the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Hilbert's paradox of the Grand Hotel 
 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.
Hilbert's paradox of the Grand Hotel 
 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.
Hilbert's paradox of the Grand Hotel 
 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.
Hilbert's paradox of the Grand Hotel 
 In a normal hotel, with a finite number of rooms, the number of odd-numbered rooms, is smaller than the total number of rooms.
Hilbert's paradox of the Grand Hotel 
 Hilbert's paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true.
Hilbert's paradox of the Grand Hotel 
 The statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms.
Hilbert's paradox of the Grand Hotel 
 The properties of "infinite collections of things" are quite different from those of "finite collections of things".
Hilbert's paradox of the Grand Hotel 
 The paradox of Hilbert's Grand Hotel can be understood by using Cantor's theory of transfinite numbers.
Hilbert's paradox of the Grand Hotel 
 In an ordinary (finite) hotel with more than one room, the number of odd-numbered rooms is obviously smaller than the total number of rooms.
Hilbert's paradox of the Grand Hotel 
 However, in Hilbert's aptly named Grand Hotel, the quantity of odd-numbered rooms is not smaller than the total "number" of rooms.
Hilbert's paradox of the Grand Hotel 
 In mathematical terms, the cardinality of the subset containing the odd-numbered rooms is the same as the cardinality of the set of all rooms.
Hilbert's paradox of the Grand Hotel 
 Put differently, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers.
Hilbert's paradox of the Grand Hotel 
 For example, the set of rational numbers—those numbers which can be written as a quotient of integers—contains the natural numbers as a subset, but is no bigger than the set of natural numbers since the rationals are countable: there is a bijection from the naturals to the rationals.
Opposite number 
 In mathematics, the opposite or additive inverse of a number  is a number  which, when added to , results in 0.
Nth root 
 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.
Nth root 
 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.
Chrysanthemum 
 Chrysanthemums are a genus (Chrysanthemum) of about 30 species of perennial flowering plants in the family Asteraceae, from Asia and northeast Europe.
Flagship 
 The term comes from the custom of the commanding officer to fly a special flag to show he was present.
Flagship 
 Used in this way, "flagship" is normally a temporary name; the flagship is wherever the officer is flying his flag.
Flagship 
 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.
Flagship 
 These include broadcasting, automobiles, cell phones, and others to mean their core products or services.
Eurasian magpie 
 The Eurasian magpie or common magpie (Pica pica) is a bird that lives in Europe, much of Asia, and northwest Africa.
Eurasian magpie 
 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 
 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.
Sui generis 
 In some ways it is like state in others like a confederation of states or an international organisation.
Sui generis 
 In the sociology of Emile Durkheim, sui generis is used to illustrate his theories on social existence.
Sui generis 
 He says that society, as it was there before any living individual was born, is independent of all individuals.
Sui generis 
 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.
Sui generis 
 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."
Sui generis 
 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."
Sui generis 
 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.
Sui generis 
 Typical of farmer fizzes, the grower rosés are utterly sui generis—in a few cases almost freakishly so."
Sui generis 
 Political commentator Dick Morris referred to the intense public interest in the 2008 US Presidential race as "clearly sui generis, and anything can happen."
Regular polygon 
 A regular polygon is 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).
Straightedge and compass construction 
 Straightedge and compass construction, also known as ruler-and-compass construction, is drawing of lengths, angles or shapes using only a ruler and compass.
Straightedge and compass construction 
 For example, there are only 32 regular polygons with an uneven number of sides which are known to be constructible.
Air Force One 
 Air Force One is the air traffic call sign (name) of any U.S. Air Force aircraft carrying the president of the United States.
Air Force One 
 The president usually flies in one of the two specially changed Boeing 747 jumbo jets (airplane) kept by the United States Air Force.
Air Force One 
 When Richard Nixon resigned as president in 1974 he flew back to his home in California in Air Force One, but halfway to California he stopped being president and the airplane was then given a new name, SAM (Special Air Mission) 2700.
Incubus 
 In the Middle Ages, people in Europe believed that Incubi (one Incubus, several Incubi) were male demons.
Incubus 
 Religious tradition holds that repeated intercourse with such a spirit by either males or females may result in bad health, or even death.
Incubus 
 Also, nocturnal arousal, orgasm or nocturnal emission could be explained by the idea of creatures causing an otherwise guilt-producing and self-conscious behavior.
Incubus 
 The influence of incubi could also have been used to explain how pregnancies happen outside marriage; such pregnancies were often "unexplainable".and unnoticed
Incubus 
 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.
Incubus 
 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.
Incubus 
 It is said that Lilu disturbs and seduces women in their sleep, while Lilitu, a female demon, appears to men in their erotic dreams.
Incubus 
 Two other demons appear as well: Ardat lili visits men by night and bears ghostly children from them.
Incubus 
 Also considered to be vampires which is another form of a demon that is said to drink blood from its victims.
Incubus 
 Incubi and succubi were said by some not to be different sexes, but the same demon able to change its sex.
Incubus 
 A succubus would be able to sleep with a man and collect his sperm, and then transform into an incubus and use that seed on women.
Incubus 
 Their offspring were thought to be supernatural in many cases, even if the actual genetic material originally came from humans.
Incubus 
 Many tales claim that the incubus is bisexual, but some indicate that it is strictly heterosexual and finds attacking a male victim either unpleasant or detrimental.
Incubus 
 There are also many stories involving the attempted exorcism of incubi or succubi who have taken refuge in the bodies of men or women.
Incubus 
 The most famous legend of such a case includes that of Merlin, the famous wizard from Arthurian legend.
Incubus 
 According to the Malleus Maleficarum, exorcism is one of the five ways to overcome the attacks of Incubi, the others being Sacramental Confession, the Sign of the Cross (or recital of the Angelic Salutation), moving the afflicted to another location, and by excommunication of the attacking entity, "which is perhaps the same as exorcism."
Incubus 
 On the other hand, the Franciscan friar Ludovico Maria Sinistrari stated that incubi "do not obey exorcists, have no dread of exorcisms, show no reverence for holy things, at the approach of which they are not in the least overawed."
Commonwealth realm 
 A Commonwealth realm is a country in the Commonwealth of Nations which has Queen Elizabeth II as monarch.
Commonwealth realm 
 It includes her home country of the United Kingdom and many of its former colonies or territories, including:
Commonwealth realm 
 In each of the countries outside the UK, the Queen appoints a Governor-General to represent her, who, after consulting with the government of the realm, has all of the powers and duties of the queen.
Commonwealth realm 
 Usually the Governor-General signs all acts of parliament into law, but can wait and ask the Queen for advice or wait for her to sign the act herself.
Commonwealth realm 
 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.
Commonwealth realm 
 Although Queen Elizabeth II 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.
Commonwealth realm 
 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."
Dashiki 
 Twelfth and thirteenth centuries burial mounds in Mali (West Africa) have revealed versions of dashikis.
Dashiki 
 African diplomats to the United Nations in New York were often seen and photographed wearing colorful dashikis.
Dashiki 
 The Afro hairstyle, faded blue jeans and the Dashiki were all popular expressions of the Black is beautiful cultural movement.
Battle of Midway 
 The Battle of Midway was an important naval battle of World War II, between the United States and the Empire of Japan.
Battle of Midway 
 This was about a month after the Battle of the Coral Sea, and six months after the Japanese attack on Pearl Harbor.
Battle of Midway 
 The United States Navy defeated a Japanese attack against Midway Atoll (northwest of Hawaii) and destroyed four Japanese aircraft carriers and a heavy cruiser.
Battle of Midway 
 The Japanese also tried to take Midway Atoll to build defenses far from their homeland and prepare to invade Fiji, Samoa, and Hawaii.
Battle of Midway 
 The Midway operation, like the attack on Pearl Harbor, was made to destroy the American strength in the Pacific Ocean.
Battle of Midway 
 This stopped the expansion of the Japanese Empire in the Pacific, and the Americans began to slowly advance towards Japan.
Battle of Midway 
 Japan had reached its first goals quickly, taking the Philippines, Malaya, Singapore, and the Dutch East Indies (now Indonesia).
Battle of Midway 
 However, disagreements between the Imperial Army and Imperial Navy, and among naval commanders, prevented finishing the plan until April 1942.
Battle of Midway 
 Yamamoto's main goal was to destroy America's carrier forces, which he saw as the main threat to the Pacific campaign.
Battle of Midway 
 In this raid, 16 US Army Air Forces B-25 Mitchell bombers launched from  bombed targets in Tokyo and several other Japanese cities.
Battle of Midway 
 The raid, while militarily unimportant, showed that American bombers could reach Japanese territory.
Battle of Midway 
 Yamamoto thought that another attack on the U.S Naval base at Pearl Harbor would make all of the American fleet to sail out to fight, including the carriers.
Battle of Midway 
 However, because of the many American land-based airplanes on Hawaii, he thought that it was too risky to attack directly.
Battle of Midway 
 Instead, he decided to attack Midway, a tiny atoll at the northwest end of the Hawaiian Island chain, approximately  from Oahu.
Battle of Midway 
 That meant submarines operating from Pearl Harbor could refuel and get new supplies, so they could go  farther west.
Battle of Midway 
 In May 1942, during the Battle of the Coral Sea,  had been sunk and  so badly damaged that the Japanese thought she had been sunk.
Battle of Midway 
 The Japanese also knew that  was being repaired on the US West Coast after getting torpedo damage from a submarine.
Battle of Midway 
 Yamamoto's battleships and cruisers went behind Vice-Admiral Chūichi Nagumo's carrier force by several hundred miles.
Battle of Midway 
 Japan's heavy surface forces would wait for the U.S. ships to come to defend Midway, and destroy them.
Battle of Midway 
 The plan was for Nagumo's carriers to cause so much harm to US ships that the Japanese could fire on them by daylight.
Battle of Midway 
 Yamamoto's choice to spread out his ships meant that none of his groups of ships could support each other.
Battle of Midway 
 The only warships larger than the 12 destroyers that protected Nagumo's fleet were two battleships, two heavy cruisers, and one light cruiser.
Battle of Midway 
 The Japanese attacks in the Aleutian Islands (Operation AL) took away yet more ships that could have attacked Midway.
Battle of Midway 
 Early twenty-first century research shows that AL was supposed to be launched at the same time as the attack on Midway.
Battle of Midway 
 However, a one-day delay in the sailing of Nagumo's ships resulted in Operation AL beginning a day before the Midway attack.
Battle of Midway 
 To battle with an enemy expected to have four or five carriers, Admiral Chester W. Nimitz, Commander in Chief, Pacific Ocean Areas, needed every U.S. carrier he could get.
Battle of Midway 
 Nimitz also called back Rear Admiral Frank Jack Fletcher's force, including the carrier Yorktown (which had major damage at Coral Sea), from the South West Pacific Area.
Battle of Midway 
 The Pearl Harbor Naval Shipyard worked all day and all night, and in 72 hours she was ready to battle for two or three weeks.
Battle of Midway 
 Her flight deck was patched, sections of internal frames were replaced, and several squadrons of aircraft were taken from Saratoga.
Battle of Midway 
 On Midway, by 4 June the USN had stationed four groups of PBYs—31 aircraft in total—for long-range reconnaissance duties, and six new Grumman TBF-1 Avengers.
Battle of Midway 
 The Marine Corps had 19 Douglas SBD Dauntlesses, seven Grumman F4F-3 Wildcats, 17 Vought SB2U-3 Vindicators, and 21 Brewster F2A-3s.
Battle of Midway 
 The USAAF sent a group of 17 B-17 Flying Fortresses and eight B-26 Marauders with torpedoes: in total 126 aircraft.
Battle of Midway 
 During the Battle of the Coral Sea one month earlier, the Japanese light carrier Shōhō had been sunk and the fleet carrier  had three bomb hits, and was in drydock undergoing repairs.
Battle of Midway 
 Although the carrier  was undamaged, she had lost almost half her airplanes and was in port in Kure awaiting new planes and pilots.
Battle of Midway 
 Japan's two most advanced aircraft carriers were not available and Admiral Nagumo would therefore have only four fleet carriers:  and ;  and .
Battle of Midway 
 At least part of this was due to overwork; Japanese carriers had been constantly operating since 7 December 1941, including raids on Darwin and Colombo.
Battle of Midway 
 The main Japanese carrier-based aircraft were the Aichi D3A1 dive bomber and the Nakajima B5N2, which was used either as a torpedo bomber or as a bomber.
Battle of Midway 
 In addition many of the aircraft being used during the June 1942 operations had been operating since late November 1941; many were almost worn out and had become increasingly unreliable.
Battle of Midway 
 These factors meant that all carriers of the Kido Butai had fewer aircraft than normal and there were not enough spare aircraft or parts.
Battle of Midway 
 This let the American carriers reach their meeting point northeast of Midway (known as "Point Luck") without being found by the subs.
Battle of Midway 
 A second attempt at scouting, using four-engine Kawanishi H8K flying boats to fly to Pearl Harbor prior to the battle and see whether the American carriers were there did not work out because Japanese subs could not refuel the planes.
Battle of Midway 
 Yamamoto, at sea on , assumed that Nagumo had received the same message from Tokyo, and he did not send the message, because he did not want the US to hear the message.
Battle of Midway 
 Since the early spring of 1942, the US had been decoding messages stating that there would soon be an operation at objective "AF".
Battle of Midway 
 HYPO was also able to determine the date of the attack as either 4 or 5 June, and to tell Nimitz exactly which Japanese ships were coming.
Battle of Midway 
 The new code, which had not yet been figured out, was used shortly before the attack began, but the important information had already been figured out.
Battle of Midway 
 Nimitz knew that the Japanese had ruined their advantage in number of ships by dividing their ships into four groups, all too separated to be able to support each other.
Battle of Midway 
 Nimitz calculated that the aircraft on his three carriers, plus those on Midway Island, gave the U.S. rough parity with Yamamoto's four carriers, mainly because American carrier air groups were larger than Japanese ones.
Battle of Midway 
 The Japanese, by contrast, remained almost totally unaware of their opponent's true strength and dispositions even after the battle began.
Battle of Midway 
 At about 09:00 on 3 June, a US Navy patrol plane spotted the Japanese Occupation Force  to the west-southwest of Midway.
Battle of Midway 
 Early the following morning the Japanese oil tanker Akebono Maru was hit by a torpedo from an attacking PBY.
Battle of Midway 
 As Nagumo's bombers and fighters were taking off, 11 PBYs were leaving Midway to search for Japanese ships.
Battle of Midway 
 They reported sighting two Japanese carriers with empty decks, which meant an air strike was on its way.
Battle of Midway 
 American radar picked up the enemy at a distance of several miles, and planes were sent off to defend Midway.
Battle of Midway 
 Midway-based Marine fighter pilots, flying F4Fs and obsolescent F2As, intercepted the Japanese and had many losses.
Battle of Midway 
 Most of the U.S. planes were shot down in the first few minutes; several were damaged, and only two could fly.
Battle of Midway 
 Of the 108 Japanese aircraft involved in this attack, 11 were destroyed, 14 were heavily damaged, and 29 were damaged.
Battle of Midway 
 The initial Japanese attack did not destroy Midway: American bombers could still use the airbase to refuel and attack the Japanese invasion force.
Battle of Midway 
 Another air attack to destroy Midway's defences would be necessary if troops were to be able to go ashore by 7 June.
Battle of Midway 
 These included six Grumman Avengers from the s VT-8 (Midway was the first combat mission for the VT-8 airmen, and it was the first combat of the TBF), Marine Scout-Bombing Squadron 241 (VMSB-241), consisting of eleven SB2U-3s and sixteen SBDs, plus four USAAF B-26s, armed with torpedoes, and fifteen B-17s.
Battle of Midway 
 This may have made Nagumo decide to launch another attack on Midway, against Yamamoto's order to keep the reserve force for anti-ship operations.
Battle of Midway 
 Nagumo reversed his order, but it took 40 minutes before Tones scout finally radioed that there was a carrier in the American force.
Battle of Midway 
 Rear Admiral Tamon Yamaguchi recommended that Nagumo strike with the forces at hand: 18 Aichi D3A dive bombers each on Sōryū and Hiryū, and half the cover patrol aircraft.
Battle of Midway 
 Because of the constant flight deck activity, the Japanese did not get their reserve planes on the flight deck for launch.
Battle of Midway 
 By launching right away, Nagumo would be using some of his reserve without proper anti-ship weapons.
Battle of Midway 
 Poor discipline caused many of the Japanese bombers to get rid of their bombs and attempt to fight intercepting F4Fs.
Battle of Midway 
 Japanese carrier rules preferred full strikes, and since Nagumo did not know the American force included a carrier, his response followed Japanese rules.
Battle of Midway 
 In addition, the arrival of another American air strike at 07:53 made Nagumo want to attack the island again.
Battle of Midway 
 Nagumo decided to wait for his first strike force to land, then launch the reserve, which would by then be armed and ready.
Battle of Midway 
 Fletcher's carriers had launched their planes beginning at 07:00, so the aircraft that attacked Nagumo were already on their way.
Battle of Midway 
 Admiral Fletcher, in command aboard Yorktown, and having PBY sighting reports from the early morning, ordered an attack on the Japanese as soon as possible.
Battle of Midway 
 Admiral Fletcher, commanding the Yorktown task force, along with Captain Elliott Buckmaster,Yorktowns commanding officer, and their staffs had experience in doing a full strike against an enemy force in the Coral Sea.
Battle of Midway 
 But they could not pass on what they had learned to Enterprise and Hornet which were ordered to launch the first strike.
Battle of Midway 
 Spruance ordered the aircraft to go to the target right away, since destroying enemy carriers was important to the safety of his ships.
Battle of Midway 
 Spruance decided it was more important to attack as soon as possible, rather than coordinate the attack by aircraft of different types and speeds (fighters, bombers, and torpedo bombers).
Battle of Midway 
 Waldron's squadron saw the enemy carriers and began attacking at 09:20, followed by Torpedo Squadron 6 (VT-6, from Enterprise) whose Wildcat fighter escorts also ran low on fuel and had to turn back at 09:40.
Battle of Midway 
 Without fighter escort, all fifteen TBD Devastators of VT-8 were shot down without being able to do any damage, with Ensign George Gay the only survivor.
Battle of Midway 
 VT-6 lost 10 of their 14 Devastators, and 10 of Yorktown's VT-3's 12 Devastators were shot down with no hits.
Battle of Midway 
 Senior Navy and Bureau of Ordnance officers never asked why six torpedoes, released so close to the Japanese carriers, produced no hits.
Battle of Midway 
 The Japanese combat air patrol, flying Mitsubishi A6M2 Zeros shot down the unescorted, slow, under-armed TBDs.
Battle of Midway 
 A few TBDs managed to get close enough to drop their torpedoes and shoot their machine guns at the enemy ships.
Battle of Midway 
 Despite their failure to get any hits, the American torpedo attacks made the Japanese carriers unable to prepare and launch their own strike.