Jesus

Jesus (c. 4 BC – AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other names and titles), was a first-century Jewish preacher and religious leader; he is the central figure of Christianity, the world's largest religion. 　Most Christians believe he is the incarnation of God the Son and the awaited Messiah (the Christ) prophesied in the Hebrew Bible. 　Virtually all modern scholars of antiquity agree that Jesus existed historically. 　Research into the historical Jesus has yielded some uncertainty on the historical reliability of the Gospels and on how closely the Jesus portrayed in the New Testament reflects the historical Jesus, as the only detailed records of Jesus' life are contained in the Gospels. 　Jesus was a Galilean Jew who was circumcised, was baptized by John the Baptist, began his own ministry, and was often referred to as "rabbi". 　Jesus debated with fellow Jews on how to best follow God, engaged in healings, taught in parables, and gathered followers. 　He was arrested and tried by the Jewish authorities, turned over to the Roman government, and crucified on the order of Pontius Pilate, the Roman prefect of Jerusalem. 　After his death, his followers believed he rose from the dead, and the community they formed eventually became the early Christian Church. 　Accounts of his teachings and life were initially conserved by oral transmission, which was the source of the written Gospels. 　Christian theology includes the beliefs that Jesus was conceived by the Holy Spirit, was born of a virgin named Mary, performed miracles, founded the Christian Church, died by crucifixion as a sacrifice to achieve atonement for sin, rose from the dead, and ascended into Heaven, from where he will return. 　Commonly, Christians believe Jesus enables people to be reconciled to God. 　The Nicene Creed asserts that Jesus will judge the living and the dead, either before or after their bodily resurrection, an event tied to the Second Coming of Jesus in Christian eschatology. 　The great majority of Christians worship Jesus as the incarnation of God the Son, the second of three persons of the Trinity; there is a small minority of Christian denominations that reject trinitarianism, wholly or partly, as non-scriptural. 　The birth of Jesus is celebrated annually on 25 December as Christmas. 　His crucifixion is honored on Good Friday and his resurrection on Easter Sunday. 　The world's most widely used calendar era—in which the current year is AD 2023 (or 2023 CE)—is based on the approximate birthdate of Jesus. 　Jesus is also revered in Baha'i faith, Druze faith, Islam and Manichaeism. 　In Islam, Jesus (often referred to by his Quranic name ʿĪsā) is considered the penultimate prophet of God and the messiah, who will return before the Day of Judgement. 　Muslims believe Jesus was born of the virgin Mary but was neither God nor a son of God. 　Most Muslims do not believe that he was killed or crucified but that God raised him into Heaven while he was still alive. 　In contrast, Judaism rejects the belief that Jesus was the awaited messiah, arguing that he did not fulfill messianic prophecies, and was neither divine nor resurrected.

Magic

Look up Magic, magic, magically, magick, or majick in Wiktionary, the free dictionary. 　Magic or Magick most commonly refers to: Magic (supernatural), beliefs and actions employed to influence supernatural beings and forces Ceremonial magic, encompasses a wide variety of rituals of magic Magical thinking, the belief that unrelated events are causally connected, particularly as a result of supernatural effects Magic (illusion), the art of appearing to perform supernatural feats Magic(k) may also refer to:

Magic (game terminology)

Magic or mana is an attribute assigned to characters within a role-playing or video game that indicates their power to use special magical abilities or "spells". 　Magic is usually measured in magic points or mana points, shortened as MP. 　Different abilities will use up different amounts of MP. 　When the MP of a character reaches zero, the character will not be able to use special abilities until some of their MP is recovered. 　Much like health, magic might be displayed as a numeric value, such as "50/100". 　Here, the first number indicates the current amount of MP a character has whereas the second number indicates the character's maximum MP. 　In video games, magic can also be displayed visually, such as with a gauge that empties itself as a character uses their abilities.　[self-published source?]

Revolution

In political science, a revolution (Latin: revolutio, 'a turn around') is a fundamental and relatively sudden change in political power and political organization which occurs when the population revolts against the government, typically due to perceived oppression (political, social, economic) or political incompetence. 　Revolutions have occurred throughout human history and vary widely in terms of methods, duration, and motivating ideology. 　Their results include major changes in culture, economy, and socio-political institutions, usually in response to perceived overwhelming autocracy or plutocracy. 　Scholarly debates about what does and does not constitute a revolution center on several issues. 　Early studies of revolutions primarily analyzed events in European history from a psychological perspective, but more modern examinations include global events and incorporate perspectives from several social sciences, including sociology and political science. 　Several generations of scholarly thought on revolutions have generated many competing theories and contributed much to the current understanding of this complex phenomenon. 　Notable revolutions in recent centuries include the creation of the United States through the American Revolutionary War (1775–1783), the French Revolution (1789–1799), the Haitian Revolution (1791–1804), the Spanish American wars of independence (1808–1826), the European Revolutions of 1848, the Russian Revolution in 1917, the Chinese Revolution of the 1940s, the Cuban Revolution in 1959, the Iranian Revolution in 1979, and the European Revolutions of 1989.

Drug

A drug is any chemical substance that causes a change in an organism's physiology or psychology when consumed. 　Drugs are typically distinguished from food and substances that provide nutritional support. 　Consumption of drugs can be via inhalation, injection, smoking, ingestion, absorption via a patch on the skin, suppository, or dissolution under the tongue. 　In pharmacology, a drug is a chemical substance, typically of known structure, which, when administered to a living organism, produces a biological effect. 　A pharmaceutical drug, also called a medication or medicine, is a chemical substance used to treat, cure, prevent, or diagnose a disease or to promote well-being. 　Traditionally drugs were obtained through extraction from medicinal plants, but more recently also by organic synthesis. 　Pharmaceutical drugs may be used for a limited duration, or on a regular basis for chronic disorders. 　Pharmaceutical drugs are often classified into drug classes—groups of related drugs that have similar chemical structures, the same mechanism of action (binding to the same biological target), a related mode of action, and that are used to treat the same disease. 　The Anatomical Therapeutic Chemical Classification System (ATC), the most widely used drug classification system, assigns drugs a unique ATC code, which is an alphanumeric code that assigns it to specific drug classes within the ATC system. 　Another major classification system is the Biopharmaceutics Classification System. 　This classifies drugs according to their solubility and permeability or absorption properties. 　Psychoactive drugs are chemical substances that affect the function of the central nervous system, altering perception, mood or consciousness. 　These drugs are divided into different groups like: stimulants, depressants, antidepressants, anxiolytics, antipsychotics, and hallucinogens. 　These psychoactive drugs have been proven useful in treating wide range of medical conditions including mental disorders around the world. 　The most widely used drugs in the world include caffeine, nicotine and alcohol, which are also considered recreational drugs, since they are used for pleasure rather than medicinal purposes. 　All drugs can have potential side effects. 　Abuse of several psychoactive drugs can cause addiction and/or physical dependence. 　Excessive use of stimulants can promote stimulant psychosis. 　Many recreational drugs are illicit and international treaties such as the Single Convention on Narcotic Drugs exist for the purpose of their prohibition.

Driving

Driving is the controlled operation and movement of a vehicle, including cars, motorcycles, trucks, buses, and bicycles. 　Permission to drive on public highways is granted based on a set of conditions being met and drivers are required to follow the established road and traffic laws in the location they are driving. 　The word driving, has etymology dating back to the 15th century and has developed as what driving has encompassed has changed from working animals in the 15th to automobiles in the 1800s. 　Driving skills have also developed since the 15th century with physical, mental and safety skills being required to drive. 　This evolution of the skills required to drive have been accompanied by the introduction of driving laws which relate to not only the driver but the driveability of a car.

Importance

Importance is a property of entities that matter or make a difference. 　For example, World War II was an important event and Albert Einstein was an important person because of how they affected the world. 　There are disagreements in the academic literature about what type of difference is required. 　According to the causal impact view, something is important if it has a big causal impact on the world. 　This view is rejected by various theorists, who insist that an additional aspect is required: that the impact in question makes a value difference. 　This is often understood in terms of how the important thing affects the well-being of people. 　So on this view, World War II was important, not just because it brought about many wide-ranging changes but because these changes had severe negative impacts on the well-being of the people involved. 　The difference in question is usually understood counterfactually as the contrast between how the world actually is and how the world would have been without the existence of the important entity. 　It is often argued that importance claims are context- or domain-dependent. 　This means that they either explicitly or implicitly assume a certain domain in relation to which something matters. 　For example, studying for an exam is important in the context of academic success but not in the context of world history. 　Importance comes in degrees: to be important usually means to matter more within the domain in question than most of the other entities within this domain. 　The term "importance" is often used in overlapping ways with various related terms, such as "meaningfulness", "value", and "caring". 　Theorists frequently try to elucidate these terms by comparing them to show what they have in common and how they differ. 　A meaningful life is usually also important in some sense. 　But meaningfulness has additional requirements: the life should be guided by the agent's intention and directed at realizing some form of higher purpose. 　In some contexts, to say that something is important means the same as saying that it is valuable. 　More generally, however, importance refers not to value itself but to a value difference. 　This difference may also be negative: some events are important because they have very bad consequences. 　Importance is often treated as an objective feature in contrast to the subjective attitude of caring about something or ascribing importance to it. 　Ideally, the two overlap: people subjectively care about things that are objectively important. 　Nonetheless, the two may come apart when people care about unimportant things or fail to care about important things. 　Some theorists distinguish between instrumental importance relative to a specific goal in contrast to a form of importance based on intrinsic or final value. 　A closely related distinction is between importance relative to someone and absolute or unrestricted importance. 　The concept of importance is central to numerous fields and issues. 　Many people desire to be important or to lead an important life. 　It has been argued that this is not always a good goal since it can also be realized in a negative way: by causing a lot of harm and thereby making an important but negative value difference. 　Common desires that are closely related include wanting power, wealth, and fame. 　In the realm of ethics, the importance of something often determines how one should act towards this thing, for example, by paying attention to it or by protecting it. 　In this regard, importance is a normative property, meaning that importance claims constitute reasons for actions, emotions, and other attitudes. 　On a psychological level, considerations of the relative importance of the aspects of a situation help the individual simplify its complexity by only focusing on its most significant features. 　A central discussion in the context of the meaning of life concerns the question of whether human life is important on the cosmic level. 　Nihilists and absurdists usually give a negative response to this question. 　This pessimistic outlook can in some cases cause an existential crisis. 　In the field of artificial intelligence, implementing artificial reasoning to assess the importance of information poses a significant challenge when trying to deal with the complexity of real-world situations.

Berlin

Berlin (/bɜːrˈlɪn/ bur-LIN, German: [bɛɐ̯ˈliːn] (listen)) is the capital and largest city of Germany by both area and population. 　Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. 　One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. 　Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. 　The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. 　Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. 　Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. 　Due to its location in the European Plain, Berlin is influenced by a temperate seasonal climate. 　About one-third of the city's area is composed of forests, parks, gardens, rivers, canals, and lakes. 　The city lies in the Central German dialect area, the Berlin dialect being a variant of the Lusatian-New Marchian dialects. 　First documented in the 13th century and at the crossing of two important historic trade routes, Berlin became the capital of the Margraviate of Brandenburg (1417–1701), Kingdom of Prussia (1701–1918), German Empire (1871–1918), Weimar Republic (1919–1933), and Nazi Germany (1933–1945). 　Berlin has served as a scientific, artistic and philosophical hub of the Enlightenment, Neoclassicism, and liberal revolution. 　The Gründerzeitcode: deu promoted to code: de era's industrialization-induced economic boom multiplied Berlin's population rapidly. 　Berlin in the roaring 1920s was the third-largest city in the world by population. 　After World War II and its subsequent occupation by the victorious countries, the devastated city was divided; West Berlin became a de facto exclave of West Germany, surrounded by the Berlin Wall (from August 1961 to November 1989) and East German territory. 　East Berlin was declared capital of East Germany, while Bonn became the West German capital. 　Following German reunification in 1990, Berlin once again became the capital of all of Germany. 　Berlin is a world city of culture, politics, media and science. 　Its economy is based on high-tech firms and the service sector, encompassing a diverse range of creative industries, startup companies, research facilities, media corporations, and convention venues. 　Berlin serves as a continental hub for air and rail traffic and has a highly complex public transportation network. 　The metropolis is a popular tourist destination. 　Significant industries also include information technology, healthcare, biomedical engineering, biotechnology, automotive, construction, electronics, social economy and clean tech. 　Berlin is home to world-renowned universities such as the Humboldt University, Technical University, Free University, University of the Arts, ESMT Berlin, Hertie School, and Bard College Berlin. 　Its Zoological Garden is the most visited zoo in Europe and one of the most popular worldwide. 　With Babelsberg being the world's first large-scale movie studio complex, Berlin is an increasingly popular location for international film productions. 　The city is well known for its festivals, diverse architecture, nightlife, contemporary arts, and a very high quality of life. 　Berlin is also home to three World Heritage Sites: Museum Island; the Palaces and Parks of Potsdam and Berlin; and the Modernism Housing Estates. 　Other landmarks include the Brandenburg Gate, Reichstag building, Potsdamer Platz, Memorial to the Murdered Jews of Europe, Berlin Wall Memorial, East Side Gallery, Berlin Victory Column, Berlin Cathedral, and Berlin Television Tower, the tallest structure in Germany. 　Berlin has numerous museums, galleries, libraries, orchestras, and sporting events including Museum Island, the German Historical Museum, Jewish Museum, Natural History Museum, State Library, State Opera, Philharmonic, and the Berlin Marathon.

Silence

Silence is the absence of ambient audible sound, the emission of sounds of such low intensity that they do not draw attention to themselves, or the state of having ceased to produce sounds; this latter sense can be extended to apply to the cessation or absence of any form of communication, whether through speech or other medium. 　Sometimes speakers fall silent when they hesitate in searching for a word, or interrupt themselves before correcting themselves. 　Discourse analysis shows that people use brief silences to mark the boundaries of prosodic units, in turn-taking, or as reactive tokens, for example, as a sign of displeasure, disagreement, embarrassment, desire to think, confusion, and the like. 　Relatively prolonged intervals of silence can be used in rituals; in some religious disciplines, people maintain silence for protracted periods, or even for the rest of their lives, as an ascetic means of spiritual transformation.

Apart

Look up apart in Wiktionary, the free dictionary. 　Apart may refer to "Apart" (The Cure song), by The Cure on their 1992 album Wish Apart (album) (1995), by Paul Schütze "Apart" (Brandy song), by Brandy on her 2002 album Full Moon Apart (2011 film), an American drama Apart (2021 film), a documentary film Apart (EP), 2018 EP by Scarlett Johansson Apart (Léon album), 2020 album by Swedish singer Léon

Politics

Politics (from Greek: Πολιτικά, politiká, 'affairs of the cities') is the set of activities that are associated with making decisions in groups, or other forms of power relations among individuals, such as the distribution of resources or status. 　The branch of social science that studies politics and government is referred to as political science. 　It may be used positively in the context of a "political solution" which is compromising and nonviolent, or descriptively as "the art or science of government", but also often carries a negative connotation. 　The concept has been defined in various ways, and different approaches have fundamentally differing views on whether it should be used extensively or limitedly, empirically or normatively, and on whether conflict or co-operation is more essential to it. 　A variety of methods are deployed in politics, which include promoting one's own political views among people, negotiation with other political subjects, making laws, and exercising internal and external force, including warfare against adversaries. 　Politics is exercised on a wide range of social levels, from clans and tribes of traditional societies, through modern local governments, companies and institutions up to sovereign states, to the international level. 　In modern nation states, people often form political parties to represent their ideas. 　Members of a party often agree to take the same position on many issues and agree to support the same changes to law and the same leaders. 　An election is usually a competition between different parties. 　A political system is a framework which defines acceptable political methods within a society. 　The history of political thought can be traced back to early antiquity, with seminal works such as Plato's Republic, Aristotle's Politics, Confucius's political manuscripts and Chanakya's Arthashastra.

Comedy

Comedy is a genre of fiction that consists of discourses or works intended to be humorous or amusing by inducing laughter, especially in theatre, film, stand-up comedy, television, radio, books, or any other entertainment medium. 　The term originated in ancient Greece: In Athenian democracy, the public opinion of voters was influenced by political satire performed by comic poets in theaters. 　The theatrical genre of Greek comedy can be described as a dramatic performance pitting two groups, ages, genders, or societies against each other in an amusing agon or conflict. 　Northrop Frye depicted these two opposing sides as a "Society of Youth" and a "Society of the Old". 　A revised view characterizes the essential agon of comedy as a struggle between a relatively powerless youth and the societal conventions posing obstacles to his hopes. 　In this struggle, the youth then becomes constrained by his lack of social authority, and is left with little choice but to resort to ruses which engender dramatic irony, which provokes laughter. 　Satire and political satire use comedy to portray people or social institutions as ridiculous or corrupt, thus alienating their audience from the object of their humor. 　Parody subverts popular genres and forms, critiquing those forms without necessarily condemning them. 　Other forms of comedy include screwball comedy, which derives its humor largely from bizarre, surprising (and improbable) situations or characters, and black comedy, which is characterized by a form of humor that includes darker aspects of human behavior or human nature. 　Similarly scatological humor, sexual humor, and race humor create comedy by violating social conventions or taboos in comic ways, which can often be taken as offensive by the subjects of said joke. 　A comedy of manners typically takes as its subject a particular part of society (usually upper-class society) and uses humor to parody or satirize the behavior and mannerisms of its members. 　Romantic comedy is a popular genre that depicts burgeoning romance in humorous terms and focuses on the foibles of those who are falling in love.

Tears

Tears are a clear liquid secreted by the lacrimal glands (tear gland) found in the eyes of all land mammals. 　Tears are made up of water, electrolytes, proteins, lipids, and mucins that form layers on the surface of eyes. 　The different types of tears—basal, reflex, and emotional—vary significantly in composition. 　The functions of tears include lubricating the eyes (basal tears), removing irritants (reflex tears), and also aiding the immune system. 　Tears also occur as a part of the body's natural pain response. 　Emotional secretion of tears may serve a biological function by excreting stress-inducing hormones built up through times of emotional distress. 　Tears have symbolic significance among humans.

Massachusetts

Massachusetts (/ˌmæsəˈtʃuːsɪts/ (listen), /-zɪts/); Massachusett: Muhsachuweesut /məhswatʃəwiːsət/), officially the Commonwealth of Massachusetts, is the most populous state in the New England region of the Northeastern United States. 　It borders on the Atlantic Ocean and Gulf of Maine to the east, Connecticut and Rhode Island to the south, New Hampshire and Vermont to the north, and New York to the west. 　Massachusetts is the 6th smallest state by land area but is the 15th most populous state and the 3rd most densely populated, after New Jersey and Rhode Island. 　The state's capital and most populous city, as well as its cultural and financial center, is Boston. 　Massachusetts is also home to the urban core of Greater Boston, the largest metropolitan area in New England and a region profoundly influential upon American history, academia, and the research economy. 　Originally dependent on agriculture, fishing, and trade. 　Massachusetts was transformed into a manufacturing center during the Industrial Revolution. 　During the 20th century, Massachusetts's economy shifted from manufacturing to services. 　Modern Massachusetts is a global leader in biotechnology, engineering, higher education, finance, and maritime trade. 　Massachusetts was a site of early English colonization: the Plymouth Colony was founded in 1620 by the Pilgrims of the Mayflower, and in 1630 the Massachusetts Bay Colony, taking its name from the indigenous Massachusett people, established settlements in Boston and Salem. 　In 1692, the town of Salem and surrounding areas experienced one of America's most infamous cases of mass hysteria, the Salem witch trials. 　In 1777, General Henry Knox founded the Springfield Armory, which, during the Industrial Revolution, catalyzed numerous important technological advances, including interchangeable parts. 　In 1786, Shays' Rebellion, a populist revolt led by disaffected American Revolutionary War veterans, influenced the United States Constitutional Convention. 　In the 18th century, the Protestant First Great Awakening, which swept Britain and the Thirteen Colonies, originated from the pulpit of Northampton preacher Jonathan Edwards. 　In the late 18th century, Boston became known as the "Cradle of Liberty" for the agitation there that later led to the American Revolution. 　Massachusetts has played a powerful scientific, commercial, and cultural role in the history of the United States. 　Before the American Civil War, Massachusetts was a center for the abolitionist, temperance, and transcendentalist movements. 　In the late 19th century, the sports of basketball and volleyball were invented in the western Massachusetts cities of Springfield and Holyoke, respectively. 　Massachusetts became the first U.S. state to legally recognize same-sex marriage as a result of the Massachusetts Supreme Judicial Court's decision in Goodridge v. Department of Public Health in 2004, and Boston is considered a hub of LGBT culture and LGBT activism in the United States. 　Prominent American political dynasties have hailed from the state, including the Adams and Kennedy families. 　Harvard University in Cambridge is the oldest institution of higher learning in the United States, with the largest financial endowment of any university. 　The university has educated eight Presidents of the United States while Harvard Law School has educated a contemporaneous majority of Justices of the Supreme Court of the United States. 　Kendall Square in Cambridge has been called "the most innovative square mile on the planet", in reference to the high concentration of entrepreneurial start-ups and quality of innovation which have emerged in the vicinity of the square since 2010. 　Both Harvard and MIT, also in Cambridge, are perennially ranked as either the most or among the most highly regarded academic institutions in the world. 　The state's public-school students place among the top tier in the world in academic performance. 　Massachusetts has been ranked as one of the top states in the United States for citizens to live in, as well as one of the most expensive. 　Massachusetts is one of the most educated, developed, and wealthiest states, ranking 1st in percentage of population 25 and over with a bachelor's degree and 1st in percentage of population 25 and over with an advanced degree, 1st on both the American Human Development Index and the standard Human Development Index, 1st in per capita income and 2nd in median household income.

Achieved

Achieved (13 May 1979 – 1993) was an Irish Thoroughbred racehorse and sire. 　He won four of his nine races in a track career which lasted from July 1981 to September 1982. 　As a two-year-old he was undefeated in three starts including the Phoenix Stakes and the Champagne Stakes and was rated the best horse of his generation in Ireland. 　In the following year he won the Tetrarch Stakes and later finished third in both the Sussex Stakes and the Queen Elizabeth II Stakes. 　He was retired at the end of the year to become a breeding stallion but had no success as a sire of winners.

Passing (sociology)

Passing is the ability of a person to be regarded as a member of an identity group or category, such as racial identity, ethnicity, caste, social class, sexual orientation, gender, religion, age and/or disability status, that is often different from their own. 　Passing may be used to increase social acceptance in order to cope with stigma by removing stigma from the presented self and could result in other social benefits as well. 　Thus, passing may serve as a form of self-preservation or self-protection in instances where expressing one's true or prior identity may be dangerous. 　Passing may require acceptance into a community and may also lead to temporary or permanent leave from another community to which an individual previously belonged. 　Thus, passing can result in separation from one's original self, family, friends, or previous living experiences. 　While successful passing may contribute to economic security, safety, and avoidance of stigma, it may take an emotional toll as a result of denial of one's previous identity and may lead to depression or self-loathing. 　When an individual deliberately attempts to 'pass' as a member of an identity group, they may actively engage in performance of behaviors they believe to be associated with membership of that group. 　Passing practices can also include information management where the passer attempts to control or conceal any stigmatizing information that may reveal disparity from their presumed identity. 　Etymologically, the term is simply the nominalisation of the verb pass in its phrasal use with for or as, as in a counterfeit passing for the genuine article or an impostor passing as another person. 　It has been in popular use since at least the late 1920s.

Spectrum (topology)

In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. 　Every such cohomology theory is representable, as follows from Brown's representability theorem. 　This means that, given a cohomology theory E ∗ : CW o p → Ab {\displaystyle {\mathcal {E}}^{*}:{\text{CW}}^{op}\to {\text{Ab}}} , there exist spaces E k {\displaystyle E^{k}} such that evaluating the cohomology theory in degree k {\displaystyle k} on a space X {\displaystyle X} is equivalent to computing the homotopy classes of maps to the space E k {\displaystyle E^{k}} , that is E k ( X ) ≅ [ X , E k ] {\displaystyle {\mathcal {E}}^{k}(X)\cong \left[X,E^{k}\right]} . 　Note there are several different categories of spectra leading to many technical difficulties, but they all determine the same homotopy category, known as the stable homotopy category. 　This is one of the key points for introducing spectra because they form a natural home for stable homotopy theory.

Spectrum

A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. 　The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. 　As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. 　It thereby became a mapping of a range of magnitudes (wavelengths) to a range of qualities, which are the perceived "colors of the rainbow" and other properties which correspond to wavelengths that lie outside of the visible light spectrum. 　Spectrum has since been applied by analogy to topics outside optics. 　Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". 　In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. 　Such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. 　Nonscientific uses of the term spectrum are sometimes misleading. 　For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. 　Political scientists use a variety of biaxial and multiaxial systems to more accurately characterize political opinion. 　In most modern usages of spectrum there is a unifying theme between the extremes at either end. 　This was not always true in older usage.

Census

A census is the procedure of systematically acquiring, recording and calculating population information about the members of a given population. 　This term is used mostly in connection with national population and housing censuses; other common censuses include censuses of agriculture, traditional culture, business, supplies, and traffic censuses. 　The United Nations (UN) defines the essential features of population and housing censuses as "individual enumeration, universality within a defined territory, simultaneity and defined periodicity", and recommends that population censuses be taken at least every ten years. 　UN recommendations also cover census topics to be collected, official definitions, classifications and other useful information to co-ordinate international practices. 　The UN's Food and Agriculture Organization (FAO), in turn, defines the census of agriculture as "a statistical operation for collecting, processing and disseminating data on the structure of agriculture, covering the whole or a significant part of a country." "In a census of agriculture, data are collected at the holding level." 　The word is of Latin origin: during the Roman Republic, the census was a list that kept track of all adult males fit for military service. 　The modern census is essential to international comparisons of any kind of statistics, and censuses collect data on many attributes of a population, not just how many people there are. 　Censuses typically began as the only method of collecting national demographic data and are now part of a larger system of different surveys. 　Although population estimates remain an important function of a census, including exactly the geographic distribution of the population or the agricultural population, statistics can be produced about combinations of attributes, e.g., education by age and sex in different regions. 　Current administrative data systems allow for other approaches to enumeration with the same level of detail but raise concerns about privacy and the possibility of biasing estimates. 　A census can be contrasted with sampling in which information is obtained only from a subset of a population; typically, main population estimates are updated by such intercensal estimates. 　Modern census data are commonly used for research, business marketing, and planning, and as a baseline for designing sample surveys by providing a sampling frame such as an address register. 　Census counts are necessary to adjust samples to be representative of a population by weighting them as is common in opinion polling. 　Similarly, stratification requires knowledge of the relative sizes of different population strata, which can be derived from census enumerations. 　In some countries, the census provides the official counts used to apportion the number of elected representatives to regions (sometimes controversially – e.g., Utah v. Evans). 　In many cases, a carefully chosen random sample can provide more accurate information than attempts to get a population census.

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. 　Like a set, it contains members (also called elements, or terms). 　The number of elements (possibly infinite) is called the length of the sequence. 　Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. 　Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. 　The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set. 　For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. 　This sequence differs from (A, R, M, Y). 　Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. 　Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6, ...). 　The position of an element in a sequence is its rank or index; it is the natural number for which the element is the image. 　The first element has index 0 or 1, depending on the context or a specific convention. 　In mathematical analysis, a sequence is often denoted by letters in the form of a n {\displaystyle a_{n}} , b n {\displaystyle b_{n}} and c n {\displaystyle c_{n}} , where the subscript n refers to the nth element of the sequence; for example, the nth element of the Fibonacci sequence F {\displaystyle F} is generally denoted as F n {\displaystyle F_{n}} . 　In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memory; infinite sequences are called streams. 　The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.

Del

Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. 　When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus. 　When applied to a field (a function defined on a multi-dimensional domain), it may denote any one of three operators depending on the way it is applied: the gradient or (locally) steepest slope of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations); the divergence of a vector field; or the curl (rotation) of a vector field. 　Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators that makes many equations easier to write and remember. 　The del symbol (or nabla) can be interpreted as a vector of partial derivative operators; and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, a dot product, and a cross product, respectively, of the "del operator" with the field. 　These formal products do not necessarily commute with other operators or products. 　These three uses, detailed below, are summarized as: Gradient: grad ⁡ f = ∇ f {\displaystyle \operatorname {grad} f=\nabla f} Divergence: div ⁡ v → = ∇ ⋅ v → {\displaystyle \operatorname {div} {\vec {v}}=\nabla \cdot {\vec {v}}} Curl: curl ⁡ v → = ∇ × v → {\displaystyle \operatorname {curl} {\vec {v}}=\nabla \times {\vec {v}}}

Yard

The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. 　Since 1959 it has been by international agreement standardized as exactly 0.9144 meter. 　A distance of 1,760 yards is equal to 1 mile. 　The US survey yard is very slightly longer.

Duty

A duty (from "due" meaning "that which is owing"; Old French: deu, did, past participle of devoir; Latin: debere, debitum, whence "debt") is a commitment or expectation to perform some action in general or if certain circumstances arise. 　A duty may arise from a system of ethics or morality, especially in an honor culture. 　Many duties are created by law, sometimes including a codified punishment or liability for non-performance. 　Performing one's duty may require some sacrifice of self-interest. 　Cicero, an early Roman philosopher who discusses duty in his work “On Duty", suggests that duties can come from four different sources: as a result of being a human as a result of one's particular place in life (one's family, one's country, one's job) as a result of one's character as a result of one's own moral expectations for oneself The specific duties imposed by law or culture vary considerably, depending on jurisdiction, religion, and social normalities.

Interior (topology)

In mathematics, specifically in topology, the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions. 　The exterior of a set S is the complement of the closure of S; it consists of the points that are in neither the set nor its boundary. 　The interior, boundary, and exterior of a subset together partition the whole space into three blocks (or fewer when one or more of these is empty).