ejaasaari/simplewiki-2025-04-01 huggingface dataset:
The Fundamental theorem of arithmetic (also called the unique factorization theorem) is a theorem of number theory. The theorem says that "every" positive integer greater than 1 can be written as a product of prime numbers (or the integer is itself a prime number). The theorem also says that there is only one way to write the number. If two people found two different ways to write the number, the only thing that can be different is the order in which the primes are written. For example, we can write: 6936 = 23 · 3 · 172   or   1200 = 24 · 3 · 52 and if somebody else finds "another" way to write 6936 or 1200 as product of prime numbers, we can put those prime numbers in the right order and find out that it is the same as what we have here. Finding the prime numbers is called factorization.  This theorem can be used in cryptography. Proof. The first person who proved the theorem was Euclid. The first detailed and correct proof was in the "Disquisitiones Arithmeticae" by Carl Friedrich Gauss.  Some people may think that the theorem is true everywhere. However, the theorem is "not" true in more general number systems, like . This was first mentioned by Ernst Kummer in 1843, in his work on Fermat's last theorem. For more information about that: read .  The proof consists of two parts: "first" we show that every number can be written as a product of primes; "second" we show that if we write a number as a product of primes for a second time, then the two lists of prime numbers must be the same.  First part of the proof. We show that if "not" every number greater than 1 can be written as a product of primes, we end up in some kind of impossibility. So after that we conclude that it "must" be true that every number can be written as a product of primes.  So, now see what happens when somebody says that they know a positive integer, greater than 1, which can "not" be written as a product of
"A Portuguesa" (, meaning "The Portuguese") is the national anthem of Portugal, adopted in 1911. The music of the song was composed by a Portuguese composer and painter named Alfredo Keil. The words of the song were written by a poet named Henrique Lopes de Mendonça, in response to the 1890 British Ultimatum for Portuguese troops to get rid of their positions in Africa between the Mozambique and Angola in the Pink Map.
Welding is a way of heating pieces of metal using electricity or a flame so that they melt and stick together. There are many kinds of welding, including arc welding, resistance welding, and gas welding. The most common type is arc welding. Anyone who is near arc welding needs to wear a special helmet or goggles because the arc is so bright. Looking at the arc without visual protection may cause permanent eye damage. It is also important to cover all your skin because it can give you something like a sunburn. Hot sparks from the weld can burn any skin that is showing. One kind of welding that does not use an arc is Oxy-fuel welding (OFW), sometimes called gas welding. OFW uses a flame to heat up the metal. There are other kinds of welding that do not use an arc. Arc welding. Any welding process that utilizes an electric arc is known as arc welding. The common forms of arc welding include:  Arc welding heats metals by making a high-current electric arc between pieces of metal to be joined and an electrode. Use of the electrode varies based on the type of welding process. In SMAW, GMAW, and related welding processes, the electrode is consumed and becomes part of the weld. The electrode is usually made of the same kind of metal to be welded. Because the electrode is consumed by the welding process, the electrode must constantly be fed into the weld. The SMAW welding process features a "stick" electrode impregnated with a weld promoter known as flux, clamped to the end. The GMAW welding process uses a thin wire on a rotating spool, as a continuous electrode. The size of this electrode varies from around 0.635 millimeters to about 4 millimeters. The welding machine has a motor-driven spool inside that feeds the wire electrode into the weld. The TIG welding (GTAW) process features an electrode that is not consumed by the welding process as the metal that makes up the weld does not have any electricity flowing through it. The electrode is made of Tungsten, so used as it will not melt while immersed in the electrical arc. A filler metal, in the form of a rod, can be
Stalking means following something or somebody secretly. In the animal kingdom, predators often hunt by stalking, or by combining stalking with ambushing.  Someone who likes to watch other people is known as a voyeur. When this is continually done to a person it can have a bad effect. Criminal stalking. Stalking in a way that makes someone feel unsafe is a crime in many countries. It is not just one event but an ongoing process that threatens or makes the victim feel scared. Someone who does this is called a stalker. The stalker may do this because they want to be involved in that person's life, because they want to have power over that person's life, or for other sexual reasons. The stalker can make that person feel scared. They may feel they do not have the power to stop the stalker. Psychologists say stalking is a way of hurting someone's mind. Sometimes a stalker may go on to hurt that person's body by assaulting, raping or murdering that person. Celebrities are often stalked. Taylor Swift, Kim Kardashian, Rihanna, Jennifer Lopez, Kendall Jenner and Kylie Jenner often have stalkers. Celebrities. People with Celebrity Worship Syndrome often stalk celebrities. Cyber-stalking. Stalking can sometimes be done on the internet. This is called cyberstalking.
William Henry Cosby Jr. (; born July 12, 1937) is a retired American former stand-up comedian, actor, author, producer, musician, and activist. He was also a regular star of movies and television. He was known for creating and starring in "The Cosby Show" and "The Cosby Mysteries".  In 2018, Cosby went to prison because of many sexual assault allegations.  He got out of prison in 2021, because the Supreme Court of Pennsylvania found that the justice system had made a mistake in the process of convicting him. Life. Early life. Cosby was born and raised in Philadelphia, Pennsylvania. He studied at Temple University. Cosby was the class president and a captain of the baseball team. Career. He is the creator of such shows as Filmation's animated "Fat Albert and the Cosby Kids", NBC's "The Cosby Show" (in which he played a doctor named Heathcliff Huxtable) and Nick at Nite's "Fatherhood" (with Blair Underwood). On television, he starred in the 1960s spy spoof "I Spy", and has also advertised Jell-o and other products. In 1983, Cosby released the concert film "Bill Cosby." Cosby performed his first TV stand-up special in 30 years. On the big screen, he appeared in "Leonard Part 6" (1987), "Ghost Dad" (1990), and "The Meteor Man" (1993). On May 2, 2015, his last show of the "Far from Finished" tour was performed at the Cobb Energy Performing Arts Centre in Atlanta, Georgia.  His last known standup performance before his conviction was held at the LaRose Jazz Club in Philadelphia on January 23, 2018. Bill Cosby was among hundreds of artists whose material was destroyed in the 2008 Universal fire. Personal life. Cosby married Camille Hanks Cosby in 1964. Together, they have five children: Erika, Erinn, Ennis, Ensa and Evin. Cosby lives in suburban Philadelphia, Pennsylvania. The Cosbys have three grandchildren. Since 2016, Cosby has been legally blind
Ham is pork that comes from a leg of a pig.  Ham can be dry-cured or wet-cured. Dry-cured ham is made by rubbing the meat with salt. Wet-cured ham is made with brine. Types of dry-cured ham: Ham is used in SPAM.
Spam is a canned meat food made by the Hormel Foods Corporation. It is made from pork shoulder meat and ham. There have been many ideas about what the word "Spam" actually means. The Hormel Foods Corporation said the meaning of the name "is known by only some people". In some dictionaries "Spam" means "spiced ham", "shoulder of "pork and ham" and Specially Produced American Meat Spam was used a lot in World War II, as there wasn't proper meat. Because of that, spam was used as a rationed item.
A mushroom (also called a toadstool) is the part of a fungus that is comparable to the fruit of a plant. Unlike plants, mushrooms do not use sunlight to generate energy for themselves. Some mushrooms are edible, and are used for cooking in many countries, such as China, Korea and Europe. Other mushrooms, however, are poisonous, and can cause severe illness or death if eaten. People who search for edible mushrooms are called "mycophagists", meaning "mushroom eater", while the act itself is called "mushrooming". Mushrooms have been known to support bone health and to regulate blood sugar in diabetics. It is available in different colours and shapes. Structure of mushrooms. Most mushrooms have a stem and a cap. The bottom of the cap usually has gills to hold spores, however, some mushrooms, such as the Porcini, have pores under the cap.
Factorization (also called factorisation and factoring) is taking a composite number apart into numbers that multiply together to get the original number. These smaller numbers are called factors or divisors. 1 is a factor of all numbers. Prime factorization is breaking apart a composite number into prime numbers that can be multiplied to give the larger number. Note that since 1 is not prime, it is not included in the prime factorization. For example, 12 can be factored as 4 × 3. Since 4 is not a prime number, that is not its prime factorization. 12's prime factorization is in fact 3 × 2 × 2. The numbers which are obtained from the factorization are usually ordered, for example, starting with the smallest number. For example, 72=2^3*3^2. The factorization of every number is unique. This generalizes to: Since finding the numbers to multiply together is very difficult for large numbers, this fact can be used in cryptography. Polynomials. This is how one type of polynomial is factored. formula_1 Find two numbers that add up to 9 and can be multiplied to get 20. Here, these numbers are 4 and 5. formula_2 formula_3 formula_4 formula_5
A joint is the place where two or more bones make contact. They allow movement (except for skull bones) and give mechanical support. Joints have cartilage in between them, which help to make the movement flexible. Joints are described structurally and functionally. Structural classification is how the bones connect to each other; function is the degree of movement between the articulating bones.  Synovial bursa. A synovial bursa is a small fluid-filled sac lined by a synovial membrane. It has an inner capillary layer of viscous synovial fluid (bit like raw egg white). The bursa is "a cushion between bones and tendons" and/or muscles around a joint. This helps to reduce friction between the bones and allows free movement.
Muhammad Hosni Said Mubarak (; 4 May 1928 – 25 February 2020), commonly known as Hosni Mubarak (), was an Egyptian politician. He served as President of Egypt from 14 October 1981 to 11 February 2011. Mubarak became the vice-president of the Republic of Egypt after moving up the ranks of the Egyptian Air Force. Then he became the President after President Anwar Sadat was assassinated on 6 October 1981. His almost thirty-year presidency made him Egypt's longest-serving ruler since Muhammad Ali Pasha. As President of Egypt, Mubarak is thought to have been one of the most powerful leaders in the region. Under the 1971 Constitution of Egypt, Mubarak exercised strong control over the country and was generally considered a dictator. In 2005, he called an election and easily won it. Many opponents believed Mubarak changed the election results so he could win. In early 2011, during the Arab Spring, there were huge protests against his government. In the end, Mubarak resigned and handed over power to the armed forces. It is hoped that elections later that year for a new government. On 2 June 2012, Mubarak was sentenced to life imprisonment for ordering the shooting of protesters in the revolution that ousted him. On 13 January 2013, Egypt's Court of Cassation overturned Mubarak's sentence and ordered a retrial. On retrial, Mubarak and his sons were convicted on 9 May 2015 of corruption and given prison sentences. Mubarak was detained in a military hospital and his sons were freed 12 October 2015 by a Cairo court. He was acquitted on 2 March 2017 by the Court of Cassation and released on 24 March 2017. He died on 25 February 2020 at a Cairo hospital after having surgery, aged 91.
Euclid of Alexandria () (about 325 BC–265 BC) was a Greek mathematician who lived in Alexandria, Egypt and worked at the Library of Alexandria. Little is known about this person, but people think he lived there when Ptolemy I was Pharaoh. It is not known where and when he was born. The Elements. Euclid collected together all that was known of geometry, which is part of mathematics. His "Elements" is the main source of ancient geometry. Textbooks based on Euclid have been used up to the present day. In the book, he starts out from a small set of axioms (that is, a group of things that everyone thinks are true). Euclid then shows the properties of geometric objects and of whole numbers, based on those axioms. The "Elements" also includes works on perspective, conic sections, spherical geometry, and possibly quadric surfaces. Apart from geometry, the work also includes number theory. Euclid came up with the idea of "greatest common divisors". They were in his "Elements". The greatest common divisor of two numbers is the greatest number that can fit evenly in both of the two numbers. The geometrical system described in the "Elements" was long known simply as geometry, and was considered to be the only geometry possible. Today that system is referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which mathematicians developed in the 19th century. Other works. In addition to the "Elements", at least five works of Euclid have survived to the present day. They follow the same logical structure as "Elements", with definitions and proved propositions.
Guadeloupe is part of France in the Caribbean Sea. It is made up of five islands. The capital is Basse-Terre.  Arawak native Americans first lived on the islands. Most died when Europeans came. Guadeloupe was first governed by the French Company of the American Islands. It was then taken over by England, given to Sweden, and given back to France.  Today, most of the people in Guadeloupe are Roman Catholic and are of African descent.
Lewis Allan "Lou" Reed (March 2, 1942 – October 27, 2013) was an American rock musician. He was originally from Long Island, New York and spent most of his life in New York City. He is remembered for being in the Velvet Underground, although he also released solo work. He was friends with artist Andy Warhol. Early life. Lewis Allan Reed was born on March 2, 1942 in Brooklyn, New York City. He studied at Syracuse University. Reed was raised Jewish. Career. Reed began his career in 1964. He is perhaps most famous for his songs "Walk on the Wild Side" (about transgender woman Candy Darling and other such people Reed had known), "Perfect Day" (which was covered by many other artists, including Duran Duran and a version used by the BBC) and "Heroin" (an "love song" about the drug. Reed's 1989 album "New York" drew attention and praise, for its matter-of-fact look at the condition of New York City in the late 1980s. At the height of his popularity as a solo artist, Reed released one of the least "commercial" recordings ever; his 1975 experimental album "Metal Machine Music". It was an hour of electric guitar feedback, and not what many people thought was music. The album did not hurt his career in the long run, and it reminded people that Reed was a unique musician. Because of his song about heroin, Reed was believed to have been addicted to the drug, but this was not the case. He was a longtime user of amphetamines, marijuana and tobacco, but gradually stopped using any drugs. He began exercising more, and enjoyed Tai Chi. In May 2000, Reed performed before Pope John Paul II at the Great Jubilee Concert in Rome. Reed was inducted into the Rock and Roll Hall of Fame with The Velvet Underground in 1996 and as a solo artist in 2015. Personal life. Reed was bisexual. He was married to Betty Reed during 1973. Then he was married to Sylvia Morales from 1980 until they divorced in 1994. Then
Anthropomorphism is the addition of human traits to something that is not a human. For example, the non-human might have human feelings, needs, and wants. It is common for people to use anthropomorphism. Anthropomorphism is often used in stories and art. The story of the "Three Little Pigs" has a wolf and three pigs who talk and act like humans. Disney's Mickey Mouse also talks and acts like a human. An anthropomorphized animal is called a "furry". The novel "The Call of the Wild" also uses anthropomorphism. The main character is a dog named Buck. Many other characters are dogs and wolves. In the story, the animals think and act more like humans than dogs. Reasons for anthropomorphism. Humans can usually explain why humans do things. Humans are not as good at explaining why non-human things do things. This can lead to people assuming non-human things will do things like humans. Humans learn about other humans early in life. They know more about humans than about things that are not humans, and they can remember it better.
The apostrophe (Ↄ, ↄ, ’), also known as the apostrophus, is a punctuation mark used in writing. It is also a diacritic. In English, it has two jobs: Examples. Its versus it's. The most common grammatical mistake in written English is to put "it's" where "its" is correct.  Its: a possessive adjective and pronoun of the personal pronoun "it".  It's: a contraction of the verbal phrase "it is" or "it has". The same applies to "yours", "theirs" and "ours" because these are also possessive adjectives of personal pronouns. Possession. Apostrophes are also used to show something belongs to someone (or something). Again, correct uses can be expanded: The intrusive apostrophe. Comes in plurals which don't ("do not") need it. Do not put an apostrophe in word ending in s, such as a plural. Put an apostrophe, or 's, at the end of the word instead. Writing dialogue or titles. Apostrophes are also used when other words are shortened, as in slang: This is just a version of the abbreviation function. Plural. To make a word that doesn't ("does not") usually exist as a plural into a plural, an apostrophe is occasionally used. See these examples:
A by-election or bye-election is a type of special election. These elections are held in between general elections. General elections are elections for all members of an elected body. By-elections are elections for just some members. A by-election could be needed if a member dies or resigns while in political office. They are also used if a person is removed from office for some reason, for example if he/she is guilty of a crime or is not qualified to be a member anymore. By-elections in the United States and the Philippines are called "special elections". In India, they are called "bypolls". In the 1980s, all 12 of the Unionist MPs in the British House of Commons resigned and all of the elections happened on the same day. Although unusual, these were still only by-elections. It is also defined as an election held in a single political constituency to fill a vacancy that has happened during a government's term of office.
A secretary is a person who is employed to help in an office, and help the people in charge of the office do their job. By definition, the main task of a secretary is to keep organized documents and electronic files for the business, school, hospital, or government agency they work for. Other common jobs that secretaries do are answering telephones; typing and writing letters; plan and schedule meetings with guests; and manage the website of their office. In different workplaces, and for different reasons, a secretary may also be called an administrative assistant, receptionist, clerk, or executive assistant. In the past, most secretaries were men. Today, 98% of secretaries are women, according to the US Census. In 1952, several groups, for example the National Secretaries Association , founded Secretary's Day. It is celebrated in the 4th week of April. It has been renamed "Administrative Professional's Week" to represent the more challenging roles of secretaries today. Other secretaries. In government, secretaries are important people who hold high positions in government. Many secretaries in government are in charge of government agencies. Most members of the United States Cabinet are called "Secretary" including the United States Secretary of State, who deals with other countries. In the United Kingdom, a Secretary of State is a senior Cabinet Minister in charge of a Government Department. In the US, United States Secretary Defense is the head of the US Department of Defense.
Happiness is a feeling of pleasure and positivity. When someone feels good, proud, excited, relieved or satisfied about something, that person is said to be "happy". Feeling happy may help people to relax and to smile.  Happiness is usually thought of as the opposite of sadness. However, it is very possible to feel both at once, often about different things, or sometimes even about the same thing. You are often excited when you are happy. Happiness can also be inspired too. Many philosophers have said that people in the world go back and forth between times of happiness and sadness, but there is nobody who is always happy or always sad. Happiness sometimes causes people to cry when they laugh because the emotion takes control of them. Happiness was thought of as the key to love in ancient civilizations such as the Inca and the Maya.
A number is called a perfect number if by adding all the positive divisors of the number (except itself), the result is the number itself. Six is the first perfect number. Its divisors (other than the number itself: six) are one, two, and three and one plus two plus three equals six. Other perfect numbers include 28, 496 and 8128. Perfect numbers that are even. Euclid discovered that the first four perfect numbers are generated by the formula 2"n"-1(2"n" - 1): for "n" = 2: 21(22 - 1) = 6 for "n" = 3: 22(23 - 1) = 28 for "n" = 5: 24(25 - 1) = 496 for "n" = 7: 26(27 - 1) = 8128  Euclid saw that 2"n" - 1 is a prime number in these four cases. He then proved that the formula 2"n"-1(2"n" - 1) gives an even perfect number whenever 2"n" - 1 is prime (Euclid, Prop. IX.36). Ancient mathematicians made many assumptions about perfect numbers based on the four they knew. Most of the assumptions were wrong. One of these assumptions was that since two, three, five, and seven are precisely the first four primes, the fifth perfect number would be obtained when "n" = 11, the fifth prime. However, 211 - 1 = 2047 = 23 × 89 is not prime and therefore "n" = 11 does not give a perfect number. Two other wrong assumptions were: The fifth perfect number (formula_1) has eight digits. This falsifies the first assumption. For the second assumption, the fifth perfect number indeed ends with a six. However, the sixth (8,589,869,056) also ends in a six. It is straightforward to show the last digit of any even perfect number must be six or eight. In order for formula_2 to be prime, it