ejaasaari/simplewiki-2025-04-01 huggingface dataset:
Hilbert's paradox of the Grand Hotel is a mathematical paradox named after the German mathematician David Hilbert. Hilbert used it as an example to show how infinity does not act in the same way as regular numbers do. The paradox. Normal hotels have a set number of rooms. This number is finite. Once every room has been assigned to a guest, any new guest that wants a room and does not have one yet cannot be served - in other words, the hotel is fully booked. Now suppose that there is a hotel that has an infinite number of rooms. As a convenience, the rooms have numbers, the first room has the number 1, the second has number 2, and so on. If all the rooms are filled, it might appear that no more guests can be taken in, as in a hotel with a finite number of rooms. This is wrong, though. A room can be provided for another guest. This can be done by moving the guest in room 1 to room 2, the guest in room 2 to room 3, and so on. In the general case, the guest in room "n" will be moved to room "n+1". After all guests have moved, room 1 is empty, and the new guest now has a room to occupy. This shows how we can find a room for a new guest even if the hotel is already full, something that could not happen in any hotel with a finite number of rooms. In case of infinitely new guests. Another thing that can be done with this imaginary hotel is to double the number of people inside, again when all the rooms are already full. This is done by asking each guest to multiply their room number by two and move to that room. (If their previous room number was "n", this time they would move to room number "2n".) This would send the guest in room 1 to room 2, the guest in room 2 to room 4, the guest in room 3 to room 6, the guest in room 4 to room 8, and so on. After finishing, we find that all the rooms with the odd numbers are empty. Then we
In mathematics, the opposite or inverse of a number formula_1 is an additive or a subtractive number formula_2 which, when added to formula_1, results in 0. The opposite of formula_4 is formula_5. For example, −7 is the opposite of 7, because formula_6.  Definition. A number formula_7 is called an opposite or inverse number of another number formula_8 if formula_9. By definition, formula_10 is the opposite number of formula_7. For example, formula_12 is the opposite number of formula_13 and vice-versa. This is because formula_14 Properties. The opposite numbers satisfy the properties listed below. References.
An "n"-th root of a number "r" is a number which, if "n" copies are multiplied together, makes "r". It is also called a radical or a radical expression. It is a number "k" for which the following equation is true: formula_1 We write the nth root of "r" as formula_3. If "n" is 2, then the radical expression is a square root. If it is 3, it is a cube root. Other values of n are referred to using ordinal numbers, such as "fourth root" and "tenth root". For example, formula_4 because formula_5. The 8 in that example is called the radicand, the 3 is called the index, and the check-shaped part is called the radical symbol or radical sign. Roots and powers can be changed as shown in formula_6. The product property of a radical expression is the statement that formula_7. The quotient property of a radical expression is the statement formula_8., b != 0. Simplifying. This is an example of how to simplify a radical. formula_9 If two radicals are the same, they can be combined. This is when both of the indexes and radicands are the same. formula_10 formula_11 This is how to find the perfect square and rationalize the denominator. formula_12
The Isle of Portland is an island in Dorset in the south of England. Portland is south of the resort of Weymouth. 13,000 people live there. It is where the famous Portland limestone was originally found. In 2012, the sailing in the Olympics took place on Portland and in Weymouth.
A flagship is the ship used by the officer who commanded a group of naval ships. The term comes from the custom of the commanding officer to fly a special flag to show he was present. Used in this way, "flagship" is normally a temporary name; the flagship is wherever the officer is flying his flag. However, admirals have always needed a special place; a meeting room large enough to hold all the captains of the fleet, and a place for the admiral's staff to make plans and draw up orders. Over the years, the term "flagship" has been borrowed by other industries. These include broadcasting, automobiles, cell phones, and others to mean their core products or services.
The Eurasian magpie or common magpie ("Pica pica") is a bird that lives in Europe, much of Asia, and northwest Africa. It is one of several birds in the crow family named as magpies. In Europe, "magpie" is used by English speakers to call the European magpie; it is the only magpie in Europe outside the Iberian Peninsula.
Sui generis (pronounced or ) is a term from Latin. It can be translated to "Of (his/her/its) own kind". It basically means that something has VERY special characteristics. They are so special, that the thing cannot really be compared to anything else. It is used in various contexts. The term was invented by philosophers. What they originally wanted to say was that an idea is so specific as to be unique, that it cannot really be part of a broader concept. Law. When lawyers talk about something being "sui generis", they mean that something is unique. It cannot be compared. With intellectual property, a design can be "sui generis". Political sciences. The European Union is something that has come to be in the last few years. In some ways it is like state in others like a confederation of states or an international organisation. It is mostly classified as "sui generis". Sociology. In the sociology of Emile Durkheim, "sui generis" is used to illustrate his theories on social existence. He says that society, as it was there before any living individual was born, is independent of all individuals. His "sui generis" (its closest English meaning in this sense being 'independent') society will furthermore continue its existence after the individual ceases to interact with it. Examples in media. Meryl Streep was praised in a "Wall Street Journal" review of "The Devil Wears Prada": "(her) pitch-perfect portrayal of Miranda is "sui generis", with a dramatic existence of its own, as unique and memorable as, say, a Bette Davis character." Martin Kettle in "The Guardian" said about hung parliaments: "Each is "sui generis", dependent on the particular parliamentary arithmetic, inter-party momentum and surrounding political circumstances." "Slate" has used the term several times; one article discussed the unique variations of French Rose Champagne: "Grower Champagnes are wines made by small farmers in the Champagne region who, bucking convention, choose to craft their own wines rather than sell their grapes to the major Champagne houses. Typical of farmer fizzes, the
A regular polygon is a shape that can be drawn on a flat surface. It has sides that are all the same length, and its angles are all the same. In other words, a polygon which is both equilateral (which means all its sides have the same length) and equiangular (which means that all its angles are the same) is a regular polygon. It always has the same number of edges and points. A polygon is also convex if there aren't any two points within it that can't be connected with a straight line, where the entire straight line is also in it. An example of a concave shape is a five-pointed star. It's concave because you can connect two of the points of a star with a straight line, and most of the straight line doesn't go through the star. If a five-pointed star is both equilateral and equiangular, it is also a regular polygon, but it isn't a convex one. All regular concave polygons are stars. Examples. The simplest examples of regular convex polygons are: Polygons with more sides look more like circles. A polygon with an infinite number of sides is called an apeirogon. Polygons can be described in text by a special symbol called a Schläfli symbol. This symbol is written as curly brackets, with some numbers inside it, like {3}. {3} is a triangle. The number inside can also be a fraction. A Schläfli symbol of {5/2} is a five-pointed star. Properties. Most mathematical objects have things that can be said about them that are always true. These are called properties. All polygons (convex and star polygons) can be rotated in place by some angle and still look the same—in other words, they're all rotationally symmetric. For example, a square could be rotated a quarter turn, and it would look the same as before. Another way of seeing this property is that any polygon can have a circle drawn around it, touching all its points, and the polygon's points are evenly spaced around the circle. A polygon can also have a circle drawn inside it, touching all its edges (but not overlapping), and the places
Straightedge and compass construction, also known as ruler-and-compass construction, is drawing of lengths, angles or shapes using only a ruler and compass.  Some things cannot be drawn this way. For example, there are only 32 regular polygons with an uneven number of sides which are known to be constructible. It has been proven that a square with the same area as the area of a circle cannot be constructed. This is called "Squaring the circle".
Air Force One is the official air traffic control call sign aircraft carrying the president of the United States. Air Force One is usually always referred to any aircraft the president and his staff travels on. The official name of the plane is the SAM 2900 and VC-25. Air Force One is one of the most recognizable symbols of the presidency not just in American culture but across the world. Emblazoned with the words “United States of America,” the United States flag, and the Seal of the President of the United States. Air Force One has an undeniable and amired presence wherever it goes and flies to. History. Air Force One is maintained and operated by the Presidential Airlift Group, part of the White House Military Office. The Airlift Group was founded in 1944 as the Presidential Pilot Office at the direction of President Franklin D. Roosevelt. For the next 15 years, various propeller-driven aircraft served until President Dwight D. Eisenhower flew to Europe aboard VC-137A, a Boeing 707 Stratoliner, in August 1959. In 1962, President John F. Kennedy became the first president to fly in a jet specifically built for presidential use a modified Boeing 707 until it retired in 1990. The current presidential aircraft, Boeing 747-200B, became the new and modified presidential plane in 1990, when President George H.W. Bush became the first president to ride on the aircraft.
In the Middle Ages, people in Europe believed that Incubi (one Incubus, several Incubi) were male demons. There were also female demons, called succubi. They lay on sleeping people, to have sexual intercourse with them. They would also do this to make other incubi. While they had sex with their victim, they drained its energy to sustain themselves. Sometimes, having sex with an incubus may result in a child, as in the legend of Merlin. Some sources say that the incubus may be identified by its unnaturally cold penis. Religious tradition holds that repeated intercourse with such a spirit by either males or females may result in bad health, or even death. Origins of the legends. People have come up with different explanations for the incubus legends. In the Middle Ages, people worried a lot about sin, especially sexual sins of women. Victims may have been experiencing waking dreams or sleep paralysis. Also, nocturnal arousal, orgasm or nocturnal emission could be explained by the idea of creatures causing an otherwise guilt-producing and self-conscious behavior. The influence of incubi could also have been used to explain how pregnancies happen outside marriage; such pregnancies were often "unexplainable".and unnoticed  Victims who claimed to have fallen prey to the influence of incubi, could in reality have been victims of sexual assault by a real person. Rapists may have attributed the rapes of sleeping women to demons in order to escape punishment. A friend or relative may have assaulted the victim in her sleep. The victims and, in some cases the clergy, may have found it easier to explain the attack as supernatural in origin rather than confront the idea that the attack came from a trusted person. Ancient and religious descriptions. One of the earliest mentions of an incubus comes from Mesopotamia on the Sumerian kings' list, ca. 2400, where the hero Gilgamesh's father is listed as Lilu (Lila). It is said that Lilu disturbs and seduces women in their sleep, while Lilitu, a female demon, appears to men in their erotic dreams. Two other demons appear as well: Ardat lili visits men by night and bears ghostly children from them
A Commonwealth realm is a country in the Commonwealth of Nations which has King Charles III as monarch. They include his home country of the United Kingdom and many of its former colonies or territories. As of 2023, there are 15 commonwealth realms: In each of the countries outside the UK, the King appoints a Governor-General to represent him, who, after consulting with the government of the realm, has all of the powers and duties of the Monarch. Usually the Governor-General signs all acts of parliament into law, but can wait and ask the King for advice or wait for him to sign the act himself. This happened in 1982 when Queen Elizabeth signed the important "Canadian Charter of Rights and Freedoms" during a visit to Ottawa, and the Australia Act 1986 in Canberra. Although King Charles III is monarch of many countries, the British government has no power in the other realms, just as the governments of the other realms have no power in the UK. This is why each realm decides on the Monarch's official title. Usually it is "Queen/King of (realm) and Her/His other Realms and Territories, Head of the Commonwealth". But two countries mention the UK in their title for the Queen: Grenada uses "Queen of the United Kingdom of Great Britain and Northern Ireland and of Grenada and Her other Realms and Territories, Head of the Commonwealth", while Canada uses the old-fashioned form, which reads "by the Grace of God, of the United Kingdom, Canada and Her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith." Not all countries use the title "Defender of the Faith".
A Dashiki is a loose fitting, brightly coloured garment associated with African culture. It is also associated with the counterculture of the 1960s in the United States. The most popular styles cover the top half of the body. It originated in West Africa. A common form is a loose-fitting pullover garment, with an ornate V-shaped collar. It often has an embroidered neck and sleeve lines. There are both casual and formal versions. History. The term "dashiki" comes from the Yoruba language, where it originally referred to a loose-fitting pullover developed in West Africa as a practical work tunic for men. The Yoruba word "dashiki" itself is derived from the Hausa term "dan ciki," which means shirt. Dashikis were worn by both men and women. This garment keeps the wearer cool in the hot African climate. The dashiki was worn as a work shirt in the shorter version.  1960s US counterculture. The dashiki became popular in the hippie culture of the 1960s. Peace Corps members returning from Africa brought back dashikis. African diplomats to the United Nations in New York were often seen and photographed wearing colorful dashikis. Dashikis were seen as a symbol of support for black racial struggles. Groups like the Black Panthers wore the Dashiki as a symbol of their black heritage. The Afro hairstyle, faded blue jeans and the Dashiki were all popular expressions of the Black is beautiful cultural movement. Musical groups. Many of the rock groups of the 60s and 70s wore Dashikis. But black performers of the 60s 70s preferred the more conventional suit and tie look. But in the 80s several black groups wore the dashiki to show their heritage. One South African vocal group, 'Ladysmith Black Mambazo', wore dashikis extensively. This identified them more as Africans than Zulus.
The Battle of Midway was an important naval battle of World War II, between the United States and the Empire of Japan. It took place from 4 June 1942 to 7 June 1942. This was about a month after the Battle of the Coral Sea, and six months after the Japanese attack on Pearl Harbor. The United States Navy defeated a Japanese attack against Midway Atoll (northwest of Hawaii) and destroyed four Japanese aircraft carriers and a heavy cruiser. The battle was a decisive victory for the Americans. It was the most important naval battle of the Pacific area in World War II. The battle weakened the Imperial Japanese Navy for the rest of the war. Japan could not build up its forces again. The United States replaced their lost ships and planes with better ones very quickly. Japan could only make a few poor quality replacements. The Japanese planned to bring America's carriers into a trap and sink them. The Japanese also tried to take Midway Atoll to build defenses far from their homeland and prepare to invade Fiji, Samoa, and Hawaii. The Midway operation, like the attack on Pearl Harbor, was made to destroy the American strength in the Pacific Ocean. This way, Japan could become the biggest power in the area and unify Asia under its control. It was also hoped that another defeat would force the U.S. to ask for peace soon. After the defeat, Imperial Japanese Navy forces retired. Japan lost four out of their six carriers, and hundreds of their best air pilots. This stopped the expansion of the Japanese Empire in the Pacific, and the Americans began to slowly advance towards Japan. Background. Japan had reached its first goals quickly, taking the Philippines, Malaya, Singapore, and the Dutch East Indies (now Indonesia). This gave Japan petroleum, which it needed to make more war. Planning for a second part of the operations started in January 1942. However, disagreements between the Imperial Army and Imperial Navy, and among naval commanders, prevented finishing the plan until April 1942. Admiral Yamamoto said he would quit if his plan for the Central Pacific was not accepted. It was accepted. Yamamoto's main goal was to destroy America's carrier forces, which he saw as the main
The Minnesota Wild are a ice hockey team based in St Paul, Minnesota The Wild joined the NHL in 2000. Their home is the Xcel Energy Center in downtown St. Paul.
The Boeing B-29 Superfortress was a heavy bomber aircraft with four engines used by the United States Army Air Forces in World War II, and by other countries' military after that. The name "Superfortress" came from its famous previous model, the B-17 Flying Fortress. The B-29 Boeing Model 345 was one of the biggest aircraft to serve during World War II. It was one of the most advanced bombers of its time. It was the most used aircraft in the U.S. bombing against Japan in the final months of World War II, and B-29s carried the atomic bombs that destroyed Hiroshima and Nagasaki. The B-29 stayed in service for a long time after the war ended. By the time it was retired in the 1960s, some 3,900 planes had been built. The American B-29 Superfortress was one of the most ambitious and expensive projects of WWII, even more expensive than the Manhattan Project. This enormous heavy bomber was equipped with numerous remote-controlled turrets and 4 powerful propellers. This heavy bomber  was used in later parts of the war, and was designed to finally supress the Japanese forces.
Sewing is stitching cloth, leather, furs, or other materials, using a needle and thread. Sewing can be done on a sewing machine, or by hand. "Plain" sewing is mostly done to make or mend clothing and household furnishings such as curtains, sheets, upholstery, and table linens. It is also used for sails, bellows, skin boats, banners and other items shaped out of flexible materials. "Fancy" sewing is done to decorate materials, such as embroidery or quilting. Sewing is an important part of shoemaking and bookbinding. Wounds are often sewn shut. If a thread becomes loose in a sewn item, the stitches may unravel and require restitching to repair them. In repair sewing, pulling the threaded needle in and out of the fabric at the same lengths and places as the other remaining stitches can make a repair nearly invisible. Replacing a missing button on a garment follows the same procedure, although there are different possible ways to place the thread to sew on a button. While repairs are usually sewn by hand, most garments are created using a machine, which can range from simple to complex.
Saipan (IPA: in English) is the largest island and capital of the United States Commonwealth of the Northern Mariana Islands (CNMI), a chain of 15 tropical islands which are part of the Marianas archipelago in the western Pacific Ocean (15°10’51”N, 145°45’21”E) with a total area of 115.39 km² (44.55 sq mi). At the 2000 census, there were more than 62,392 people. Saipan is at latitude of 15.25° north and longitude of 145.75° east, about 200 km (120 mi) north of Guam. Saipan is about 20 km (12.5 mi) long and 9 km (5.5 mi) wide. It is a popular tourist destination in the Pacific.
Knitting creates flexible fabric by looping thread or yarn together using two or more knitting needles or a knitting machine. Types of knitting. Flat knitting. Flat knitting, which is usually done on two straight needles, makes a length of cloth and is used to create things like blankets, scarves, and the backs, fronts, and sides of sweaters. Circular knitting. Circular knitting, which is done on circular needles, or needles that have points on both ends, produces a seamless tube and is used to create things like hats, socks, mittens, rings, and sleeves. Cable knitting. Patterns called "cables" are typically used on sweaters, particularly on fancy Aran sweaters from Ireland. Different kinds of stitches create different patterns in knitting. For example, the stretchy ends of knitted sleeves are called "ribbing". Materials. Yarn. Yarn for knitting can be made from any number of natural or synthetic (man made) fibers such as wool, cotton, silk, or acrylic. Some yarns are made from a blend of several kinds of fibers. Yarns come in many thicknesses or "weights" from fine to thick: lace, fingering, sock, sport, double-knit (or DK), worsted, Aran, bulky, and super-bulky. Thinner yarns are generally used with smaller knitting needles, and thicker yarns are used with larger knitting needles. Needles. Knitting needles come in various shapes: straight, double-pointed, cable, and circular. They can be made from bamboo, aluminum, steel, or plastic.
Yarn is a long, continuous length of fibers that have been spun or felted together. Yarn is used to make cloth or different wearable accessories including shoes, hats, scarfs, etc. by knitting, crocheting or weaving. Yarn is sold in a shape called a skein to prevent the yarn from becoming tangled or knotted. Yarn can be made from any number of natural or synthetic fibers such as wool, cotton, silk, or acrylic. Some yarns are made from a blend of several kinds of fibers. Yarns come in many thicknesses or weights from fine to thick: lace, fingering, sock, sport, double-knit (or DK), worsted, aran, bulky, and super-bulky. Very fine yarn is called thread and is used in sewing and embroidery. Yarn can also be used to crochet.