zero, number denoting the absence of quantity. Represented by the symbol “0,” it plays a foundational role in arithmetic, algebra, computing, and scientific measurement. It lies at the center of the number line, separating positive numbers from negative numbers, and it operates as a placeholder in

aleph-null (ℵ0), in mathematics, the cardinality of the infinite set of natural numbers {1, 2, 3, …}. The cardinality, or cardinal number, of a set is the number of elements of a set. For example, the number 3 is the cardinality of the set {1, 2, 3} as well as of any set that can be put into a

Liu Xiaobo: …2008 Liu helped draft “Charter 08,” a 19-point program that called for greater political freedoms in China and concluded with the signatures of more than 300 academics and intellectuals. Liu was arrested hours before the document’s release onto the Internet, and, at a trial the following year, he was…

If you’re a regular follower of financial news, you’ve probably seen media reports about a relatively new phenomenon called zero-days-to-expiration (0DTE) options trading. As the name implies, this refers to options traders getting in and out of options positions on the day they expire. At first

Middle Eastern religion: Association of religion with the arts and sciences: The most perfect number was one, for by advancing from zero to one men believed they proceeded from nonexistence to existence. Moreover, all other whole numbers were regarded as multiples of one, representative of the Creator, the Prime Mover, of the universe. The Egyptians called Re “the one One”; the…

books of the Chronicles, two Old Testament books that were originally part of a larger work that included the books of Ezra and Nehemiah. These three (Ezra and Nehemiah were one book in the Jewish canon) were the final books of the Hebrew Bible. Together they survey Israel’s history from Adam to

Big Star: …Big Star’s 1972 debut album, #1 Record. Although the record was subsequently hailed as a masterpiece, it initially sold so poorly that a discouraged Bell left the group. The follow-up, Radio City (1974), included a few Bell songs but was largely driven by Chilton, who pursued a slightly tougher-sounding but…

One Thousand Guineas, one of the five English Classic horse races, run over a straight mile (1.6 km) on the Rowley Mile course at the Newmarket (Suffolk) spring meeting. The race was first run in 1814. It is for three-year-old fillies and is run on the Friday following the Wednesday running of the

tetrachloroethane: The other isomer, 1,1,1,2-tetrachloroethane, has no commercial application.

DDT, a synthetic insecticide that belongs to the family of organic halogen compounds and is highly toxic toward a wide variety of insects as a contact poison that apparently exerts its effects by disorganizing the nervous system. DDT, prepared by the reaction of chloral with chlorobenzene in the

methoxychlor, a largely banned synthetic insecticide. Methoxychlor, a colourless crystalline organic halogen compound, is very similar to DDT but acts more rapidly, is less persistent, and does not accumulate in the fatty tissues of animals as DDT does. Effective against flies, mosquitoes,

trichloroethane: One isomer, 1,1,1-trichloroethane, was used as a solvent for cleaning and degreasing metal and electronic machinery. It was also used as a coolant and in the manufacture of other chemicals and products, including insecticides and household cleaners. It was produced by the reaction of 1,1-dichloroethylene and hydrogen…

tetrachloroethane: One isomer, 1,1,2,2-tetrachloroethane, also called acetylene tetrachloride, is highly toxic. Almost the entire production of the compound is consumed in manufacturing chlorinated solvents, especially trichloroethylene and tetrachloroethylene; it has minor uses as a solvent and as an insecticide, particularly against the greenhouse white fly. It is made…

trichloroethane: …produced by the reaction of 1,1-dichloroethylene and hydrogen chloride.

organohalogen compound: Reactions: to vinyl chloride to yield 1,1-dichloroethane. The product is a geminal dihalide (both halogens are bonded to the same carbon).

vinylidene chloride, a colourless, dense, toxic, volatile, flammable liquid belonging to the family of organic halogen compounds, used principally in combination with vinyl chloride, acrylonitrile, or methyl methacrylate for the manufacture of a class of plastics called saran. Vinylidene chloride

benzene hexachloride (BHC), any of several stereoisomers of 1,2,3,4,5,6-hexachlorocyclohexane formed by the light-induced addition of chlorine to benzene. One of these isomers is an insecticide called lindane, or Gammexane. Benzene hexachloride was first prepared in 1825; the insecticidal

pyrogallol, an organic compound belonging to the phenol family, used as a photographic film developer and in the preparation of other chemicals. Pyrogallol was first obtained in 1786 from gallic acid, obtainable from galls and barks of various trees. It is converted to pyrogallol by heating with

phthalic acid, colourless, crystalline organic compound ordinarily produced and sold in the form of its anhydride. The annual production of phthalic anhydride exceeded 1,000,000 metric tons in the late 20th century; most of it was used as an ingredient of polyesters, including alkyd resins

ethylene bromide (C2H4Br2), a colourless, sweet-smelling, nonflammable, toxic liquid belonging to the family of organohalogen compounds. Ethylene bromide was once used in conjunction with lead-containing antiknock agents as a component of gasoline; however, this use disappeared with the banning of

ethylene chloride (C2H4Cl2), a colourless, toxic, volatile liquid having an odour resembling that of chloroform. It is denser than water, and it is practically insoluble in water. Ethylene chloride is produced by the reaction of ethylene and chlorine. The annual production of ethylene chloride

isomerism: Conformational isomers: …for deuterium atoms to make 1,2-dideuterioethane—isomeric staggered forms become possible. These staggered forms, called “anti” and “gauche,” of 1,2-dideuterioethane are different but are interconverted through rotations around the central carbon-carbon bond and are called “conformational isomers.”

hydrocarbon: Stereoisomerism: Methyl groups in 1,2-dimethylcyclopropane, for example, may be on the same (cis) or opposite (trans) sides of the plane defined by the ring. The resulting two substances are different compounds, each having its own properties such as boiling point (abbreviated bp here):

organosulfur compound: Preparation: …acetylene with sulfur yields a 1,2-dithiete, a four-membered ring compound with two sulfur atoms that exhibits aromatic stability similar to thiophenes. 1,2-Dithiins, six-membered ring disulfides found in thiarubrines, can be prepared by reaction of titanacyclopentadienes (formed in one step from acetylenes) with sulfur monochloride (S2Cl2) or thiocyanogen (SCN)2 and samarium…

ethylene glycol, the simplest member of the glycol family of organic compounds. A glycol is an alcohol with two hydroxyl groups on adjacent carbon atoms (a 1,2-diol). The common name ethylene glycol literally means “the glycol derived from ethylene.” Ethylene glycol is a clear, sweet, slightly

propylene glycol, synthetic organic compound with the chemical formula C3H8O2. Propylene glycol is a colourless liquid that is relatively viscous, has no odour, and tastes slightly sweet. It is hygroscopic, meaning that it readily absorbs water from the surrounding environment. Annual production of

renal system: Nonexcretory functions: …reaching the body tissues; and 1,25-dihydroxycholecalciferol, which is the metabolically active form of vitamin D. Finally, although the kidneys are subject to both nervous and humoral (hormonal) control, they do possess a considerable degree of autonomy; i.e., function continues in an organ isolated from the nervous system but kept alive…

butadiene, either of two aliphatic organic compounds that have the formula C4H6. The term ordinarily signifies the more important of the two, 1,3-butadiene, which is the major constituent of many synthetic rubbers. It was first manufactured in Germany during World War I from acetylene. During World

metabolism: The formation of ATP: …a high-energy phosphate compound—namely, as 1,3-diphosphoglycerate, an anhydride of a carboxylic acid and phosphoric acid. The hydrogen atoms or electrons removed from the aldehyde group during its oxidation are accepted by a coenzyme (so called because it functions in conjunction with an enzyme) involved in hydrogen or electron transfer. The…

organosulfur compound: Reactions: …derivative of the cyclic bis-sulfide 1,3-dithiane, widely used in the synthesis of ketones and aldehydes (the Corey-Seebach reaction, shown below). 1,3-Dithiane and other thioacetals can also be converted to olefins by the Takeda olefination reaction.

hydroquinone, colourless, crystalline organic compound formed by chemical reduction of benzoquinone. See

Herb Elliott: …was world-record holder in the 1,500-metre (metric-mile) race (1958–67) and the mile race (1958–62). As a senior runner, he never lost a mile or a 1,500-metre race.

PCP, hallucinogenic drug with anesthetic properties, having the chemical name 1-(1-phenylcyclohexyl)piperidine. PCP was first developed in 1956 by Parke Davis Laboratories of Detroit for use as an anesthetic in veterinary medicine, though it is no longer used in this capacity. Used for a brief time

antiprotozoal drug: Metronidazole is usually given orally for the treatment of vaginal infections caused by Trichomonas vaginalis, and it is effective in treating bacterial infections caused by anaerobes (organisms that can survive without oxygen). It affects these organisms by causing nicks in, or breakage of, strands of…

amantadine, drug used to treat infections caused by influenza type A virus, the most common cause of influenza epidemics. Amantadine and its derivative, rimantadine, can be used successfully in the prevention and treatment of influenza A; however, these agents have no effect against influenza B

organohalogen compound: Synthesis: …in the following synthesis of 1-bromobutane.

liquid: Partial miscibility: …the solubility (weight percent) of n-butyl alcohol in water is 6.5 percent, whereas that of water in n-butyl alcohol is 22.4 percent. At 127° C, the upper consolute temperature, complete miscibility is attained: above 127° C the two liquids mix in all proportions, but below 127° C they show a…

butene: The isomeric forms are 1-butene, cis-2-butene, trans-2-butene, and isobutylene. All four butenes are gases at room temperature and pressure.

organohalogen compound: Reactions: … to the halogen, as in 1-chloro-4-nitrobenzene:

cetyl alcohol, [CH3(CH2)15OH], a solid organic compound that was one of the first alcohols to be isolated from fats. Cetyl alcohol was discovered in 1817 by the French chemist Michel Chevreul. When he heated a sample of spermaceti (a solid wax formed by the cooling of sperm whale oil) with caustic

parkinsonism: …neurotoxin known as MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine), previously found in contaminated heroin, also causes a form of toxin-induced parkinsonism. The ability of this substance to destroy neurons suggests that an environmental toxin similar to MPTP may be responsible for Parkinson disease. Pugilistic parkinsonism results from head trauma and has affected professional…

stearyl alcohol, waxy solid alcohol formerly obtained from whale or dolphin oil and used as a lubricant and antifoam agent and to retard evaporation of water from reservoirs. It is now manufactured by chemical reduction of stearic

acetophenone (C6H5COCH3), an organic compound used as an ingredient in perfumes and as a chemical intermediate in the manufacture of pharmaceuticals, resins, flavouring agents, and a form of tear gas. It also has been used as a drug to induce sleep. The compound can be synthesized from benzene and

chemical industry: Other alcohols: …is called n-propyl alcohol (or 1-propanol), the other isopropyl alcohol (or 2-propanol).

golden ratio, in mathematics, the irrational number 1 + √ 5 2 , often denoted by the Greek letters ϕ (phi) and sometimes τ (tau). Its value is approximately 1.618. The golden ratio is defined as the proportion in which a line segment is divided into two unequal parts such that the ratio of the

Blake Edwards: Films of the 1970s: …the United States to make 10 (1979), a romantic comedy that became an enormous hit. Dudley Moore was much praised for his deft comic timing in the role of man going through a midlife crisis who becomes smitten with a beautiful younger woman (Bo Derek). Andrews played his patient fiancée.

decimal system: …mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It also requires a dot (decimal point) to represent decimal fractions. In this scheme, the numerals used in denoting a number take different place…

In July 1957 British Prime Minister Harold Macmillan told fellow Conservatives at a rally in Bedford, England, that “most of our people have never had it so good.” The generation of novelists, playwrights, directors, and filmmakers who became known as the “Angry Young Men” couldn’t have disagreed

From frogs that give birth through their mouths to crabs with 6-foot legs, these animals are some of the strangest you’ll hopefully never have to see. list, animals, nightmare, weird, creepy, interesting, strange, crabs, frogs, fish, insects, birds, mammals Besides just looking strange, these crabs

Using algorithms, spreadsheets, statistics, and slide rules, I have determined the best ice hockey players ever. Kidding! I don’t even know what an algorithm is. However, I do know my hockey. So, relying solely on my deeply held opinions, I’ve come up with a very subjective list of the top 10

The 10 novels on this list have it all: suspense, drama, comedy, and, especially, great scenery. Set in lands beautiful, powerful, and ancient and in cities brooding and struggling for modern identity, the books presented here leave readers walking away as though they have just returned from a

They differed in style, skill, innovation, and popularity, and nothing incites more heated debate among classical music scholars and fans than determining which of these composers of Western classical music are the most essential. The three composers that consistently appear in the top spots are

Bradley Cooper: …cast of the horror film 10 Cloverfield Lane.

Going to school is an important part of every child’s life, valuable for learning useful skills such as math and reading and how to live and thrive in society and the wider world. Earlier versions of these questions and answers first appeared in the second edition of The Handy Answer Book for Kids

India’s wildlife includes many vertebrate animals that are among the most threatened forms of life in the world. Some are classified as critically endangered by the International Union for Conservation of Nature (IUCN) and face a high risk of extinction in the wild. Found in diverse ecosystems such

Cyclones are among the most devastating natural phenomena, capable of destroying entire coastal communities and claiming several thousand lives in a single event. They can bring not only violent winds but also torrential rains and massive storm surges, which are created when a storm’s air-pressure

Tropical cyclones in the western North Pacific region around the Philippines, Japan, and China with sustained wind speeds of at least 74 mph (119 km/hr) are called typhoons. When the same phenomenon occurs in the North Atlantic Ocean and the eastern North Pacific, the resulting storm is called a

Everybody knows that big animals can be deadly. Lions, for instance, have sharp teeth and claws and are good at chasing down their prey. Shark Week always comes around and reminds us that although shark attacks aren’t as common as Hollywood would have you think, sharks and their vast quantities of

Godfather of heavy metal, self-proclaimed “Prince of Darkness,” reality TV star, and not-so-secret family man. British singer and musician Ozzy Osbourne died at age 76 on July 22, 2025, leaving behind a legacy as one of the titans of rock and roll. Starting out in the late 1960s with the

As the oldest political party in the United States—and one of the oldest political parties in the world—the Democratic Party has a long history of making history. Its origins trace to 1792, and since then the party has been home to a number of politicians who redefined the political landscape. Read

From delivering powerful critiques of toxic cultural practices to displaying the strength of the human spirit in the face of severe punishment from baneful authoritarians, dystopian novels have served as indispensable teachers to their readers by through propelling them into worryingly plausible

10 Downing Street, address in London of the official office and residence of the prime minister of the United Kingdom and, by extension, the name of the building itself. It has been associated with the prime minister since that office came into being in the 18th century, and it has served as the

When it comes to Native cultures in the Americas, many people may be familiar with powwows, tepees, warbonnets, ceremonial (peace) pipes, and fry bread. What they may not realize is that many everyday items used outside of Indigenous communities can be credited to the ingenuity of the Indigenous

Religious leaders, scientists, and even a hen (or so it seemed) have been making predictions for the end of the world almost as long as the world has been around. They’ve predicted the destruction of the world through floods, fires, and comets—luckily for us, none of it has come to pass. list,

One of the great Renaissance painters, Leonardo da Vinci continually tested artistic traditions and techniques. He created innovative compositions, investigated anatomy to accurately represent the human body, considered the human psyche to illustrate character, and experimented with methods of

Harmless jokers or evil lunatics? While clowns usually aim for laughs, the reaction from many—especially those who suffer from coulrophobia (fear of clowns)—is more like fear. Why? Maybe it’s the masklike makeup. Or because of recent “creepy clown” sightings. One thing’s for sure, clowns seem to

Duels have a long and colorful—though sometimes tragic—history. The origins of dueling are uncertain, but by the 16th century duels had become a popular means of settling real or imagined slights. Despite efforts to ban them, duels remained widespread for several centuries; the last one in France

Learn more about megalodon, the biggest fish that ever lived. Companion, sharks, prehistoric creatures, megalodon, fossils, fish, biggest

Europeans had ventured westward to the New World long before the Taino Indians discovered Christopher Columbus sailing the Caribbean Ocean blue in 1492 around Guanahani (probably San Salvador Island, though maybe another Bahamian island or the Turks and Caicos Islands, depending on which historians

From distraught English majors cramming for a final to aspiring writers trying to figure out new ways to spice up their prose to amateur sitcom critics attempting to describe the comic genius that is Larry David, distinguishing between closely associated literary terms can serve a variety of

Does familiarity breed contempt? It seems to when rivals compete. Stakes are higher and emotions stronger when adversaries have a history. Again and again, the desire to best an old foe has led to electrifying accomplishments (Thomas Edison versus Nikola Tesla), eleventh-hour drama (David Letterman

Ah, the crack of the bat. The smell of fresh-cut grass. Munching on Cracker Jack while trying to avoid being splashed by the massive beer barely clung onto by the inebriated fan sitting behind you. Nothing says summer quite like baseball, the American national pastime. Baseball’s place in the

asteroid: Size and albedo: …km (320 miles), and (10) Hygiea at 410 km (250 miles). Three asteroids are between 300 and 400 km (190 and 250 miles) in diameter, and about 23 are between 200 and 300 km (120 and 190 miles). It has been estimated that 250 asteroids are larger than 100 km…

The history of Spain is written in the architecture of its churches. Here are 10 of the most iconic ones. Earlier versions of the descriptions of these churches first appeared in 1001 Amazing Places You Must See Before You Die, edited by Richard Cavendish (2016). Writers’ names appear in

The question of whether life could have started on Mars has been asked for centuries—but there’s much more to Mars than that. Here are 10 dates that brought new revelations about the Red Planet. list, space, astronomy, science, mars, exploration, life on mars, martians, meteorites, telescopes,

Always an oddity as a planet, Pluto was demoted to dwarf planet in 2006. That fateful day is, however, just one of many notable dates during its brief run as the solar system’s smallest planet. list, astronomy, space exploration, solar system, PlutoIn 1902 astronomer Percival Lowell noted that the

Reader, consider the egg. It can be poached, scrambled, scotched, roasted, hard-boiled, devilled, pickled, and soft-boiled, all by itself. It can be part of a larger whole: a frittata, an omelette, a salad, benedict, with potatoes, bacon, cheese, green peppers, tabasco, paprika, salt, and pepper.

Physicians throughout history have made groundbreaking contributions to medicine, significantly shaping medical practice, knowledge, and understanding. Today that tradition of innovation and compassion to alleviate human suffering is carried on by new generations of physicians, some striving to

The Normandy Invasion was launched on June 6, 1944, with the landing of U.S., British, and Canadian forces on five beaches on the northern coast of France. Even though D-Day is a generic military term for any day on which an operation is to occur, the Normandy Invasion was such an important and

Butterflies are sometimes called “winged jewels” for their vibrant colors and extraordinary beauty, but they are not the only insects worthy of comparison to precious gemstones. There is a diverse array of six-legged species with incredible iridescent exoskeletons or shimmering scales that reflect

You may think you can’t live without your tablet computer and your cordless electric drill, but what about the inventions that came before them? Humans have been innovating since the dawn of time to get us to where we are today. Here are just 10 of the hundreds of inventions that profoundly changed

Dick Francis: … (1995), To the Hilt (1996), 10 Lb. Penalty (1997), Second Wind (1999), Shattered (2000), and Under Orders (2006). Late in life he began coauthoring novels with his son Felix, including Dead Heat (2007), Silks (2008), and Even Money (2009). Hot Money (1987) is considered one of his best works.

People around the world have been dreaming up creatures as part of their legends, folklore, and religious traditions for millennia. There are hundreds—or maybe thousands!—of creatures that have been talked about either with fear or reverence and woven into memorable tales. Here are just a few of

Throughout history outbreaks of disease have reshaped communities, altered political destinies, and advanced medical understanding. Unlike pandemics, which sweep across continents, epidemics are outbreaks that strike within a specific region or population—often with devastating intensity. Epidemics

The turn of the 20th century was a time rife with change, chiefly in the way in which people began to perceive civilization as a whole and its overall goal. The outbreak of World War I, or the supposed War to End All Wars, and the unprecedented devastation that ensued challenged the foundations of

Landing a number-one hit on Billboard magazine’s Hot 100—the premiere pop singles chart in the United States—is by itself a remarkable achievement. A handful of recording artists, however, have managed the feat at least 10 times since the 1950s, when the chart originated. As you might expect, the

Poetry is one of the world’s oldest and most adaptable art forms. A poem can be spoken, sung, read, or performed. It can take the form of a nursery rhyme, an epic, a ghazal, a tanka, a limerick, a film, or even a dance. English poet Samuel Taylor Coleridge defined poetry as “the best words in the

The Ashmolean Museum opened in 1683 at the University of Oxford. Its collection is vastly wide-ranging. This list highlights just 10 of its notable paintings. Earlier versions of the descriptions of these paintings first appeared in 1001 Paintings You Must See Before You Die, edited by Stephen

To some extent, wildfires are a natural part of a healthy forest ecosystem. Blazes can help strip dead organic materials and release nutrients. Some plants even require fire to sprout. But, whether started by abandoned campfires or lightning strikes, fires that reach a high intensity and that

Many people around the world depend on fishes or products made from fishes for their food and economic livelihood. More than 30,000 different species ply Earth’s oceans and bodies of fresh water. The beauty of many fish species is highlighted in fish stores, aquariums, and in home collections. Some

With his signature voice and familiar demeanor, naturalist David Attenborough has been hailed as one of the greatest broadcasters of our time. A passionate environmentalist and educator, Attenborough has inspired and informed viewers all over the globe with his engaging and emotive nature shows and

The National Galleries of Scotland are made up of the Scottish National Gallery, Scottish National Gallery of Modern Art, and Scottish National Portrait Gallery, all in Edinburgh. The museums trace their history back to 1850, when construction began on the National Gallery. The paintings in this

These ten paintings have caused scandals and sparked mysteries—and you can find them only at the Metropolitan Museum of Art in New York City. Start to unravel the complicated histories of Madame X, The Horse Fair, and more in this list. Earlier versions of the descriptions of these paintings first

Ah, Paris the incomparable! For us it’s soaked in romance. Whether you’ve suddenly found yourself with travel brochures in your hand or you prefer to travel from your armchair, Paris is one of those cities with wide open arms. (Cue Maurice Chevalier singing “Paris sera toujours Paris” or Ella

Having a tough time deciding where to go on vacation? Do you want to go someplace with startling natural beauty that isn’t overrun with tourists? Do you want to go somewhere where you won’t need to take a passport or get vaccinations? If you look up in the night sky, you’ll see a few of these

Whether it’s on the pitch, the links, the ice, the courts, or the tracks, women have always excelled at sport, and here we’ve selected 10 of the greatest women athletes of all time. Winnowing it down to 10, of course, is always difficult. Did we miss one of your favorites? This list was adapted

Oh no, it’s a bug! There are many different kinds of insects in many different shapes and sizes. Some frighten people, while others delight them. And some play an important role in helping people get healthy. This list will help you gain a greater understanding of bugs. Earlier versions of these

Richard Fleischer: Later work: …and found box-office success with 10 Rillington Place (1971), a pseudodocumentary about the John Reginald Christie–Timothy Evans murder case that shocked England in the 1940s; Richard Attenborough starred as the mass murderer, and John Hurt played the simpleminded man framed for one of the killings and hanged. In 1971 Fleischer…

There’s this musical that’s been getting some attention lately, Hamilton. Maybe you’ve heard of it. The show and its creator, Lin-Manuel Miranda, cleaned house at the 2016 Tony Awards by marrying hip-hop and Broadway in previously unimaginable ways, infusing blind casting with new meaning, making

Soccer, basketball, baseball, and the like are popular all around the world. Yawn. Looking for something a bit different? This list explains 10 unusual sports that you may or may not have heard of. These unusual sports are often violent, painful, or both. Some of them are takes on other sports,