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Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set. Writing A = means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example, are subsets of A. Sets can themselves be elements. For example, consider the set B =; the elements of B are not 1, 2, 3, 4. Rather, there are only three elements of B, namely the numbers 1 and 2, the set; the elements of a set can be anything. For example, C =, is the set whose elements are the colors red and blue; the relation "is an element of" called set membership, is denoted by the symbol "∈". Writing x ∈ A means that "x is an element of A". Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A"; the expressions "A includes x" and "A contains x" are used to mean set membership, however some authors use them to mean instead "x is a subset of A". Logician George Boolos urged that "contains" be used for membership only and "includes" for the subset relation only.

For the relation ∈, the converse relation ∈T may be written A ∋ x, meaning "A contains x". The negation of set membership is denoted by the symbol "∉". Writing x ∉ A means that "x is not an element of A"; the symbol ∈ was first used by Giuseppe Peano 1889 in his work Arithmetices principia, nova methodo exposita. Here he wrote on page X: Signum ∈ significat est. Ita a ∈ b legitur a est quoddam b. So a ∈ b is read; the number of elements in a particular set is a property known as cardinality. In the above examples the cardinality of the set A is 4, while the cardinality of either of the sets B and C is 3. An infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number of elements; the above examples are examples of finite sets. An example of an infinite set is the set of positive integers. Using the sets defined above, namely A =, B = and C =: 2 ∈ A 5 ∉ A ∈ B 3 ∉ B 4 ∉ B Yellow ∉ C Halmos, Paul R. Naive Set Theory, Undergraduate Texts in Mathematics, NY: Springer-Verlag, ISBN 0-387-90092-6 - "Naive" means that it is not axiomatized, not that it is silly or easy.

Jech, Thomas, "Set Theory", Stanford Encyclopedia of Philosophy Suppes, Axiomatic Set Theory, NY: Dover Publications, Inc. ISBN 0-486-61630-4 - Both the notion of set, membership or element-hood, the axiom of extension, the axiom of separation, the union axiom are needed for a more thorough understanding of "set element". Weisstein, Eric W. "Element". MathWorld


The Romaleidae or lubber grasshoppers are a family of grasshoppers, based on the type genus Romalea. The species in this family can be found in the Americas; the Orthoptera Species File Online database lists two subfamilies: Bactrophorini Andeomezentia Amédégnato & Poulain, 1994 Bactrophora Westwood, 1842 Bora Amédégnato & Descamps, 1979 Cristobalina Rehn, 1938 Hyleacris Amédégnato & Descamps, 1979 Mezentia Stål, 1878 Panamacris Rehn, 1938 Rhicnoderma Gerstaecker, 1889 Silacris Amédégnato & Descamps, 1979 Ophthalmolampini Adrolampis Descamps, 1977 Aphanolampis Descamps, 1978 Apophylacris Descamps, 1983 Caenolampis Descamps, 1978 Chromolampis Descamps, 1977 Drypetacris Descamps, 1978 Elutrolampis Descamps, 1978 Euprepacris Descamps, 1977 Habrolampis Descamps, 1978 Hekistolampis Descamps, 1978 Helicopacris Descamps, 1978 Helolampis Descamps, 1978 Lagarolampis Descamps, 1978 Nautia Stål, 1878 Nothonautia Descamps, 1983 Ophthalmolampis Saussure, 1859 Othnacris Peruviacris Descamps, 1978 Poecilolampis Descamps, 1978 Pseudonautia Descamps, 1978 Tikaodacris Descamps, 1978 Xenonautia Descamps, 1977 Zoumolampis Descamps, 1978 Taeniophorini Hylephilacris Descamps, 1978 Megacephalacris Descamps & Amédégnato, 1971 Megacheilacris Descamps, 1978 Taeniophora Stål, 1873 Auth.: Eurostacrini Eurostacris Descamps, 1978 Pseudeurostacris Descamps, 1978 Hisychiini Acrideumerus Descamps, 1979 Acridophaea Descamps, 1979 Cloephoracris Descamps, 1979 Hisychius Stål, 1878 Pareusychius Amédégnato & Poulain, 1994 Porphoracris Descamps, 1979 Pseudhisychius Descamps, 1979 Leguini Ampiacris Amédégnato & Poulain, 1986 Legua Walker, 1870 Proracris Uvarov, 1940 Phaeopariini Abila Stål, 1878 Albinella Carbonell, 2002 Aristia Stål, 1876 Costarica Koçak & Kemal, 2008 Epiprora Gerstaecker, 1889 Graciliparia Amédégnato & Poulain, 1994 Maculiparia Jago, 1980 Phaeoparia Stål, 1873 Pseudaristia Carbonell, 2002 Stornophilacris Amédégnato & Descamps, 1978 Tepuiacris Carbonell, 2002 Procolpini Romaleini Romalea Serville, 1831 - monotypic - Romalea microptera Trybliophorini Trybliophorus Serville, 1831 Genus Quitus Hebard, 1924 Media related to Romaleidae at Wikimedia Commons Data related to Romaleidae at Wikispecies

Hamish Carter

Hamish Clive Carter is a New Zealand triathlete. He won the gold medal in triathlon at his second Olympic games. Carter competed on the International Triathlon Union World Cup circuit as a professional for many years, culminating in a silver medal in 2006 before announcing his retirement early in 2007. During his career he won twelve ITU world cup races. Carter attended Auckland Grammar School where he was a successful rower, competing twice in the Maadi Cup. Carter won the bronze medal in triathlon at the 2002 Commonwealth Games and went on to win the triathlon gold medal at the 2004 Summer Olympics, defeating fellow New Zealander, Bevan Docherty. Carter's time was 1:51:07.73, less than eight seconds faster than Docherty's. On 3 September 2006 in Lausanne, Carter won silver at the World Championships after finishing 17 seconds behind Tim Don. In October 2006, Hamish Carter won the Xterra World Championship in Maui, Hawaii defeating a field of more experienced off-road triathletes. On 6 March 2007 he announced his retirement

1918 Vanderbilt Commodores football team

The 1918 Vanderbilt Commodores football team represented Vanderbilt University in the 1918 Southern Intercollegiate Athletic Association football season, interim head coach Ray Morrison's first year as a head coach. Coach Morrison was asked to fill in for Dan McGugin, in the US Army at the time; the Commodores usual coach, Dan McGugin, was on leave from Vanderbilt for Army duty, leaving future Vanderbilt head coach Ray Morrison as the interim head coach. Coach Morrison played at Vanderbilt from 1908 to 1911 playing quarterback for McGugin. After leaving Vanderbilt as a player he moved to coaching. Vanderbilt program considers the game between the two schools as an official game, University of Tennessee does not since most of their team was enlisted in the military fighting in World War I. During the two-year period of 1917 and 1918 without varsity football, two unofficial teams were formed from Army recruits and students. One of these unofficial teams that represented the University of Tennessee was the Student Army Training Corps, which came to play in Nashville in 1918.

There was a game played that afternoon on Vanderbilt's original Dudley Field. According to the Nashville Tennessean and the Nashville American, the game was to benefit the United War Work Fund. Reserved seats were $1.00. "When the Tennessee clan comes down from the eastern mountains and comes to Dudley Field around 2:30 o'clock today, the Commodores will have quite a little argument to settle with them. It dates back to the fall of 1916, when the Vol eleven surprised Vandy with a 10−6 defeat and crawled into their hole for two years gloating over their accomplishment. Yes, the Black and Gold must be vindicated today." The Journal and Tribune in Knoxville reported before the game, "It is expected that the Orange and White players will give a good account of themselves in the game today, when the S. A. T. C. Eleven goes against Vanderbilt, at Nashville." This is a clear reference to the football team representing UT as the Student Army Training Corps. Vanderbilt won the game by a score of 74–0 and the Vols were always referred to as the University of Tennessee and not Student Army Training Corps.

The Journal and Tribune reported on the game's results: "Against the University of Tennessee weak resistance, the Vanderbilt football eleven today ran rampant and piled up a score of 74−0. Berryhill, the sensational Vanderbilt back, had one of the greatest days of his football career accounting for six of the eleven's dozen touchdowns against the Knoxville clan." Sports writer Cicero Slack of the Tennessean wrote: "Crumbling the University of Tennessee eleven like to a page of tissue in the mailed fist of a giant, the Commodores yesterday out on Dudley Field walked over their prostrate foe to a 74−0 victory and gained sweet revenge for the 1916 defeat." Berryhill's six touchdowns are not in the Vanderbilt record book because this would not be considered the modern era. Frank Mordica's five touchdowns in 1978 are listed as the Vanderbilt record for most touchdowns in a single game. An authority on Vanderbilt football history was the late Nashville Banner sportswriter Fred Russell. In Russell's book Fifty Years of Vanderbilt Football published in 1938, he writes about the 1918 Vanderbilt–Tennessee football game: "Salient after salient was wiped out by Gen. Morrison's forces and Tennessee's reinforcements could not check the tide.

The retreat turned into a hopeless rout. Berryhill was cited for bravery for his wonderful outflanking the enemy, by which he took six positions single-handedly; the result was 76−0." Russell records the game in his book as a victory for the Commodores. Vanderbilt beat the rival Sewanee Tigers 40 -- a larger score than had been expected. Bunt Beasley was the star of the game, scoring three touchdowns; the starting lineup was Baker, Reed, Reeves, Goar, Berryhill, Beasley

Laurelvale F.C.

Laurelvale Football Club is an intermediate-level football club playing in the Intermediate A division of the Mid-Ulster Football League in Northern Ireland. The club is based in County Armagh. In their 25th Anniversary year, Laurelvale enjoyed a strong season, winning the Intermediate League in addition to the Marshall Cup; the County Armagh club reached the last 16 in the Irish Intermediate Cup and claimed the scalps of senior Irish Premier League sides, Armagh City and Loughgall on their way to the semi-final of the Mid-Ulster Cup, where they lost to Glenavon. In the following season, Laurelvale added the Premier Cup to their trophy cabinet meaning all three trophies were held by Laurelvale. Mark Robinson's second team enjoyed success by winning the Mid Ulster Reserve League Division 3 with a thrilling final day climax. There was success on a great scale when the first team made it to the fifth round of the Irish Cup; the club take its club colours from the famous English football club Newcastle United.

Mid-Ulster Football League: 2 2002–03, 2005–06Mid Ulster Intermdiate B 2018-19 Daily Mirror Mid-Ulster Football League Official website -

St. Paul Curling Club

The St. Paul Curling Club is an historic curling club located in Saint Paul, United States, on Selby Avenue, it is the curling club with the largest active membership in the United States at over 1200 members. It was first established in 1885, the present St. Paul CC was established when the Capitol City Curling Club and Nushka Curling Club merged in 1912, it is the oldest curling club in Minnesota. The club hosted the 2011 World Mixed Doubles Curling Championship and the 2011 World Senior Curling Championships in April 2011; the first St. Paul Curling Club was incorporated on November 16, 1885; the first curling game held in St. Paul were played on the Mississippi River; the St. Paul Curling Club built its first facilities on Raspberry Island in 1891, became a part of the Northwest Curling Association along with other clubs from Minnesota, North Dakota and Illinois a year later; the original St. Paul CC was replaced by the Capitol City CC the next year. However, the Capitol City CC and the Nushka CC merged to form the new St. Paul CC in 1912, permanent facilities were set up at a two-story clubhouse with six sheets of natural ice on Selby Avenue.

Artificial ice was added in gradual stages from 1939–1947. The Metro League and the Mixed League were formed in 1961 and 1962 to attract more curlers, but club membership dropped in the 1960s and 1970s, there were discussions on disbandment; the club remained and continued to renovate and expand its facilities. The club hosted the men's nationals in 1988, becoming the first club in the US to host every national curling championship event; the St. Paul Curling Club has a number of different curling leagues. All are club leagues; the club championship is held annually. Allison Pottinger – 2003 World Champion, 1996, 1999, 2006 World Championships runner-up, 2010 Olympian, 2011 US Nationals runner-up John Benton – 2009 US Men's National Champion, 2010 Olympian Margie Smith St. Paul Curling Club St. Paul Curling Club at MNopedia Photographs at the Minnesota Historical Society