OpenLLM-France/wikimedia huggingface dataset:
# Simple theorems in the algebra of sets

The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix ') of sets.
These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denoted. The algebra of sets describes the properties of all possible subsets of U, called the power set of U and denoted P(U). P(U) is assumed closed under union, intersection, and set complement. The algebra of sets is an interpretation or model of Boolean algebra, with union, intersection, set complement, U, and interpreting Boolean sum, product, complement, 1, and 0, respectively.
The properties below are stated without proof, but can be derived from a small number of properties taken as axioms. A "*" follows the algebra of sets interpretation of Huntington's (1904) classic postulate set for Boolean algebra. These properties can be visualized with Venn diagrams. They also follow from the fact that P(U) is a Boolean lattice. The properties followed by "L" interpret the lattice axioms.
Elementary discrete mathematics courses sometimes leave students with the impression that the subject matter of set theory is no more than these properties. For more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. For an introduction to set theory at a higher level, see also axiomatic set theory, cardinal number, ordinal number, Cantor–Bernstein–Schroeder theorem, Cantor's diagonal argument, Cantor's first uncountability proof, Cantor's theorem, well-ordering theorem, axiom of choice, and Zorn's lemma.
The properties below include a defined binary operation, relative complement, denoted by the infix operator "\". The "relative complement of A in B," denoted B \A, is defined as (A ∪B′)′ and as A′ ∩B.
PROPOSITION 1. For any U and any subset A of U:
*′ = U;
* 'U'′ =;
* A \ = A;
* \ A =;
* A ∩ =;
* A ∪ = A; *
* A ∩ U = A; *
* A ∪ U = U;
* A′ ∪ A = U; *
* A′ ∩ A =; *
* A \ A =;
* U \ A = A′;
* A \ U =;
* A′′ = A;
* A ∩ A = A;
* A ∪ A = A.
PROPOSITION 2. For any sets A, B, and C:
   * A ∩ B = B ∩ A; * L
   * A ∪ B = B ∪ A; * L
   * A ∪ (A ∩ B) = A; L
   * A ∩ (A ∪ B) = A; L
   * (A ∪ B) \ A = B \ A;
   * A ∩ B = if and only if B \ A = B;
   * (A′ ∪ B)′ ∪ (A′ ∪ B′)′ = A;
   * (A ∩ B) ∩ C = A ∩ (B ∩ C); L
   * (A ∪ B) ∪ C = A ∪ (B ∪ C); L
   * C \ (A ∩ B) = (C \ A) ∪ (C \ B);
   * C \ (A ∪ B) = (C \ A) ∩ (C \ B);
   * C \ (B \ A) = (C \ B) ∪(C ∩ A);
   * (B \ A) ∩ C = (B ∩ C) \ A = B ∩ (C \ A);
   * (B \ A) ∪ C = (B ∪ C) \ (A \ C).
The distributive laws:
   * A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C); *
   * A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). *
PROPOSITION 3. Some properties of ⊆:
   * A ⊆ B if and only if A ∩ B = A;
   * A ⊆ B if and only if A ∪ B = B;
   * A ⊆ B if and only if B′ ⊆ A′;
   * A ⊆ B if and only if A \ B =;
   * A ∩ B ⊆ A ⊆ A ∪ B.
# Sector, West Virginia

Sector is an unincorporated community in Hampshire County in the U.S. state of West Virginia. It is located along the west bank of the South Branch Potomac River on Fleming-Sector Road (West Virginia Secondary Route 8/3) across the river from the community of Glebe.
Sector grew as a result of its operation of a post office and station on the South Branch Valley Railroad in the early 20th century. On the railroad, it was known as Glebe Station because of its proximity to Glebe. A suspension bridge once connected the two communities via Fleming-Sector Road, but this was repeatedly demolished by a succession of serious floods, most recently in the late 1930s or early 1940s after which it was not rebuilt.
# HMS Nottingham

Four ships of the Royal Navy have borne the name HMS Nottingham, after the city of Nottingham in the East Midlands, or alternatively after Lord High Admiral Charles Howard, 1st Earl of Nottingham, who commanded the English fleet against the Spanish Armada in 1588. The first ship was rebuilt twice, and each is sometimes considered a separate ship:
* HMS Nottingham (1703) was a 60-gun fourth rate launched in 1703. She was rebuilt in 1719 and 1745, and was sunk in 1773 as a breakwater.
* HMS Nottingham (1794), was a 3-gun gunvessel, formerly a barge. She was purchased in 1796 and sold in 1800.
* HMS Nottingham (1913) was a Town-class cruiser launched in 1913 and sunk in 1916.
* HMS Nottingham (D91) was a batch two Type 42 destroyer launched in 1980, decommissioned in 2010 and scrapped from 2011.

## Battle honours

Ships named Nottingham have been awarded the following battle honours:
* Gibraltar, 1704
* Velez Malaga, 1704
* Marbella, 1705
* Finisterre, 1747
* Ushant, 1747
* Magnanime, 1748
* Louisburg, 1758
* Martinique, 1762
* Havana, 1762
* Heligoland, 1914
* Dogger Bank, 1915
* Jutland, 1916
# Tomoplagia obliqua

Tomoplagia obliqua is a species of tephritid or fruit flies in the genus Tomoplagia of the family Tephritidae.

## Distribution

United States, Costa Rica, Bahamas & Cuba.
# Téhiri

Téhiri is a village in southern Ivory Coast. It is in the sub-prefecture of Bayota, Gagnoa Department, Gôh Region, Gôh-Djiboua District.
Téhiri was a commune until March 2012, when it became one of 1126 communes nationwide that were abolished.
# JøKleBa

JøKleBa (establishesd 1990 in Oslo, Norway) is a Norwegian Jazz band with a free improvising expression.
All the band members are still very active in different projects, but in recent years has played very few concerts as JøKleBa, but on the tenth anniversary of Finsejazz they excited the Winter Jazz Audience. In 2011 they got into a new active period with festival appearances and a new album, Nu Jøk?.

## Band members

* Per Jørgensen – trumpet, guitar, percussion, vocals
* Audun Kleive – drums, keyboards, percussion, vocals
* Jon Balke – keyboards, percussion, vocals

## Discography

* 1991: On and On (Odin)
* 1992: JøKleBa! (Odin)
* 1996: JøKleBa Live! (Curling Legs)
* 2011: Nu Jøk? (EmArcy, Universal Norway)
* 2014: Outland (ECM)
# Rachel Oldroyd

Rachel Oldroyd was until 2022 the managing editor at the Bureau of Investigative Journalism. She previously worked at The Mail on Sunday, where she launched the Reportage section.
In 2011, she was awarded an Amnesty International UK Media Award for her work on the Iraq war logs.
# Race knife

Race knife also known as a timber scribe (scorer, tree marker) is a knife with a U-shaped end sometimes called a scoop knife for cutting marks in wood by lumbermen, carpenters, coopers, surveyors, and others. The reasons for making marks varies and includes keeping count (tally marks), identifying parts (carpenter's marks), numbering, and tracing patterns around a template as a part of marking out. The gouges left by the timber scribe are more durable than pencil or chalk marks.
Two basic forms of race knife are a simple, fixed or folding, scooped blade and a scooped blade paired with a point around which the blade cut a circle or partial circle. The circles and partial circles allowed more variety in the patterns of marks rather than only using Roman numeral-like marks.
The numbering with a race knife resembles Roman numerals but the number four is usually marked IIII rather than IV and nine VIIII rather than IX because the four and nine could be mistaken for a six or eleven.
# Copelatus lamottei

Copelatus lamottei is a species of diving beetle. It is part of the genus Copelatus in the subfamily Copelatinae of the family Dytiscidae. It was described by Legros in 1954.
# Simplecortex

The Simplecortex is a development board which can host shields designed for the Arduino, since it has compliant headers, pin-out and spacing. However, the board itself is not Arduino-compatible, i.e. it doesn't use the Arduino IDE and is not source code compatible.
It has an onboard debugger and an ARM Cortex M3 microcontroller from NXP. It uses an Eclipse-based programming environment. The Simplecortex is made as a school project and the hardware is open source under the CC-BY-SA 3.0 License.
# HMS Portia

Two ships of the Royal Navy have borne the name HMS Portia. Another was renamed before being launched, while yet another was never completed:
* HMS Portia (1810) was a 14-gun brig-sloop launched in 1810 and sold in 1817.
* HMS Portia was to have been a Philomel-class gunvessel. She was laid down in 1861, but cancelled in 1863.
* HMS Portia (1906) was a fleet messenger sunk in 1915 by SM U-28
* HMS Portia was to have been a Laforey-class destroyer. She was renamed HMS Lennox (1914) in 1913, and launched in 1914.
* HMS Portia (1916) was an Admiralty M-class destroyer launched in 1916. She was sold in 1921 and scrapped in 1922.
# Coronium wilhelmense

Coronium wilhelmense is a species of sea snail, a marine gastropod mollusc, in the family Muricidae, the murex snails or rock snails.
# Edward Gantt

Edward Gantt (died 1837) was an Episcopal clergyman who served as Chaplain of the Senate of the United States (1801–1804).

## Early life

Edward Gantt was born , the son of Rachel Smith and Thomas Gantt III. He received his bachelor of arts from Princeton University in 1762, and thereafter studied medicine with Benjamin Rush in Philadelphia and in Edinburgh. He also studied at the University of Leiden in the Netherlands where he matriculated 6 April 1767. Gantt received the degree of M.D. on this University 17 April 1767 The title description of his thesis is: Dissertatio medica inauguralis, de variolis, quam,…, ex Auctoritate Magnifici Rectoris, Davidis Ruhnkeniii, …, Eruditorum Examini submittit Eduardus Gantt, A.B. Anglo-Americanus…. - Lugduni Batavorum : Apud Theodorum Haak, 1767. - 33 p. + p. ; 4oct. Variolis = Smallpox. Later he was entering in the practice of medicine in Somerset County, Maryland. Sensing a call to ministry, he went to England where he obtained orders in 1770.

## Ministry

Gantt returned home and for a time officiated in his native parish, Christ Church, Calvert County. On January 28, 1776 he began to preach at All Hallow’s Parish in Worcester County. Four years later he became rector of his native parish, and sustained himself by practicing medicine. In 1795 Gantt moved to Georgetown in the District of Columbia. His work in Washington continued to combine ministry and medicine as indicated by an invoice in the White House Historical Association's archives; the doctor’s bill for President Thomas Jefferson’s household dated March 22, 1802, lists the medical services provided to several servants by Dr. Edward Gantt.
From President Jefferson, Dr. Gantt received a supply of smallpox vaccine; soon after January 17, 1802 he vaccinated Miami chief Little Turtle and a group of Miami diplomats who were in Washington, The supply sufficed to vaccinate over three hundred persons connected with the Executive Mansion.

## Chaplain of the Senate

Starting on December 9, 1800 through November 6, 1804, Gantt served as Chaplain of the Senate.

## After Washington

About 1807, under the auspices of Bishop Thomas John Claggett, he went to Kentucky, in the interests of the Episcopal Church.

## Personal life

Edward Gantt and Ann Stoughton Sloss, the daughter of Thomas and Mary Sloss, were married June 26, 1768, by the Rev. Thomas John Claggett, Gantt's cousin, later to be Bishop of Maryland. Their fifteen children include: Thomas Sloss Gantt, William Stoughton Gantt, Edward Sloss Gantt and Captain John Gantt (1790-1849).
Gantt died near Louisville, Kentucky, 1837.
# Estadio Ruca Che

Estadio Ruca Che is an indoor arena and multi-purpose stadium in the city of Neuquén, capital of the homonymous province and largest city in the Argentine Patagonia. It was built in 1995 to host the Americas Basketball Championship.
The name of this sport venue is in the mapuche language: the word Ruka means house while Che means people. Therefore, this is the House of the People.
Two teams make use of the stadium regularly. Gigantes del Sur plays its home matches for the Serie A1, the top level of the Argentine men's volleyball league system, while Independiente de Neuquén plays some of their home matches for the Torneo Federal de Básquetbol, the third level of the Argentine basketball league system, after the Liga Nacional de Básquet and the Torneo Nacional de Ascenso.
It also has an auxiliary gym, outdoor basketball courts and volleyball facilities, and parking lot for 150 vehicles.

## Sporting events

* 1995 Americas Basketball Championship
* 2001 Americas Basketball Championship

## Concerts

Some of the artists that have played at this stadium are Alejandro Lerner, Attaque 77, Bersuit Vergarabat, Catupecu Machu, Charly García, Chayanne, Diego Torres, Divididos, Europe, Joan Manuel Serrat, Jorge Rojas, La Ley, La Renga, Los Piojos, La Mona Jiménez, León Gieco, Luis Eduardo Aute, Los Nocheros, Maná, Mercedes Sosa, Víctor Heredia, Marco Antonio Solís, Ismael Serrano, Soledad Pastorutti, The Wailers, Manu Chao, Gustavo Cerati, Celia Cruz, Ricardo Montaner, José Luis Perales, Marcos Witt, Danilo Montero, Violetta, Roxette, Les Luthiers, No Te Va Gustar, Ricky Martin and Calle 13.
# Jötunvillur

Jötunvillur are a set of runic code inscriptions dating back to the Viking Age. Although previously untranslatable, a proposed solution to the code was announced by the runologist K Jonas Nordby in 2014.
# Rachel Oakes Preston

Rachel (Harris) Oakes Preston (March 2, 1809 – February 1, 1868) was a Seventh Day Baptist who persuaded a group of Adventist Millerites to accept Saturday, instead of Sunday, as Sabbath. This Sabbatarian group organised as the Seventh-day Adventist Church in 1863.

## Life

Born in Vernon, Vermont, Rachel, daughter of Sylvanus Harris, first joined the Methodist Church. After marrying Amory Oakes, Rachel moved to Verona, New York, where her husband soon died. In 1837 Rachel and her daughter, Rachel Delight Oakes, joined the Seventh Day Baptist Church of Verona. In 1843 the widowed Rachel and her daughter moved to Washington, New Hampshire, where her daughter would teach school. While attending the "Christian Brethren" church with her daughter, Rachel tried to present her views on seventh-day Sabbath. However, the congregation, being Millerites, were focused in preparing for the Second Coming of Christ, which they earnestly thought would occur in 1843 or 1844.
Due to Rachel's influence, Frederick Wheeler (1811–1910), an ordained minister of the Methodist Episcopal Church, and promoter of the prophetic teachings of William Miller, preached his first sermon on seventh-day Sabbath to his "Christian Brethren" congregation on March 16, 1844.
Further due to Rachel's influence, William Farnsworth (1807–1888), after the Great Disappointment of October 22, 1844, stated publicly to the "Christian Brethren" congregation his conviction that Saturday, being the seventh day of the week, was Sabbath. His brother Cyrus (who became the husband of Rachel's daughter Delight), and several others, also made their convictions known.
Later, when Rachel married Nathan T. Preston, she was referred to as Rachel Oakes Preston.
# Radial piston pump

A radial piston pump is a form of hydraulic pump. The working pistons extend in a radial direction symmetrically around the drive shaft, in contrast to the axial piston pump.

## Construction

The stroke of each piston is caused by an eccentric drive shaft or an external eccentric tappet (e.g., stroke ring).
When filling the workspace of the pumping pistons from "inside" (e.g., over a hollow shaft) it is called an inside impinged (but outside braced) radial piston pump (picture 1). If the workspace is filled from "outside" it's called an outside impinged radial piston pump (but inside braced) (picture 2).

## Function

The general mode of operation will be explained at the movement of one pumping piston by means of picture 1: The outer ring for bracing of the pumping pistons is in eccentric position to the hollow shaft in the center. This eccentricity determines the stroke of the pumping piston.
The piston starts in the inner dead center (IDC) with suction process. After a rotation angle of 180° it is finished and the workspace of the piston is filled with the moved medium. The piston is now in the outer dead center (ODC). From this point on the piston displaces the previously sucked medium in the pressure channel of the pump.

## Attributes

These kinds of piston pumps are characterized by the following advantages:
* high efficiency
* high pressure (up to 1,000 bar or 14000psi)
* low flow and pressure ripple (due to the small dead volume in the workspace of the pumping piston)
* low noise level
* very high load at lowest speed due to the hydrostatically balanced parts possible
* no axial internal forces at the drive shaft bearing
* high reliability
A disadvantage is the bigger radial dimensions in comparison to the axial piston pump, but it could be compensated with the shorter construction in axial direction.

## Applications

Due to the hydrostatically balanced parts it is possible to use the pump with various hydraulic fluids like mineral oil, biodegradable oil, HFA (oil in water), HFC (water-glycol), HFD (synthetic ester) or cutting emulsion. That implies the following main applications for a radial piston pump:
* machine tools (e.g., displace of cutting emulsion, supply for hydraulic equipment like cylinders)
* high pressure units (HPU) (e.g., for overload protection of presses)
* test rigs
* automotive sector (e.g., automatic transmission, hydraulic suspension control in upper-class cars)
* plastic- and powder injection molding
* wind energy
# Convolute

Convolute may refer to:
* Convolute (botany)
* Convolute (manuscript), a volume containing several manuscripts
* Convolute (segment), along with gores, material segments used in pressure suit joints to allow for increased mobility
* Convolute laminations in geology
* Convoluted tubule, in anatomy
** Distal convoluted tubule
# Singapore Cooperation Programme

The Singapore Cooperation Programme (SCP) is a series of programmes offered by the Government of Singapore to facilitate the sharing with other developing countries the technical and systems skills that Singapore has learned and acquired over the years. SCP was established in 1992 to consolidate technical assistance initiatives offered by Singapore since the 1960s.
Technical assistance focuses on training and increasing the skills of a nation. As a country whose only resource is its people, Singapore believes human resource development is vital for economic and social progress. Singapore had also benefited from technical assistance from other countries and international organisations.

## Beginnings

In the 1970s, Singapore started to exchange its experiences with friends around the world through various programmes. These programmes were brought under a single framework when the Singapore Cooperation Programme (SCP) was established in 1992 under the Technical Cooperation Directorate (TCD) of the Ministry of Foreign Affairs. Through the SCP, Singapore has been sharing its development experience through courses, seminars, workshops, consultancy as well as hosting study visits in a range of fields.

## Areas of interest

The main fields of training include Education, Law and Judiciary, Sustainable Development, Communications and Transport, Economic Development and Trade Promotion, Healthcare, Public Administration and Digital Government.
Some of the TCTP partners include Australia, Canada, European Commission, France, Germany, Japan, The Holy See, the Republic of Korea, Luxembourg, New Zealand, Norway, Thailand, the Asia Development Bank, Commonwealth of Learning, Colombo Plan Secretariat, Commonwealth Secretariat, Economic and Social Commission for Asia and the Pacific, Hanns Seidel Foundation, International Atomic Energy Agency, International Civil Aviation Organisation, International Maritime Organisation, International Monetary Fund, United Nations Children's Fund, United Nations Development Programme, US Vietnam Trade Council, World Bank, World Health Organisation, World Intellectual Property Organisation and World Trade Organisation.

## Participating countries

As of 2015, there are 100,000 officials who had participated in SCP. SCP hosted over 6,000 officials from 170 countries who attended about 300 courses and workshops yearly.
As of January 2017, more than 112,000 officials from 170 countries have been trained.
# Buck's of Woodside

37°25′46.8″N 122°15′18.4″W﻿ / ﻿37.429667°N 122.255111°W﻿ / 37.429667; -122.255111
Buck's of Woodside (Locally known as: Buck's) is a restaurant in Woodside, California, that has gained fame as a meeting place for venture capitalists and tech entrepreneurs. Like nearby Sand Hill Road, Buck's has become a fixture of Silicon Valley.

## About

Jamis MacNiven left his career in construction to open the restaurant in 1991. Unhappy with local restaurants, MacNiven decided to create his own. By 1995, when the dot-com boom began, word of mouth spread that Buck's was a hotspot for Silicon Valley's most powerful.
The restaurant is close to both Sand Hill Road—home to the majority of Silicon Valley's venture capitalists—and Stanford University. Netscape, PayPal, Hotmail and Tesla Motors are among the companies whose entrepreneurs held early meetings at Buck's.
"Breakfast at Buck's" is the title of the introduction of the book, The Startup Game: Inside the Partnership between Venture Capitalists and Entrepreneurs, by venture capitalist Bill Draper.
In 2003, Forbes magazine named Buck's one of its top business restaurants.
The interior of Buck's features colorful decor, including cowboy boots, a talking buffalo head, a model of the Statue of Liberty holding an Ice cream Sunday, and a stuffed alligator.
According to MacNiven, Steve Jobs is one of the few Silicon Valley icons who never set foot in his restaurant; MacNiven and the Apple co-founder had a falling out in the 1980s after Jobs hired him to remodel his house. Buck's nevertheless has a rare photo of Jobs, wearing a set of Groucho glasses, on display.
When the COVID-19 pandemic hit in the spring of 2020, and the resulting restaurant shut-down, Jamis MacNiven decided to retire. In August 2020 Buck's was re-opened by his sons (Dylan, Tyler & Rowan MacNiven) who now run it.
# Xike railway station

Xike (Chinese: 汐科) is a railway station in New Taipei, Taiwan served by Taiwan Railways. Located near Xizhi's technology park, it experiences heavy traffic during the morning and early evening rush hours.

## Construction

Construction started in June 2005 and finished on schedule in December 2007. During planning the names South Xizhi Station (南汐止站) and Xizhi Technology Park (汐科園區站) were mooted, but eventually the name Xike Station (汐科站) was chosen.

## Usage

Media reports have highlighted Xike Station as part of the "MRT-ization" plan for Taiwan's urban railways, offering convenient transport for commuters, spurring new residential construction, and raising property prices in the vicinity of the station. This station only stops Local Trains.

## Future expansion

The planned Minsheng–Xizhi line of the Taipei Metro (MRT) system would see Xike Station transformed into a TRA and MRT interchange station.

## Around the station

Farglory U-Town (next to the station)
Acer Inc. Headquarters (300m to the south)
Oriental Science Park (450m to the southeast)
# Corybantes delopia

Corybantes delopia is a moth in the family Castniidae first described by Herbert Druce in 1907. It is found in Ecuador.