter

text: In the 2006 World Baseball Classic, Shairon Martis pitched a no-hitter for the Netherlands against Panama, however it was only for seven innings due to the mercy rule.


title: No-hitter

text: Considered to be one of the greatest amateur pitchers in Ontario in the 1950s and 60s, southpaw Jack Roberts pitched two consecutive no-hitters for the Campbellville Merchants – a team with a .771 winning percentage – in an Ontario Baseball Association Intermediate C round-robin final in 1966.


title: No-hitter

text: Unlike the MLB and WBSC (global sanctioning body of baseball) definitions, a no-hitter is called a "no hit, no run" game in Eastern Asian professional leagues. The requirements are different than the traditional definition; the game is a shutout victory where the starting pitcher pitches the entire game while allowing no hits, and no runs are scored (a no-hitter by the traditional definition runs may score by walk, hit by pitch, defensive interference, errors, stolen bases, and balks). In those leagues, a no-hitter is not regarded as official record unless the starting pitcher pitches the whole game and the opposing team scores zero runs, and the team either wins or the game ends in a tie, which happens when the innings limit is reached. There is a twelve-inning limit in these leagues.


title: No-hitter

text: One of the most common baseball superstitions is that it is bad luck to mention a no-hitter in progress, especially to the pitcher and in particular by their teammates (who sometimes even go so far as to avoid even going "near" the pitcher). Some sportscasters observe this taboo while others have no reservations about mentioning no-hitters before completion. When Sandy Koufax pitched his no-hitter against the Mets in 1962, one of their 120 losses that season, Mets' coach Solly Hemus, apparently trying to jinx Koufax, kept heckling him through the game about pitching a no-hitter, according to a post-game interview Koufax gave after pitching his third no-hitter in 1964. An early biography of Koufax quoted him as telling his catcher, during that 1964 no-hitter, "Let's just go to the fastball and get this no-hit thing over with." Mickey Mantle, in an interview for Ken Burns' 1994 "Baseball" documentary series, related that Don Larsen, famed for his 1956 World Series perfect game, tried to talk about his no-hitter throughout the contest but much to his chagrin his Yankee teammates avoided his conversation and maintained the superstition.


title: No-hitter

text: When Los Angeles Angels rookie Bo Belinsky entered the final inning of his no-hitter in 1962, Baltimore Orioles outfielder Jackie Brandt passed him on the field as the teams changed sides. According to Belinsky biographer Maury Allen, Brandt told Belinsky, "Nice game, Bo, but it's over. I'm leading off with a bunt single." Belinsky got Brandt out to start the final inning of his no-hitter.


title: No-hitter

text: In 2009, when Mark Buehrle was pitching his perfect game, as he exited the field after the eighth inning, White Sox broadcaster Ken Harrelson exclaimed, "Call your sons! Call your daughters! Call your friends! Call your neighbors! Mark Buehrle has a perfect game going into the ninth!" Buehrle retired the side in the ninth to complete the perfect game.


title: No-hitter

text: When Jim Bunning was pitching his perfect game in 1964, he deliberately violated this superstition, talking to his teammates about the perfect game's progress in order to dispel the tension in the dugout.


title: Punta Arenas

text: Punta Arenas (; historically Sandy Point in English) is the capital city of Chile's southernmost region, Magallanes and Antarctica Chilena. The city was officially renamed as Magallanes in 1927, but in 1938 it was changed back to "Punta Arenas". It is the largest city south of the 46th parallel south, and at the same time the most populous southernmost city in Chile and in the Americas, and due to its location, the coldest coastal city with more than 100,000 inhabitants in Latin America. It is one of the most southerly ports in the world, serving as an Antarctic gateway city.


title: Punta Arenas

text: As of 1977, Punta Arenas has been one of only two free ports in Chile, the other one being Iquique, in the country's far north.


title: Punta Arenas

text: Located on the Brunswick Peninsula north of the Strait of Magellan, Punta Arenas was originally established by the Chilean government in 1848 as a tiny penal colony to assert sovereignty over the Strait. During the remainder of the 1800s, Punta Arenas grew in size and importance due to the increasing maritime traffic and trade travelling to the west coasts of South and North America. This period of growth also resulted from the waves of European immigrants, mainly from Croatia and Russia, attracted to a gold rush and sheep farming boom in the 1880s and early 1900s. The largest sheep company, controlling 10,000 square kilometres in Chile and Argentina, was based in Punta Arenas, and its owners lived there.


title: Punta Arenas

text: Since its founding Chile has used Punta Arenas as a base to defend its sovereignty claims in the southernmost part of South America. This led, among other things, to the Strait of Magellan being recognized as Chilean territory in the Boundary treaty of 1881 between Chile and Argentina. The geopolitical importance of Punta Arenas has remained high in the 20th and 21st centuries because of its logistic importance in accessing the Antarctic Peninsula.


title: Punta Arenas

text: Since 2017, the city and its region have their own time zone: they use summer time during the whole year (UTC−3). The city is supplied with water from San Juan River.


title: Punta Arenas

text: The name Sandy Point derives from the voyage of John Narborough in 1669-1671. He wrote in his account:


title: Punta Arenas

text: The English 18th-century explorer John Byron is sometimes erroneously credited with naming this area.


title: Punta Arenas

text: It was not until 1843 that the government tried to establish a fort and settlement at Fuerte Bulnes. The name "Punta Arenas" was derived from the Spanish term "Punta Arenosa", a literal translation of the English name "Sandy Point". The city has also been known as "Magallanes". Today that term is normally used to describe the administrative region which includes the city.


title: Punta Arenas

text: Punta Arenas has been nicknamed "the city of the red roofs" for the red-painted metal roofs that characterized the city for many years. Since about 1970, the availability of other colours in protective finishes has resulted in greater variety in the characteristic metal roofs.


title: Punta Arenas

text: Located on the Brunswick Peninsula, Punta Arenas is among the largest cities in Patagonia. In 2012, it had a population of 127,454. It is roughly from the coast of Antarctica and from Ushuaia, the capital of the Argentine province of Tierra Del Fuego.


title: Punta Arenas

text: The Magallanes region is considered part of Chilean Patagonia. Magallanes is Spanish for Magellan, and was named after Ferdinand Magellan, the Portuguese explorer sailing for Spain. While circumnavigating the earth for Spain, he passed close to the present site of Punta Arenas in 1520. Early English navigational documents referred to this site as "Sandy Point."


title: Punta Arenas

text: The city proper is located on the northeastern shore of Brunswick Peninsula. Except for the eastern shore, containing the settlements of Guairabo, Rio Amarillo and Punta San Juan, the peninsula is largely uninhabited. The municipality of Punta Arenas includes all of Brunswick Peninsula, as well as all islands west of the "Isla Grande de Tierra del Fuego" and north of Cockburn and Magdalena channels.


title: Punta Arenas

text: Except Dawson Island, which had a population of about 301 in 2002, the islands are largely uninhabited. Clarence Island had a population of five.


title: Punta Arenas

text: Due to its far southern latitude, Punta Arenas has a subpolar oceanic climate (Köppen climate classification "Cfc") bordering on a tundra climate. The seasonal temperature in Punta Arenas is greatly moderated by its proximity to the ocean, with average lows in July near and highs in January of .


title: Punta Arenas

text: It is known for stable constant temperatures, which vary only slightly with the seasons. Rainfall is highest in April and May, and the snowy season runs all through the Chilean winter (June until September). As in most of Patagonia, average annual precipitation is quite low, only because of a rain shadow created by the Andes. The average temperature does not go below . The city is also known for its strong winds (up to ), which are strongest during the summer. City officials have put up ropes between buildings in the downtown area to assist pedestrians with managing the strong downdrafts.


title: Punta Arenas

text: Since 1986, Punta Arenas has been the first significantly populated city in the world to be affected directly by the thinning ozone layer. Its residents are considered to be exposed to potentially damaging levels of ultraviolet radiation.


title: Punta Arenas

text: Two early Spanish settlements were attempted along this coast (on the Straits of Magellan). The first was founded in 1584 and was called "Nombre de Jesús." It failed due to the harsh weather and difficulty in the settlers' obtaining food and water, and the enormous distances from other Spanish ports. A second colony, "Ciudad del Rey don Felipe", was attempted about 80 kilometres south of Punta Arenas. This became known later as "Puerto del Hambre", which translates to "Port Famine". Spain had established these settlements in an attempt to protect its shipping and prevent piracy by English pirates, by controlling the Straits of Magellan. An English pirate captain, Thomas Cavendish during his circumnavigation, rescued the last surviving member of Puerto del Hambre in 1587.


title: Punta Arenas

text: In 1843 the Chilean government sent an expedition to build a fort and establish a permanent settlement on the shores of the Strait of Magellan. It built and commissioned a schooner called "Goleta Ancud." Under the command of John Williams Wilson, Chilean Navy, it transported a crew of 21 people (captain, eighteen crew, and two women), plus cargo, to accomplish the mandate. The founding act of the settlement took place on 21 September 1843.


title: Punta Arenas

text: The fort was well-positioned on a small rocky peninsula, but the location could not support a proper civilian settlement. With this in mind the Military Governor, José de los Santos Mardones, decided in 1848 to move the settlement to its current location, along the "Las Minas" river, and renamed it Punta Arenas.


title: Punta Arenas

text: In the mid-19th century, Chile used Punta Arenas as a penal colony and a disciplinary posting for military personnel with "problematic" behaviour. It also settled immigrants there. In December 1851, a prisoners' mutiny led by Lieutenant Cambiaso, resulted in the murder of Governor Muñoz Gamero and the priest, and the destruction of the church and the hospital. The mutiny was put down by Commander Stewart of assisted by two Chilean ships: "Indefatigable" and "Meteoro".


title: Punta Arenas

text: In 1867, President José Joaquín Pérez issued a decree offering land grants in an effort to get Chileans or foreigners to settle around Punta Arenas. The first British immigrants arrived in 1867, and their number increased as sheep farming grew in the Chilean Magallanes. The greatest immigration continued to be by the British until 1906, when Croatians surpassed them in numbers.


title: Punta Arenas

text: An 1877 mutiny, known as "El motín de los artilleros" (Mutiny of the Artillerymen), led to the destruction of a large part of the town and the murder of many civilians not directly associated with the prison. In time the city was restored. The growth of the sheep farming industry and the discovery of gold, as well as increasing trade via sailing ships, attracted many new settlers, and the town began to prosper.


title: Punta Arenas

text: Between about 1890 and 1940, the Magallanes region became an important sheep-raising region, with one company ("Sociedad Explotadora de Tierra del Fuego") controlling over . In 1910, Sociedad Explotadora merged with Sociedad Ganader, resulting in a company possessing 3 million hectares in southern Chile and Argentina, with over 2 million head of sheep. The headquarters of this company and the residences of the owners were in Punta Arenas. The Sarah Braun Museum is now established at the former Braun-Menéndez mansion, in the centre of Punta Arenas.


title: Punta Arenas

text: The Punta Arenas harbour, although exposed to storms, was considered one of the most important in Chile before the construction of the Panama Canal. It was used as a coaling station by the steamships transiting between the Atlantic and Pacific oceans. Today it is mostly used by tourism cruises and scientific expeditions.


title: Punta Arenas

text: The city is often a base for Antarctic expeditions; Ushuaia (Argentina) and Christchurch (New Zealand) are also common starting points.


title: Punta Arenas

text: In 2012 Punta Arenas recorded a population of over 127,000 inhabitants for the (2012 Census) by the National Statistics Institute. The population grew by 5.1% (5,830 persons) between the 1992 and 2002 censuses and further rose to 127,454 at the 2012 Census.


title: Punta Arenas

text: The city was populated by many colonists from Spain and Croatia in the mid-nineteenth century, and many of their descendants remain. Other national ethnic groups represented are German, English, Italian, Swiss and Irish.


title: Punta Arenas

text: Croatian immigration to Punta Arenas was a crucial development in the region of Magallanes and the city in particular. Currently, this influence is still reflected in the names of shops, streets and many buildings.


title: Punta Arenas

text: Punta Arenas is home to the southernmost Hindu temple in the world, which is used by the relatively small, but significant, Sindhi community in Punta Arenas. Sindhi merchants began arriving in the area during the early 1900s, and today constitute one of the largest communities of Indians in Chile.


title: Punta Arenas

text: By 2006 the economy of Punta Arenas and the region had diversified. Chile's principal oil reserves are close by, along with some low-grade coal.


title: Punta Arenas

text: Tourism has contributed to the city's economy and steady growth. Tourist destinations include the Cathedral and other notable churches, the city cemetery, and the statue of Magellan. Some cruise ships to Antarctica depart from Punta Arenas's port, which also serves as a hub for many cruise lines that travel along the channels and fjords of the region.


title: Punta Arenas

text: A scheduled ferry service connects Punta Arenas with the main island of Tierra del Fuego, and a less frequent ferry runs to the Chilean town of Puerto Williams.


title: Punta Arenas

text: University of Magallanes (UMAG) is in the southern Chilean city of Punta Arenas. It is part of the Chilean Traditional Universities. The University of Magallanes was established in 1981 during the neoliberal reforms of Chile's military regime as the successor of Universidad Técnica del Estado's Punta Arenas section. Universidad Técnica del Estado had established the Punta Arenas section in 1961.


title: Punta Arenas

text: The University of Magallanes has campuses in Punta Arenas and Puerto Natales as well as a university centre in Puerto Williams. University of Magallanes publishes the humanities and social sciences journal "Magallania" twice a year.


title: Punta Arenas

text: This museum exhibits a full-size replica of the first ship ever to circumnavigate the world: Ferdinand Magellan's "Nao Victoria." Since October 2011, the museum has added a full-size replica of the "James Caird", used by Ernest Shackleton during his Imperial Trans-Antarctic Expedition with the "Endurance". The museum is located 7.5 km north on Route Y-565 to Rio Seco.


title: Punta Arenas

text: As a "comuna" (commune) Punta Arenas is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2016–2020 alcalde is Claudio Radonich (National Renewal).


title: Punta Arenas

text: Within the electoral divisions of Chile, Punta Arenas is represented in the Chamber of Deputies by Sandra Amar (UDI), Karim Bianchi (IND-PRSD) and Gabriel Boric (CS) as part of the 60th electoral district, which includes the entire Magallanes and Antartica Chilena Region. The commune is represented in the Senate by Carlos Bianchi Chelech (Ind.) and Carolina Goic B. (DC) as part of the 19th senatorial constituency (Magallanes Region).


title: Punta Arenas

text: Carlos Ibáñez del Campo airport is located 20 kilometers from the city centre. Rental car services, duty-free shops and custom office services are available in the building (there is no duty-free shop in the terminal, despite the representations of tourist literature). Airlines serving the airport include LATAM Chile and Sky Airline, as well as charter flights. The civilian airport and the military airport make up the larger complex.


title: Punta Arenas

text: The city has sea, land, and air connections. By road, a connection to other regions of Chile requires passing through Argentine territory. By sea, several cruises and ferries can take visitors to the city, although the costs are higher because they include stops at tourist sites along the route.


title: Zee Bangla

text: Zee Bangla is an Indian general entertainment pay television channel broadcasting in the Bengali language. It is owned by the Zee Entertainment Enterprises. It is the first Bengali-language satellite television channel in India, officially commencing broadcasts on 15 September 1999. The channel was first launched as Alpha Bangla which was later renamed to Zee Bangla on 28 March 2005. The channel launched its HD version on 20 November 2016. According to BARC, Zee Bangla is the second most-watched television channel in West Bengal.


title: Zee Bangla

text: The channel was first launched in 1996, but halted transmissions within two months due to its poor ratings. It was relaunched on 15 September 1999 as Alpha TV Bangla, along with Alpha TV Marathi, Alpha TV Telugu and Alpha TV Punjabi. It was the first Bengali-language satellite television channel in India. In 2005, Zee TV went for a major brand revamp. It unveiled a new logo on 28 March 2005 at the Zee Cine Awards and thereafter Alpha Bangla was renamed to Zee Bangla with a modified version of the new Zee TV logo which is also used by other regional of Zee Network.


title: Zee Bangla

text: On 19 June 2011, all Zee channels rebranded with a new logo which was like number two instead of alphabet Z.


title: Zee Bangla

text: On 1 January 2017, the top right corner of all Zee channels was closed which continued unless all the Zee channels rebranded with a new logo on 15 October 2017 to celebrate the 25th anniversary.


title: Zee Bangla

text: On 15 October 2017, all the Zee channels had changed their logos where the logo has started showing on the left side. In 2019, Samrat Ghosh became the head of the channel. The channel's new graphics was revealed during "Sa Re Ga Ma Pa" on 7 October 2018. It is one of the largest Bengali-language television channels in India by viewership.


title: Zee Bangla

text: On 30 September 2021, Bangladesh imposed a blackout on foreign television channels, including Zee Bangla, that broadcast commercials. However, after 2 weeks, via clean feed, Zee Bangla resumed broadcasting in that country.


title: Zee Bangla

text: Zee Bangla Cinema is an Indian Bengali language movie channel owned by Zee Entertainment Enterprises. It was launched on 12 September 2012 as a sister channel of Zee Bangla.


title: Zee Bangla

text: Zee 24 Ghanta is an Indian Bengali language news channel owned by Zee Media Corporation. It was launched in 2007.


title: Sloppy joe

text: A sloppy joe is a sandwich consisting of ground beef, onions, tomato sauce or ketchup, Worcestershire sauce, and other seasonings, served on a hamburger bun. There are several theories about the sandwich's origin.


title: Sloppy joe

text: Early and mid-20th century American cookbooks offer plenty of sloppy joe-type recipes, though they go by different names: Toasted Deviled Hamburgers, Chopped Meat Sandwiches, Spanish Hamburgers, Hamburg a la Creole, Beef Mironton, and Minced Beef Spanish Style.


title: Sloppy joe

text: One theory of the sandwich's origin is that in 1917, Havana, Cuba, bar owner José "Sloppy Joe" Abeal y Otero created "a simple sandwich filled with ground beef stewed in tomatoes." This was possibly his interpretation of ropa vieja. His bar was reportedly frequented by Americans and Brits, including Errol Flynn, Ernest Hemingway, and Graham Greene. Circa 1937, Hemingway convinced Joe Russell, a bar owner in Key West, Florida, to rename his Silver Slipper bar to Sloppy Joe's.


title: Sloppy joe

text: Marilyn Brown, director of the consumer test kitchen at H.J. Heinz in Pittsburgh, says their research at the Carnegie Library suggests that the sloppy joe's origins lie with the "loose meat sandwiches" sold in Sioux City, Iowa, in the 1930s and were the creation of a cook named Joe.


title: Sloppy joe

text: A 1940 advertisement illustrates another use for the term "Sloppy Joe;" a women's cardigan sweater, described as "ever popular."


title: Sloppy joe

text: References to sloppy joes as sandwiches begin by the 1940s. One example from Ohio is a 1944 "Coshocton Tribune" ad under the heading Good Things to Eat' says 'Sloppy Joes' – 10c – Originated in Cuba – You'll ask for more – The Hamburg Shop" and elsewhere on the same page, "Hap is introducing that new sandwich at The Hamburg Shop – Sloppy Joes – 10c".


title: Sloppy joe

text: Food companies began producing packaged sloppy joe, in cans with meat, or just the sauce, such as Manwich, by the 1960s.


title: Sloppy joe

text: A 1975 "Dictionary of American Slang" defines "sloppy joe" as any cheap restaurant or lunch counter serving cheap food quickly.


title: Sloppy joe

text: Several variations of the sloppy joe exist in North America. In Quebec, Canada, sandwiches of stewed ground beef such as "pain à la viande" and "pain fourré gumbo" are usually served on hot dog buns. A similar sandwich, the "dynamite", exists in the area around Woonsocket, Rhode Island, and is distinguished by the use of onions, bell peppers, and sometimes celery.


title: Sloppy joe

text: Stewed meat sandwiches are common in several other culinary traditions as well. The "rou jia mo", from China's Shaanxi Province, consists of stewed pork, beef, or lamb on "baijimo", a type of flatbread. "Keema pav" of Indian cuisine uses a "pav" (from Portuguese "pão", a country-style soft roll) bread roll filled with keema, a minced, stewed, curried meat.


title: Sloppy joe

text: A sloppy joe differs from a traditional loose meat or tavern sandwich owing largely to its tomato-based sauce.


title: Sloppy joe

text: In some stores in northern New Jersey, an unrelated sandwich made with a combination of deli meat, such as turkey, roast beef or especially ham, with coleslaw, Russian dressing and Swiss cheese on three slices of rye bread is also known as a sloppy joe.


title: Act of Contrition

text: An Act of Contrition is a Christian prayer genre that expresses sorrow for sins. It may be used in a liturgical service or be used privately, especially in connection with an examination of conscience. Special formulae for acts of contrition are in use in the Anglican, Catholic, Lutheran, Methodist and Reformed Churches.


title: Act of Contrition

text: The Catholic Church does not restrict the term "act of contrition" to any one formula. Its "Handbook on Indulgences" mentions examples of approved formulas for an act of contrition the "Confiteor", the Psalm "De Profundis", the Psalm "Miserere", the Gradual Psalms and the Penitential Psalms.


title: Act of Contrition

text: The Act of Contrition is part of the Sacrament of Penance and is prayed by the penitent after the priest assigns a penance and before he gives the penitent absolution. It is also customarily said especially before one goes to bed at night. It is generally supposed that individuals might have recourse to an Act of Contrition when they find themselves "in extremis". Fulton Sheen recounts a story told of John Vianney. When a recent widow bemoaned the death of her husband who committed suicide by jumping off a bridge, Monsieur le Curé observed, "Remember, Madam, that there is a little distance between the bridge and the water." By this he meant that her husband had time to make an Act of Contrition. This is analogous to the well-known quote, "Between the stirrup and the ground, he something sought and something found," indicating that mercy is available when sought. (The original quote is from the sixteenth century English antiquarian William Camden; the more familiar version is from Graham Greene's 1938 novel "Brighton Rock".)


title: Act of Contrition

text: Within the Catholic Church, the term "act of contrition" is often applied to one particular formula, which is not given expressly in the handbook of Indulgences.


title: Act of Contrition

text: The "Catechism of the Catholic Church" notes that "Among the penitent’s acts, contrition occupies first place. Contrition is 'sorrow of the soul and detestation for the sin committed together with the resolution not to sin again.' When it arises from a love by which God is loved above all else, contrition is called ‘perfect’ (contrition of charity). Such contrition remits venial sins; it also obtains forgiveness of mortal sins if it includes the firm resolution to have recourse to sacramental confession as soon as possible" (CCC 1451–1452).


title: Act of Contrition

text: Catholic teaching holds that "imperfect" contrition, is also a gift of God. Born of fear of eternal damnation or other penalties, it is nonetheless sufficient to inspire a valid Act of Contrition.


title: Act of Contrition

text: There are different versions of the Act of Contrition, but all generally include an expression of sorrow, an acknowledgment of wrongdoing and a promise to amend one's life and avoid sin. The Latin text and a number of English versions that approximate to the Latin text are given here.


title: Act of Contrition

text: O my God, I am heartily sorry for having offended Thee: and I detest my sins most sincerely because they displease Thee, my God, Who art so deserving of all my love for Thy infinite goodness and most amiable perfections: and I firmly purpose by Thy holy grace never more to offend Thee.


title: Act of Contrition

text: “O my God, because You are so good, I am truly sorry that I have sinned against You and by the help of Your grace, I will not sin again.”


title: Act of Contrition

text: "Sacrosanctum concilium" (the Constitution on the Sacred Liturgy) called for the revision of the Rite of Penance so that it more clearly express both the nature and effect of the sacrament. Consequently, the Rite of Penance was revised in 1973. The revised rite offered several possible options for making an Act of Contrition. One may choose one of the general formula prayers or other prayers of contrition.


title: Act of Contrition

text: The following are some formulas for acts of contrition that differ more considerably from the Latin text given above.


title: Act of Contrition

text: In the Church of England Reconciliation of a Penitent the Act of Contrition "expresses the desire and intention before God to turn away from sin and walk in newness of life. The penitent may use his or her own words or the form provided."


title: Act of Contrition

text: The Anglican Communion, which includes the Church of England, The Episcopal Church (in the United States) and other member churches, has its own act of contrition, referred to in the Prayer Book as the General Confession. This is said by the Congregation en masse during worship. The 1662 "Book of Common Prayer" contains two versions. The first (for use at Matins and Evensong) is:


title: Act of Contrition

text: The Lutheran Church also has its own act of contrition, which is said during Holy Absolution. The following version, taken from the Lutheran Service Book (2006), says:


title: Andrew Klavan

text: Andrew Klavan (; born July 13, 1954) is an American writer of crime and suspense novels. Klavan has been nominated for the Edgar Award five times and has won twice.


title: Andrew Klavan

text: Klavan has also worked in film and as an essayist and video satirist. He is also known as a conservative commentator and hosts "The Andrew Klavan Show" podcast on the conservative site "The Daily Wire", a media company associated with political commentator Ben Shapiro.


title: Andrew Klavan

text: Klavan was born to a secular Jewish family in New York City and grew up in Great Neck, Long Island, one of four sons born to father Gene Klavan, a New York disc jockey, and mother Phyllis, a homemaker. He graduated from the University of California, Berkeley with a degree in English Literature. He worked as a radio and newspaper reporter and a radio news writer before becoming a full-time writer.


title: Andrew Klavan

text: In 1980, he married Ellen Flanagan, daughter of Thomas Flanagan and sister of Caitlin Flanagan. They have two children, Spencer Klavan and Faith Moore and live in Nashville, Tennessee. Spencer Klavan is an Oxford-trained classicist who is married to Joshua Herr, general counsel for the Daily Wire.


title: Andrew Klavan

text: After graduating from Berkeley, Klavan began his writing career as a liberal. He became a conservative during the Reagan administration.


title: Andrew Klavan

text: Klavan converted to Christianity at the age of 49 and was baptized privately. Initially he attended the Episcopal Church, but has since left for the Anglican Church in North America.


title: Andrew Klavan

text: Klavan began his crime-writing career using the pseudonym Keith Peterson. Under that name, he wrote the four John Wells mysteries, about a crime-solving newspaper reporter, and also "The Scarred Man", his first novel of psychological suspense.


title: Andrew Klavan

text: Under his own name, Klavan has written crime novels, and the "Homelanders" series for young adults. His novels have been translated around the world. He has won two Edgar Awards from the Mystery Writers of America, the Thumping Good Read Award from W.H. Smith, and been nominated for Anthony Awards and the International Thriller Writers award.


title: Andrew Klavan

text: "True Crime" was filmed by Clint Eastwood in 1999. "Don’t Say a Word" was filmed starring Michael Douglas in 2001. Donald Cammell's 1987 "White of the Eye" was based on the novel "Mrs. White", which Klavan co-wrote under the pseudonym Margaret Tracy with his brother, playwright Laurence Klavan. Andrew wrote the screenplay for the 1990 Michael Caine film "Shock to the System", based on the novel by Simon Brett, and for the 2008 horror film "One Missed Call", which starred Shannyn Sossamon and Ed Burns. He also wrote the screenplay for the movie-in-an-app "Haunting Melissa" and its sequel, "Haunting Melissa 2: Dark Hearts". He recently scripted "", a crime film based on the true story of an abortion doctor convicted of murder.


title: Andrew Klavan

text: Klavan has produced several satirical online video series including "Klavan on the Culture" for PJ Media, "The Revolting Truth" for "TruthRevolt", and "A Very Serious Commentary" for Glenn Beck's Blaze Media. He currently does a weekly podcast for the "Daily Wire" called the "Andrew Klavan Show".


title: Andrew Klavan

text: "The Great Good Thing: A Secular Jew Comes to Faith in Christ", Klavan's first non-fiction book, was published in 2016. It is a memoir of his spiritual journey from secular Judaism and agnosticism to Christianity.


title: Andrew Klavan

text: "When Christmas Comes" was published in 2021; it is Klavan's 36th novel and features themes of Christmas, tradition, and murder. In fact, it is a thriller novel situated in, and vaguely centered upon, Christmas, in an idyllic town.


title: Andrew Klavan

text: Klavan's book "Mrs. White", which he wrote under the pen-name Margaret Tracy, won the 1984 Edgar Award for Best Paperback Original. In 1989, his novel "Trapdoor" was nominated in the Best Paperback Original category. In 1990, he won the Edgar Award in the Best Paperback Original category for "The Rain", as well as a nomination at the 1990 Anthony Awards for "Rough Justice" in the paperback category. Klavan was nominated for an Edgar Award for Best Novel in 1992 for his first novel, "Don't Say a Word". He received an Anthony Awards nomination at the 1996 ceremony for "True Crime" in the Best Novel category.


title: Peano axioms

text: In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete.


title: Peano axioms

text: The need to formalize arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction. In 1881, Charles Sanders Peirce provided an axiomatization of natural-number arithmetic. In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic, and in 1889, Peano published a simplified version of them as a collection of axioms in his book, "The principles of arithmetic presented by a new method" ().


title: Peano axioms

text: The nine Peano axioms contain three types of statements. The first axiom asserts the existence of at least one member of the set of natural numbers. The next four are general statements about equality; in modern treatments these are often not taken as part of the Peano axioms, but rather as axioms of the "underlying logic". The next three axioms are first-order statements about natural numbers expressing the fundamental properties of the successor operation. The ninth, final axiom is a second-order statement of the principle of mathematical induction over the natural numbers, which makes this formulation close to second-order arithmetic. A weaker first-order system called Peano arithmetic is obtained by explicitly adding the addition and multiplication operation symbols and replacing the second-order induction axiom with a first-order axiom schema.


title: Peano axioms

text: When Peano formulated his axioms, the language of mathematical logic was in its infancy. The system of logical notation he created to present the axioms did not prove to be popular, although it was the genesis of the modern notation for set membership (∈, which comes from Peano's ε) and implication (⊃, which comes from Peano's reversed 'C'.) Peano maintained a clear distinction between mathematical and logical symbols, which was not yet common in mathematics; such a separation had first been introduced in the "Begriffsschrift" by Gottlob Frege, published in 1879. Peano was unaware of Frege's work and independently recreated his logical apparatus based on the work of Boole and Schröder.


title: Peano axioms

text: The Peano axioms define the arithmetical properties of "natural numbers", usually represented as a set N or formula_1 The non-logical symbols for the axioms consist of a constant symbol 0 and a unary function symbol "S".


title: Peano axioms

text: Peano's original formulation of the axioms used 1 instead of 0 as the "first" natural number, while the axioms in "Formulario mathematico" include zero.


title: Peano axioms

text: The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.


title: Peano axioms

text: The remaining axioms define the arithmetical properties of the natural numbers. The naturals are assumed to be closed under a single-valued "successor" function "S".


title: Peano axioms

text: Axioms 1, 6, 7, 8 define a unary representation of the intuitive notion of natural numbers: the number 1 can be defined as "S"(0), 2 as "S"("S"(0)), etc. However, considering the notion of natural numbers as being defined by these axioms, axioms 1, 6, 7, 8 do not imply that the successor function generates all the natural numbers different from 0.


title: Peano axioms

text: The intuitive notion that each natural number can be obtained by applying "successor" sufficiently often to zero requires an additional axiom, which is sometimes called the "axiom of induction".


title: Peano axioms

text: In Peano's original formulation, the induction axiom is a second-order axiom. It is now common to replace this second-order principle with a weaker first-order induction scheme. There are important differences between the second-order and first-order formulations, as discussed in the section below.


title: Peano axioms

text: If we use the second-order induction axiom, it is possible to define addition, multiplication, and total (linear) ordering on N directly using the axioms. However, and addition and multiplication are often added as axioms. The respective functions and relations are constructed in set theory or second-order logic, and can be shown to be unique using the Peano axioms.


title: Peano axioms

text: Addition is a function that maps two natural numbers (two elements of N) to another one. It is defined recursively as:


title: Peano axioms

text: The structure is a commutative monoid with identity element 0. is also a cancellative magma, and thus embeddable in a group. The smallest group embedding N is the integers.


title: Peano axioms

text: Similarly, multiplication is a function mapping two natural numbers to another one. Given addition, it is defined recursively as:


title: Peano axioms

text: It is easy to see that formula_5 (or "1", in the familiar language of decimal representation) is the multiplicative right identity:


title: Peano axioms

text: To show that formula_5 is also the multiplicative left identity requires the induction axiom due to the way multiplication is defined:


title: Peano axioms

text: Therefore, by the induction axiom formula_5 is the multiplicative left identity of all natural numbers. Moreover, it can be shown that multiplication is commutative and distributes over addition:


title: Peano axioms

text: The usual total order relation ≤ on natural numbers can be defined as follows, assuming 0 is a natural number:


title: Peano axioms

text: Thus, the structure is an ordered semiring; because there is no natural number between 0 and 1, it is a discrete ordered semiring.


title: Peano axioms

text: The axiom of induction is sometimes stated in the following form that uses a stronger hypothesis, making use of the order relation "≤":


title: Peano axioms

text: This form of the induction axiom, called "strong induction", is a consequence of the standard formulation, but is often better suited for reasoning about the ≤ order. For example, to show that the naturals are well-ordered—every nonempty subset of N has a least element—one can reason as follows. Let a nonempty be given and assume "X" has no least element.


title: Peano axioms

text: Thus, by the strong induction principle, for every , . Thus, , which contradicts "X" being a nonempty subset of N. Thus "X" has a least element.


title: Peano axioms

text: A model of the Peano axioms is a triple , where N is a (necessarily infinite) set, and satisfies the axioms above. Dedekind proved in his 1888 book, "The Nature and Meaning of Numbers" (, i.e., “What are the numbers and what are they good for?”) that any two models of the Peano axioms (including the second-order induction axiom) are isomorphic. In particular, given two models and of the Peano axioms, there is a unique homomorphism satisfying


title: Peano axioms

text: and it is a bijection. This means that the second-order Peano axioms are categorical. (This is not the case with any first-order reformulation of the Peano axioms, below.)


title: Peano axioms

text: The Peano axioms can be derived from set theoretic constructions of the natural numbers and axioms of set theory such as ZF. The standard construction of the naturals, due to John von Neumann, starts from a definition of 0 as the empty set, ∅, and an operator "s" on sets defined as:


title: Peano axioms

text: The set of natural numbers N is defined as the intersection of all sets closed under "s" that contain the empty set. Each natural number is equal (as a set) to the set of natural numbers less than it:


title: Peano axioms

text: Peano arithmetic is equiconsistent with several weak systems of set theory. One such system is ZFC with the axiom of infinity replaced by its negation. Another such system consists of general set theory (extensionality, existence of the empty set, and the axiom of adjunction), augmented by an axiom schema stating that a property that holds for the empty set and holds of an adjunction whenever it holds of the adjunct must hold for all sets.


title: Peano axioms

text: The Peano axioms can also be understood using category theory. Let "C" be a category with terminal object 1, and define the category of pointed unary systems, US("C") as follows:


title: Peano axioms

text: Then "C" is said to satisfy the Dedekind–Peano axioms if US("C") has an initial object; this initial object is known as a natural number object in "C". If is this initial object, and is any other object, then the unique map is such that


title: Peano axioms

text: When the Peano axioms were first proposed, Bertrand Russell and others agreed that these axioms implicitly defined what we mean by a "natural number". Henri Poincaré was more cautious, saying they only defined natural numbers if they were "consistent"; if there is a proof that starts from just these axioms and derives a contradiction such as 0 = 1, then the axioms are inconsistent, and don't define anything. In 1900, David Hilbert posed the problem of proving their consistency using only finitistic methods as the second of his twenty-three problems. In 1931, Kurt Gödel proved his second incompleteness theorem, which shows that such a consistency proof cannot be formalized within Peano arithmetic itself.


title: Peano axioms

text: Although it is widely claimed that Gödel's theorem rules out the possibility of a finitistic consistency proof for Peano arithmetic, this depends on exactly what one means by a finitistic proof. Gödel himself pointed out the possibility of giving a finitistic consistency proof of Peano arithmetic or stronger systems by using finitistic methods that are not formalizable in Peano arithmetic, and in 1958, Gödel published a method for proving the consistency of arithmetic using type theory. In 1936, Gerhard Gentzen gave a proof of the consistency of Peano's axioms, using transfinite induction up to an ordinal called ε. Gentzen explained: "The aim of the present paper is to prove the consistency of elementary number theory or, rather, to reduce the question of consistency to certain fundamental principles". Gentzen's proof is arguably finitistic, since the transfinite ordinal ε can be encoded in terms of finite objects (for example, as a Turing machine describing a suitable order on the integers, or more abstractly as consisting of the finite trees, suitably linearly ordered). Whether or not Gentzen's proof meets the requirements Hilbert envisioned is unclear: there is no generally accepted definition of exactly what is meant by a finitistic proof, and Hilbert himself never gave a precise definition.


title: Peano axioms

text: The vast majority of contemporary mathematicians believe that Peano's axioms are consistent, relying either on intuition or the acceptance of a consistency proof such as Gentzen's proof. A small number of philosophers and mathematicians, some of whom also advocate ultrafinitism, reject Peano's axioms because accepting the axioms amounts to accepting the infinite collection of natural numbers. In particular, addition (including the successor function) and multiplication are assumed to be total. Curiously, there are self-verifying theories that are similar to PA but have subtraction and division instead of addition and multiplication, which are axiomatized in such a way to avoid proving sentences that correspond to the totality of addition and multiplication, but which are still able to prove all true formula_24 theorems of PA, and yet can be extended to a consistent theory that proves its own consistency (stated as the non-existence of a Hilbert-style proof of "0=1").


title: Peano axioms

text: All of the Peano axioms except the ninth axiom (the induction axiom) are statements in first-order logic. The arithmetical operations of addition and multiplication and the order relation can also be defined using first-order axioms. The axiom of induction above is second-order, since it quantifies over predicates (equivalently, sets of natural numbers rather than natural numbers). As an alternative one can consider a first-order "axiom schema" of induction. Such a schema includes one axiom per predicate definable in the first-order language of Peano arithmetic, making it weaker than the second-order axiom. The reason that it is weaker is that the number of predicates in first-order language is countable, whereas the number of sets of natural numbers is uncountable. Thus, there exist sets that cannot be described in first-order language (in fact, most sets have this property).


title: Peano axioms

text: First-order axiomatizations of Peano arithmetic have another technical limitation. In second-order logic, it is possible to define the addition and multiplication operations from the successor operation, but this cannot be done in the more restrictive setting of first-order logic. Therefore, the addition and multiplication operations are directly included in the signature of Peano arithmetic, and axioms are included that relate the three operations to each other.


title: Peano axioms

text: The following list of axioms (along with the usual axioms of equality), which contains six of the seven axioms of Robinson arithmetic, is sufficient for this purpose:


title: Peano axioms

text: In addition to this list of numerical axioms, Peano arithmetic contains the induction schema, which consists of a recursively enumerable and even decidable set of axioms. For each formula in the language of Peano arithmetic, the first-order induction axiom for "φ" is the sentence


title: Peano axioms

text: where formula_32 is an abbreviation for "y"...,"y". The first-order induction schema includes every instance of the first-order induction axiom; that is, it includes the induction axiom for every formula "φ".


title: Peano axioms

text: There are many different, but equivalent, axiomatizations of Peano arithmetic. While some axiomatizations, such as the one just described, use a signature that only has symbols for 0 and the successor, addition, and multiplications operations, other axiomatizations use the language of ordered semirings, including an additional order relation symbol. One such axiomatization begins with the following axioms that describe a discrete ordered semiring.


title: Peano axioms

text: The theory defined by these axioms is known as PA; the theory PA is obtained by adding the first-order induction schema. An important property of PA is that any structure formula_48 satisfying this theory has an initial segment (ordered by formula_49) isomorphic to formula_50. Elements in that segment are called standard elements, while other elements are called nonstandard elements.


title: Peano axioms

text: According to Gödel's incompleteness theorems, the theory of PA (if consistent) is incomplete. Consequently, there are sentences of first-order logic (FOL) that are true in the standard model of PA but are not a consequence of the FOL axiomatization. Essential incompleteness already arises for theories with weaker axioms, such as Robinson arithmetic.


title: Peano axioms

text: Closely related to the above incompleteness result (via Gödel's completeness theorem for FOL) it follows that there is no algorithm for deciding whether a given FOL sentence is a consequence of a first-order axiomatization of Peano arithmetic or not. Hence, PA is an example of an undecidable theory. Undecidability arises already for the existential sentences of PA, due to the negative answer to Hilbert's tenth problem, whose proof implies that all computably enumerable sets are diophantine sets, and thus definable by existentially quantified formulas (with free variables) of PA. Formulas of PA with higher quantifier rank (more quantifier alternations) than existential formulas are more expressive, and define sets in the higher levels of the arithmetical hierarchy.


title: Peano axioms

text: Although the usual natural numbers satisfy the axioms of PA, there are other models as well (called "non-standard models"); the compactness theorem implies that the existence of nonstandard elements cannot be excluded in first-order logic. The upward Löwenheim–Skolem theorem shows that there are nonstandard models of PA of all infinite cardinalities. This is not the case for the original (second-order) Peano axioms, which have only one model, up to isomorphism. This illustrates one way the first-order system PA is weaker than the second-order Peano axioms.


title: Peano axioms

text: When interpreted as a proof within a first-order set theory, such as ZFC, Dedekind's categoricity proof for PA shows that each model of set theory has a unique model of the Peano axioms, up to isomorphism, that embeds as an initial segment of all other models of PA contained within that model of set theory. In the standard model of set theory, this smallest model of PA is the standard model of PA; however, in a nonstandard model of set theory, it may be a nonstandard model of PA. This situation cannot be avoided with any first-order formalization of set theory.


title: Peano axioms

text: It is natural to ask whether a countable nonstandard model can be explicitly constructed. The answer is affirmative as Skolem in 1933 provided an explicit construction of such a nonstandard model. On the other hand, Tennenbaum's theorem, proved in 1959, shows that there is no countable nonstandard model of PA in which either the addition or multiplication operation is computable. This result shows it is difficult to be completely explicit in describing the addition and multiplication operations of a countable nonstandard model of PA. There is only one possible order type of a countable nonstandard model. Letting "ω" be the order type of the natural numbers, "ζ" be the order type of the integers, and "η" be the order type of the rationals, the order type of any countable nonstandard model of PA is , which can be visualized as a copy of the natural numbers followed by a dense linear ordering of copies of the integers.


title: Peano axioms

text: A cut in a nonstandard model "M" is a nonempty subset "C" of "M" so that "C" is downward closed ("x" < "y" and "y" ∈ "C" ⇒ "x" ∈ "C") and "C" is closed under successor. A proper cut is a cut that is a proper subset of "M". Each nonstandard model has many proper cuts, including one that corresponds to the standard natural numbers. However, the induction scheme in Peano arithmetic prevents any proper cut from being definable. The overspill lemma, first proved by Abraham Robinson, formalizes this fact.


title: Formula Three

text: Formula Three, also called Formula 3, abbreviated as F3, is a third-tier class of open-wheel formula racing. The various championships held in Europe, Australia, South America and Asia form an important step for many prospective Formula One drivers.


title: Formula Three

text: Formula Three (adopted by the FIA in 1950) evolved from postwar auto racing, with lightweight tube-frame chassis powered by 500 cc motorcycle engines (notably Nortons and JAP speedway). The 500 cc formula originally evolved in 1946 from low-cost "special" racing organised by enthusiasts in Bristol, England, just before the Second World War; British motorsport after the war picked up slowly, partly due to petrol rationing which continued for a number of years and home-built 500 cc cars engines were intended to be accessible to the "impecunious enthusiast". The second post-war motor race in Britain was organised by the VSCC in July 1947 at RAF Gransden Lodge, 500cc cars being the only post-war class to run that day. Three of the seven entrants were non-starters, and, of the four runners, all but one retired on the first lap, leaving Eric Brandon in his Cooper Prototype (T2) trailing round to a virtual walk-over at an average speed of , though his best lap (which was the fastest recorded for any 500) was .


title: Formula Three

text: Cooper came to dominate the formula with mass-produced cars, and the income this generated enabled the company to develop into the senior categories. Other notable marques included Kieft, JBS and Emeryson in England, and Effyh, Monopoletta and Scampolo in Europe. John Cooper, along with most other 500 builders, decided to place the engine in the middle of the car, driving the rear wheels. This was mostly due to the practical limitations imposed by chain drive but it gave these cars exceptionally good handling characteristics which eventually led to the mid-engined revolution in single-seater racing.


title: Formula Three

text: The 500cc formula was the usual route into motor racing through the early and mid-1950s (and stars like Stirling Moss continued to enter selected F3 events even during their GP careers). Other notable 500 cc Formula 3 drivers include Stuart Lewis-Evans, Ivor Bueb, Jim Russell, Peter Collins, Don Parker, Ken Tyrrell, and Bernie Ecclestone.


title: Formula Three

text: From a statistical point of view, Parker was the most successful F3 driver. Although coming to motor racing late in life (at age 41 in 1949), he won a total of 126 F3 races altogether, and was described by "Motor Sport" magazine (in his 1998 obituary) as "the most successful Formula 3 driver in history". Although Stirling Moss was already a star by 1953, Parker beat him more than any other driver, and was Formula 3 Champion in 1952, again in 1953, and in 1954 he only lost the title by a half-point. He took the title for a third time in 1959.


title: Formula Three

text: 500cc Formula Three declined at an international level during the late 1950s, although it continued at a national level into the early 60s, being eclipsed by Formula Junior for 1000 or 1100 cc cars (on a sliding scale of weights).


title: Formula Three

text: A one-litre Formula Three category for four-cylinder carburetted cars, with heavily tuned production engines, was reintroduced in 1964 based on the Formula Junior rules and ran to 1970. These engines (a short-stroke unit based on the Ford Anglia with a special 2-valve Cosworth or Holbay OHV down-draught head, initially pioneered by Brian Hart, being by far the most efficient and popular) tended to rev very highly and were popularly known as "screamers"; F3 races tended to involve large packs of slipstreaming cars. The "screamer" years were dominated by Brabham, Lotus and Tecno, with March beginning in 1970. Early one-litre F3 chassis tended to descend from Formula Junior designs but quickly evolved.


title: Formula Three

text: For 1971 new regulations allowing 1600 cc engines with a restricted air intake were introduced. The 1971–73 seasons were contested with these cars, as aerodynamics started to become important.


title: Formula Three

text: Two-litre engine rules were introduced for 1974, still with restricted air intakes. engine regulations remain basically unchanged in F3, a remarkable case of stability in racing regulations.


title: Formula Three

text: As the likes of Lotus and Brabham faded from F3 to concentrate on Formula One, F3 constructors of the 1970s included Alpine, Lola, March, Modus, GRD, Ralt, and Ensign.


title: Formula Three

text: By the start of the 1980s however, Formula Three had evolved well beyond its humble beginnings to something closely resembling the modern formula. It was seen as the main training ground for future Formula One drivers, many of them bypassing Formula Two to go straight into Grand Prix racing. The chassis became increasingly sophisticated, mirroring the more senior formulae – ground effects were briefly used in the early 1980s but were banned, in line with other FIA single-seater formulae; carbon fibre chassis started to be introduced from the mid-1980s.


title: Formula Three

text: Historically, March (up to 1981), Ralt (up to the early 1990s) and Reynard (1985–1992) had been the main chassis manufacturers in two-litre F3, with Martini fairly strong in France; Reynard pioneered use of carbon fibre in the mid-1980s replacing traditional aluminium or steel monocoque structures. Dallara however, after an unsuccessful Formula One project, focussed their attention on the formula in the early nineties and obliterated all the other marques with their F393. Within a couple of years, the chassis was considered a prerequisite to competitiveness, and today Dallara chassis are ubiquitous to the formula. In order to keep costs down, their chassis have had a three-year life-cycle, with only minor annual updates. It was agreed however to extend the life-cycle of the current F308 to four years to assist teams; this chassis however, has been replaced in 2012 with the new F312 chassis, intended to be run until 2017. Most F3 championships, most notably the British series, offer a secondary class for cars from the previous life-cycle in order to provide a cheap point of entry for lesser funded teams and drivers.


title: Formula Three

text: Formula Three cars are monocoque chassis, using slick racing tyres and wings. Currently, Dallara manufactures the overwhelming majority of F3 cars, though Mygale, Lola (formerly in partnership with Dome of Japan), Arttech, and SLC also have a limited output. In many smaller or amateur F3 racing series older cars are frequently seen. Usually these series are divided into two or more classes, to allow more participation.


title: Formula Three

text: Engines in others Formula 3 series must be built from a production model block ("stock block"), and often must be sealed by race or series organizers, so no private tuning can be carried out. Honda engines (prepared by Mugen) have perennially been popular, as have engines produced by Volkswagen, Alfa Romeo, or Renault. Currently the HWA-tuned Mercedes and the Volkswagen engines dominate the British and European series, with Mugen, TOM'S–Toyota, Opel, and Fiat being used by some teams.


title: Formula Three

text: Until the launch of the FIA Formula 3 Championship in 2019, there has never been a World Championship for Formula Three. In the 1970s and into the 1980s the European Formula Three Championship and British Formula 3 Championship (once one series had emerged from the competing British series in the 1970s) were the most prominent, with a number of future Formula One champions coming from them. France, Germany, and Italy also had important Formula Three series, but interest in these was originally subsidiary to national formulae – Formula Renault in France and Formula Super Vee in Germany. These nations eventually drifted towards Formula Three. The Italian series tended to attract older drivers who moved straight across from karting whereas in other nations drivers typically graduated to F3 after a couple of years in minor categories. The European series died out in the mid-1980s and the national series became correspondingly more important. For 2003, French and German F3, both suffering from a lack of competitive entrants, merged to recreate the Formula 3 Euro Series.


title: Formula Three

text: Brazil's SudAm Formula Three Championship, which now has the most powerful engine of all Formula Three series, was known for producing excellent drivers who polished their skills in the British Formula 3 championship. Perhaps the most curious of all was the small All-Japan Formula Three Championship. Although few drivers spent a significant amount of time there, future stars such as Ralf Schumacher and Jacques Villeneuve scored victories there. An Asian series was established in 2001 and grew to produce past A1 drivers for Indonesia and Australia.


title: Formula Three

text: In addition to the many national series, Formula Three is known for major non-championship races typically including entries from the national series, the best-known of which is the FIA World Cup at Macau. The first Formula Three Grand Prix of Macau was held in 1983 and won by Ayrton Senna. Michael Schumacher, David Coulthard, Ralf Schumacher, and Takuma Sato have also won there. The Formula Three Grand Prix of Macau traditionally marks the end of the Formula Three season, with drivers from almost every national series participating.


title: Formula Three

text: Other major races include the Pau Grand Prix (from 1999 to 2006), the Masters of Formula 3 (traditionally held at Zandvoort), and the Korea Super Prix at Changwon. These events give fans in locations not visited by other major series a way to experience major international racing.


title: Formula Three

text: The Monaco F3 Grand Prix held until 1997 was also a famous special race. It was restored in 2005 only, as a part of the F3 Euro Series.


title: Finnic languages

text: The Finnic (Fennic) or more precisely Balto-Finnic (Balto-Fennic, Baltic Finnic, Baltic Fennic) languages constitute a branch of the Uralic language family spoken around the Baltic Sea by the Baltic Finnic peoples. There are around 7 million speakers, who live mainly in Finland and Estonia.


title: Finnic languages

text: Traditionally, eight Finnic languages have been recognized. The major modern representatives of the family are Finnish and Estonian, the official languages of their respective nation states. The other Finnic languages in the Baltic Sea region are Ingrian and Votic, spoken in Ingria by the Gulf of Finland, and Livonian, once spoken around the Gulf of Riga. Spoken farther northeast are Karelian, Ludic, and Veps, in the region of Lakes Onega and Ladoga.


title: Finnic languages

text: In addition, since the 1990s, several Finnic-speaking minority groups have emerged to seek recognition for their languages as distinct from the ones they have been considered dialects of in the past. Some of these groups have established their own orthographies and standardised languages. Võro and Seto, which are spoken in southeastern Estonia and in some parts of Russia, are considered dialects of Estonian by some linguists, while other linguists consider them separate languages. Meänkieli and Kven are spoken in northern Sweden and Norway respectively and have the legal status of independent minority languages. They were earlier considered dialects of Finnish and are somewhat mutually intelligible with it, depending on the dialect. Additionally, the Karelian language was not officially recognised as its own language in Finland until 2009, despite there being no linguistic confusion about its status.


title: Finnic languages

text: The smaller languages are endangered. The last native speaker of Livonian died in 2013, and only about a dozen native speakers of Votic remain. Regardless, even for these languages, the shaping of a standard language and education in it continues.


title: Finnic languages

text: The geographic centre of the maximum divergence between the languages is located east of the Gulf of Finland around Saint Petersburg. A glottochronological study estimates the age of the common ancestor of existing languages to a little more than 1000 years. However, Mikko Heikkilä dates the beginning of the diversification (with South Estonian as the first split) rather precisely to about 150 AD, based on loanword evidence (and previous estimates tend to be even older, like Pekka Sammallahti's of 1000–600 BC). There is now wide agreement that Proto-Finnic was probably spoken at the coasts of the Gulf of Finland.


title: Finnic languages

text: The Finnic languages are located at the western end of the Uralic language family. A close affinity to their northern neighbors, the Sami languages, has long been assumed, though many of the similarities (particularly lexical ones) can be shown to result from common influence from Germanic languages and, to a lesser extent, Baltic languages. Innovations are also shared between Finnic and the Mordvinic languages, and in recent times Finnic, Samic and Moksha are sometimes grouped together.


title: Finnic languages

text: There is no grammatical gender in any of the Finnic languages, nor are there articles or definite or indefinite forms.


title: Finnic languages

text: The morphophonology (the way the grammatical function of a morpheme affects its production) is complex. Morphological elements found in the Finnic languages include grammatical case suffixes, verb tempus, mood and person markers (singular and plural, the Finnic languages do not have dual) as well as participles and several infinitive forms, possessive suffixes, clitics and more. The number of grammatical cases tends to be high while the number of verb infinitive forms varies more by language.


title: Finnic languages

text: One of the more important processes is the characteristic consonant gradation. Two kinds of gradation occur: radical gradation and suffix gradation. They both affect the plosives , and , and involve the process known as lenition, in which the consonant is changed into a "weaker" form. This occurs in some (but not all) of the oblique case forms. For geminates, the process is simple to describe: they become simple stops, e.g. "kuppi" + "-n" → "kupin" (Finnish: "cup"). For simple consonants, the process complicates immensely and the results vary by the environment. For example, "haka" + "-n" → "haan", "kyky" + "-n" → "kyvyn", "järki" + "-n" → "järjen" (Finnish: "pasture", "ability", "intellect"). The specifics of consonants gradation vary by language (see the separate article for more details). Apocope (strongest in Livonian, Võro and Estonian) has, in some cases, left a phonemic status to the phonological variation in the stem (variation caused by the now historical morphological elements), which results in three phonemic lengths in these languages.


title: Finnic languages

text: Vowel harmony is also characteristic of the Finnic languages, despite having been lost in Livonian, Estonian and Veps.


title: Finnic languages

text: The original Uralic palatalization was lost in proto-Finnic, but most of the diverging dialects reacquired it. Palatalization is a part of the Estonian literary language and is an essential feature in Võro, as well as Veps, Karelian, and other eastern Finnic languages. It is also found in East Finnish dialects, and is only missing from West Finnish dialects and Standard Finnish.


title: Finnic languages

text: A special characteristic of the languages is the large number of diphthongs. There are 16 diphthongs in Finnish and 25 in Estonian; at the same time the frequency of diphthong use is greater in Finnish than in Estonian due to certain historical long vowels having diphthongised in Finnish but not in Estonian. On a global scale the Finnic languages have a high number of vowels.


title: Finnic languages

text: The Finnic languages form a complex dialect continuum with few clear-cut boundaries. Innovations have often spread through a variety of areas, even after variety-specific changes.


title: Finnic languages

text: A broad twofold conventional division of the Finnic varieties recognizes the Southern Finnic and Northern Finnic groups (though the position of some varieties within this division is uncertain):


title: Finnic languages

text: A more-or-less genetic subdivision can be also determined, based on the relative chronology of sound changes within varieties, which provides a rather different view. The following grouping follows among others Sammallahti (1977), Viitso (1998), and Kallio (2014):


title: Finnic languages

text: The division between South Estonian and the remaining Finnic varieties has isoglosses that must be very old. For the most part, these features have been known for long. Their position as very early in the relative chronology of Finnic, in part representing archaisms in South Estonian, has been shown by Kallio (2007, 2014).


title: Finnic languages

text: However, due to the strong areal nature of many later innovations, this tree structure has been distorted and sprachbunds have formed. In particular, South Estonian and Livonian show many similarities with the Central Finnic group that must be attributed to later contact, due to the influence of literary North Estonian. Thus, contemporary "Southern Finnic" is a sprachbund that includes these languages, while diachronically they are not closely related.


title: Finnic languages

text: Viitso (2000) surveys 59 isoglosses separating the family into 58 dialect areas (finer division is possible), finding that an unambiguous perimeter can be set up only for South Estonian, Livonian, Votic, and Veps. In particular, no isogloss exactly coincides with the geographical division into 'Estonian' south of the Gulf of Finland and 'Finnish' north of it. Despite this, standard Finnish and Estonian are not mutually intelligible.


title: Finnic languages

text: The Southern Finnic languages consist of North and South Estonian (excluding the Coastal Estonian dialect group), Livonian and Votic (except the highly Ingrian-influenced Kukkuzi Votic). These languages are not closely related genetically, as noted above; it is a paraphyletic grouping, consisting of all Finnic languages except the Northern Finnic languages. The languages regardless share a number of features, such as the presence of a ninth vowel phoneme "õ", usually a close-mid back unrounded (but a close central unrounded in Livonian), as well as loss of "*n" before "*s" with compensatory lengthening.


title: Finnic languages

text: (North) Estonian-Votic has been suggested to possibly constitute an actual genetic subgroup (called varyingly Maa by Viitso (1998, 2000) or Central Finnic by Kallio (2014)), though the evidence is weak: almost all innovations shared by Estonian and Votic have also spread to South Estonian and/or Livonian. A possible defining innovation is the loss of "*h" after sonorants ("*n, *l, *r").


title: Finnic languages

text: The Northern Finnic group has more evidence for being an actual historical/genetic subgroup. Phonetical innovations would include two changes in unstressed syllables: *ej > *ij, and *o > "ö" after front-harmonic vowels. The lack of "õ" in these languages as an innovation rather than a retention has been proposed, and recently resurrected. Germanic loanwords found throughout Northern Finnic but absent in Southern are also abundant, and even several Baltic examples of this are known.


title: Finnic languages

text: Northern Finnic in turn divides into two main groups. The most Eastern Finnic group consists of the East Finnish dialects as well as Ingrian, Karelian and Veps; the proto-language of these was likely spoken in the vicinity of Lake Ladoga. The Western Finnic group consists of the West Finnish dialects, originally spoken on the western coast of Finland, and within which the oldest division is that into Southwestern, Tavastian and Southern Ostrobothnian dialects. Among these, at least the Southwestern dialects have later come under Estonian influence.


title: Finnic languages

text: Numerous new dialects have also arisen through contacts of the old dialects: these include e.g. the more northern Finnish dialects (a mixture of West and East Finnish), and the Livvi and Ludic varieties (probably originally Veps dialects but heavily influenced by Karelian).


title: Finnic languages

text: Salminen (2003) present the following list of Finnic languages and their respective number of speakers.


title: Finnic languages

text: Superstrate influence of the neighboring Indo-European language groups (Baltic and Germanic) has been proposed as an explanation for a majority of these changes, though for most of the phonetical details the case is not particularly strong.


title: Dell OptiPlex

text: OptiPlex (a portmanteau of "optimal" and "-plex") is a line of business-oriented desktop and all-in-one computers aimed at corporate enterprises, healthcare, government, and education markets released in 1993 by Dell. The systems typically contain Intel CPUs, beginning with Celeron and Pentium and with the Core microarchitecture (i3, i5, i7, i9). Business-oriented components, such as Gigabit Ethernet, DisplayPort, Tool-less Chassis and software such as data protection utilities, along with management features such as Intel vPro often come standard with OptiPlex systems. OptiPlex configurations can be completed by the purchaser for components such as CPU, GPU, RAM, Storage and Wireless options, as well as Dell Pro support.


title: Dell OptiPlex

text: In 1993, Dell released the OptiPlex and NetPlex lines in the wake of its first quarterly loss. Its disappointing results were partially attributed to poor returns on its notebook division; however, Dell's desktop and server lines continued to see success, particularly within the enterprise market.


title: Dell OptiPlex

text: The new offerings were positioned accordingly. The NetPlex line consisted of inexpensive i486 workstations designed to be used as corporate network clients. The OptiPlex line offered the same networking capabilities as the NetPlex along with additional features such as VESA Local Bus expansion slots, expandable VRAM, and stronger processor models. It also targeted large enterprises with features such as embedded diagnostics.


title: Dell OptiPlex

text: Dell OptiPlex from 2005 to 2009 followed Intel's BTX standard. The first model to sport the new BTX layout was the OptiPlex 170L and also the OptiPlex GX280 had a BTX variant albeit uncommon. The last model to be BTX is the OptiPlex 980. 7xx Series DT models can be configured with a riser card to accommodate two full height cards. The riser card fits over the top PCIe x16 slot and middle PCI which is slightly longer with extra pins, this is however not PCI-X. Features DirectDetect system health status indicators for troubleshooting and diagnostics.


title: Dell OptiPlex

text: OptiPlex models (mostly produced in 2003 and 2004), notably the GX270, suffered from frequent failures due to faulty capacitors supplied by Nichicon as part of the capacitor plague. These capacitors would bulge and leak, resulting in product failure after only a few years of use. Leaked internal documents allege that Dell knew that the computers were likely to fail, and continued to ship them.


title: Dell OptiPlex

text: The OptiPlex 960 introduced a new style of cases, made with recyclable plastics. The first two models, namely the 960 and 980 were based on BTX, However the rest of this series was built upon the standard ATX and DTX. From the x020 and onwards, Dell switched over from a standard 24 pin power connector to a proprietary 12v only 8 pin connector for better power efficiency. The DT and SSF models from this series used standard TFX and LFX power supplies, respectively (the LFX power supplies do have a nonstandard depth of 240mm, however), while the MT models used standard ATX power supplies.


title: Dell OptiPlex

text: Dell OptiPlex computers sold from 2015 to 2020 use cases that resembled the style used in Dell laptops of the same era. These OptiPlex machines are no longer standard ATX or MicroATX.


title: Dell OptiPlex

text: Windows 11 requires TPM 2.0 and an 8th generation Intel or newer processor. Some models in Series 5 between 2015 and 2019 shipped with TPM 1.2, but are capable of meeting these requirements with a firmware upgrade to TPM 2.0 and the appropriate minimum CPU.


title: Dell OptiPlex

text: Potential models that may be able to support Windows 11 include: Intel H370 chipset (3060 / 3070), Intel Q370 chipset (5060 / 5070, 5260 / 5270, 7060 / 7070 / 7070 Ultra, 7460 / 7470, 7760 / 7770).


title: Dell OptiPlex

text: The Dell OptiPlex chassis now follows the Pro 2 chassis introduced with the OptiPlex 7071 and now also on the 3080, 5080 and 7080 models. Up to a 500W 92% 80+ Platinum PSU and support for Nvidia RTX Graphics Cards. All Models including All-in-ones offer 802.11ax WiFi 6 Options and all Desktop models offer a Serial Port Adapter, which can be expanded with a variety of ports including; Serial Ports, VGA, DisplayPorts, HDMI, and USB Type C alt DisplayPorts. OptiPlex offers Energy Star 8.0 configurations, as well as EPEAT Silver and Gold configurations to its customers.


title: Dell OptiPlex

text: The Dell OptiPlex XE is a special version designed for equipment manufacturer, retail/point-of-sale (POS) systems. They are based on the standard OptiPlex models with added features; such as a higher heat threshold, MIL-STD 810G testing and powered USB/Serial.


The National Center for Biotechnology Information (NCBI) is part of the United States National Library of Medicine (NLM), a branch of the National Institutes of Health (NIH). It is approved and funded by the government of the United States. The NCBI is located in Bethesda, Maryland, and was founded in 1988 through legislation sponsored by US Congressman Claude Pepper.


title: National Center for Biotechnology Information

text: The NCBI houses a series of databases relevant to biotechnology and biomedicine and is an important resource for bioinformatics tools and services. Major databases include GenBank for DNA sequences and PubMed, a bibliographic database for biomedical literature. Other databases include the NCBI Epigenomics database. All these databases are available online through the Entrez search engine. NCBI was directed by David Lipman, one of the original authors of the BLAST sequence alignment program and a widely respected figure in bioinformatics.


text: NCBI had responsibility for making available the GenBank DNA sequence database since 1992. GenBank coordinates with individual laboratories and other sequence databases, such as those of the European Molecular Biology Laboratory (EMBL) and the DNA Data Bank of Japan (DDBJ).


text: Since 1992, NCBI has grown to provide other databases in addition to GenBank. NCBI provides Gene, Online Mendelian Inheritance in Man, the Molecular Modeling Database (3D protein structures), dbSNP (a database of single-nucleotide polymorphisms), the Reference Sequence Collection, a map of the human genome, and a taxonomy browser, and coordinates with the National Cancer Institute to provide the Cancer Genome Anatomy Project. The NCBI assigns a unique identifier (taxonomy ID number) to each species of organism.


text: The NCBI has software tools that are available through internet browsers or by FTP. For example, BLAST is a sequence similarity searching program. BLAST can do sequence comparisons against the GenBank DNA database in less than 15 seconds.