The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a real or complex number a is the power series f ( a ) + f ′ ( a ) 1 ! ( x − a ) + f ″ ( a ) 2 ! ( x − a ) 2 + f ‴ ( a ) 3 ! ( x − a ) 3 + ⋯ , {\displaystyle f(a)+{\frac {f'(a)}{1!}}(x-a)+{\frac {f''(a)}{2!}}(x-a)^{2}+{\frac {f'''(a)}{3!}}(x-a)^{3}+\cdots ,}

Lexical (semiotics) or content word, words referring to things, as opposed to having only grammatical meaning

The hierarchical structure of semantic fields can be mostly seen in hyponymy.

A hyponym is a word or phrase whose semantic field is more specific than its hypernym.

A hyponym refers to a type. A meronym refers to a part. For example, a hyponym of tree is pine tree or oak tree (a type of tree), but a meronym of tree is bark or leaf (a part of tree).

faithful functor

Intuitively, a subcategory of C is a category obtained from C by "removing" some of its objects and arrows.

is the vocabulary of a language or branch of knowledge (such as nautical or medical)

The lexicon of a language is its vocabulary. Lexicon is also a synonym for a dictionary or encyclopedic dictionary

Windshield phenomenon

In a broader sense, taxonomy also applies to relationship schemes other than parent-child hierarchies, such as network structures. Taxonomies may then include a single child with multi-parents, for example, "Car" might appear with both parents "Vehicle" and "Steel Mechanisms"

Taxonomies are often represented as is-a hierarchies where each level is more specific (in mathematical language "a subset of") the level above it. For example, a basic biology taxonomy would have concepts such as mammal, which is a subset of animal, and dogs and cats, which are subsets of mammal. This kind of taxonomy is called an is-a model because the specific objects are considered as instances of a concept. For example, Fido is-an instance of the concept dog and Fluffy is-a cat.

Mutually exclusive categories can be beneficial. If categories appear several places, it's called cross-listing or polyhierarchical. The hierarchy will lose its value if cross-listing appears too often. Cross-listing often appears when working with ambiguous categories that fits more than one place.

Researchers reported that large populations consistently develop highly similar category systems. This may be relevant to lexical aspects of large communication networks and cultures such as folksonomies and language or human communication, and sense-making in general.

In the simple biology example, dog is a hypernym and Fido is one of its hyponyms. A word can be both a hyponym and a hypernym. For example, dog is a hyponym of mammal and also a hypernym of Fido.

words that are examples of categories are hyponyms

Two of the predominant types of relationships in knowledge-representation systems are predication and the universally quantified conditional.

Mathematically, a hierarchical taxonomy is a tree structure of classifications for a given set of objects.

Taxonomy is different from meronomy, which is dealing with the categorisation of parts of a whole.

Tree (data structure)

Tree structure

In computer science, a tree is a widely used abstract data type that simulates a hierarchical tree structure

Not to be confused with tree (graph theory), a specific type of mathematical object.

Not to be confused with trie, a specific type of tree data structure. Not to be confused with tree (graph theory), a specific type of mathematical object.

graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects

A semantic class contains words that share a semantic feature.

For example within nouns there are two sub classes, concrete nouns and abstract nouns.

The concrete nouns include people, plants, animals, materials and objects while the abstract nouns refer to concepts such as qualities, actions, and processes.

Semantic classes may intersect. The intersection of female and young can be girl.

Model theory recognizes and is intimately concerned with a duality: it examines semantical elements (meaning and truth) by means of syntactical elements (formulas and proofs) of a corresponding language

Roughly speaking, a category may be thought of as a type theory shorn of its syntax.

In fact categories can themselves be viewed as type theories of a certain kind

Some types exist as descriptions of objects, but not as tangible physical objects. One can show someone a particular bicycle, but cannot show someone, explicitly, the type "bicycle", as in "the bicycle is popular."

Property types (e.g. "height in metres" or "thorny") are often understood ontologically as concepts. Property instances (e.g. height = 1.74) are sometimes understood as measured values, and sometimes understood as sensations or observations of reality.

The words type, concept, property, quality, feature and attribute (all used in describing things) tend to be used with different verbs. E.g. Suppose a rose bush is defined as a plant that is "thorny", "flowering" and "bushy". You might say a rose bush instantiates these three types, or embodies these three concepts, or exhibits these three properties, or possesses these three qualities, features or attributes.

The distinction in computer programming between classes and objects is related, though in this context, "class" sometimes refers to a set of objects (with class-level attribute or operations) rather than a description of an object in the set, as "type" would.

The distinction is important in disciplines such as logic, linguistics, metalogic, typography, and computer programming.

The sentence "they drive the same car" is ambiguous. Do they drive the same type of car (the same model) or the same instance of a car type (a single vehicle)?

A semantic similarity network (SSN) is a special form of semantic network.[1] designed to represent concepts and their semantic similarity. Its main contribution is reducing the complexity of calculating semantic distances.

There is obvious connections between the flow paths of a use case and its test cases. Deriving functional test cases from a use case through its scenarios (running instances of a use case) is straightforward.

With content based upon an action or event flow structure, a model of well-written use cases also serves as an excellent groundwork and valuable guidelines for the design of test cases

Originally he had used the terms usage scenarios and usage case – the latter a direct translation of his Swedish term användningsfall – but found that neither of these terms sounded natural in English, and eventually he settled on use case.

Use cases are not only texts, but also diagrams, if needed.

Title: "goal the use case is trying to satisfy"[23]:101 Main Success Scenario: numbered list of steps[23]:101 Step: "a simple statement of the interaction between the actor and a system"[23]:101 Extensions: separately numbered lists, one per Extension[23]:101 Extension: "a condition that results in different interactions from .. the main success scenario". An extension from main step 3 is numbered 3a, etc.

the phrase use case is a polyseme with two senses

The is-a relationship may also be contrasted with the instance-of relationship between objects (instances) and types (classes): see Type–token distinction.

In autoepistemic logic, which rejects the law of excluded middle, predicates may be true, false, or simply unknown

The precise semantic interpretation of an atomic formula and an atomic sentence will vary from theory to theory.

A predicate whose quantifiers all apply to individual elements, and not to sets or predicates, is called a first-order predicate.

While propositional logic can only express facts, autoepistemic logic can express knowledge and lack of knowledge about facts.

The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge.

'female' + 'performer' = 'actress'

An individual semantic feature constitutes one component of a word's intention, which is the inherent sense or concept evoked.

The semantic features of a word can be notated using a binary feature notation common to the framework of componential analysis.[11] A semantic property is specified in square brackets and a plus or minus sign indicates the existence or non-existence of that property.

a class is an implementation‍—‌a concrete data structure and collection of subroutines‍—‌while a type is an interface

but narrowly speaking objects have type

In casual use, people often refer to the "class" of an object

Semantic class

semantic fields are constantly flowing into each other

The English word "man" used to mean "human being" exclusively, while today it predominantly means "adult male," but its semantic field still extends in some uses to the generic "human"

Synonymy requires the sharing of a sememe or seme, but the semantic field is a larger area surrounding those.

A general and intuitive description is that words in a semantic field are not necessarily synonymous, but are all used to talk about the same general phenomenon.

A semantic field denotes a segment of reality symbolized by a set of related words. The words in a semantic field share a common semantic property

grouped semantically (by meaning)

There may only be historical reasons that, for example, the periodic table is called a classification rather than a taxonomy

Taxonomy was first used in biology, but the term has spread to other domains.

Categorization is, for example, mostly used by cognitive psychologists for what other call classification

Synonyms and near-synonyms for the term classification

Categorization is sometimes considered synonymous with classification

Categorization is grounded in the features that distinguish the category's members from nonmembers.

Categorization is the human ability and activity of recognizing shared features or similarities between the elements of the experience of the world (such as objects, events, or ideas), organizing and classifying experience by associating them to a more abstract group (that is, a category, class, or type),[1][2] on the basis of their traits, features, similarities or other criteria.

place

semantic domain or semantic field

For instance English has a domain ‘Rain’, which includes words such as rain, drizzle, downpour, raindrop, puddle.

For instance, in basketball there are many words that are specific to the sport. Free throw, court, half court, three pointer, and point guard are all terms that are specific to the sport of basketball. These words make very little sense when used outside of the semantic domain of basketball.

In lexicography a semantic domain or semantic field is defined as "an area of meaning and the words used to talk about it

Semantic domains are the foundational concept for initial stages of vernacular dictionary building projects.

This uses techniques such as SIL International's Dictionary Development Process (DDP),[4][5] RapidWords, or software such as WeSay[6] or FLEx. These techniques rely on extensive lists of semantic domains that are relevant to vernacular languages.

Sometimes lexicography is considered to be a part or a branch of lexicology, but properly speaking, only lexicologists who write dictionaries are lexicographers.

Some consider this a distinction of theory vs. practice.

An allied science to lexicology is lexicography, which also studies words, but primarily in relation with dictionaries – it is concerned with the inclusion of words in dictionaries and from that perspective with the whole lexicon

Not to be confused with lexicography.

For example, in the Dyirbal language, the morpheme balam marks each entity in its noun class with the semantic property of edibility,[8] and Burmese encodes the semantic property for the ability to cut or pierce. Encoding the functional property for transportation, housing, and speech are also attested in world languages.

meaningful or meaningless – for example, whether a given word is part of a language's lexicon with a generally understood meaning

Basic semantic properties include being meaningful or meaningless – for example, whether a given word is part of a language's lexicon with a generally understood meaning

those aspects of a linguistic unit, such as a morpheme, word, or sentence,

Every woman talked to a student. This has two interpretations. Under one reading, every woman talked to the same student (the class president, for example), and here the noun phrase a student is specific. Under the second reading, various students were talked to. In this case, a student is non-specific.

a stative verb is one that describes a state of being, in contrast to a dynamic verb, which describes an action

Semantics: deals with the formal properties and interrelation of signs and symbols, without regard to meaning.

any form of activity, conduct, or process that involves signs, including the production of meaning. A sign is anything that communicates a meaning, that is not the sign itself, to the interpreter of the sign. The meaning can be intentional such as a word uttered with a specific meaning, or unintentional, such as a symptom being a sign of a particular medical condition. Signs can communicate through any of the senses, visual, auditory, tactile, olfactory, or taste.

However, if the distinctions between the two concepts appear to be superficial, intentional conflation may be desirable for the sake of conciseness and recall

All bats are animals. Some wooden objects are bats. Therefore, some wooden objects are animals.

Using words with different meanings can help clarify, or can cause real confusion.

often in error

In logic, it is the practice of treating two distinct concepts as if they were one, which produces errors or misunderstandings as a fusion of distinct subjects tends to obscure analysis of relationships which are emphasized by contrasts

Function (computer science) Function (engineering) Function (mathematics)

Analysis involves reaching a richer and more precise understanding of each requirement and representing sets of requirements in multiple, complementary ways.

Use cases, user stories, functional requirements, and visual analysis models are popular choices for requirements specification.

Requirements Triage or prioritization of requirements is another activity which often follows analysis.

A polyseme is a word or phrase with different, but related senses.

is the capacity for a word or phrase to have multiple meanings, usually related by contiguity of meaning within a semantic field.

Dictionary writers list polysemes under the same entry; homonyms are defined separately.

Polysemy is thus distinct from homonymy—or homophony—which is an accidental similarity between two words (such as bear the animal, and the verb to bear); while homonymy is often a mere linguistic coincidence, polysemy is not.

Intentional community

Spontaneous symmetry breaking illustrated

Internet addiction disorder

Social media and psychology

Studies of great ape behavior show that they are good at cooperating in situations where there is no potential of deception, but behave egotistically in situations where there are motives for deception, suggesting that their "lack of cooperativeness" is not a lack of a cognitive ability at all, but rather a necessary adaptation to a society full of deception.[citation needed] This suggests that human cooperativeness began when proto-humans began to successfully avoid competition, which is also supported by the fact that the oldest evidence of care for the long-term sick and disabled are from shortly after the first emigration of hominins out of Africa about 1.8 million years ago

His life and legacy of scientific and political achievement, and his status as one of America's most influential Founding Fathers, have seen Franklin honored more than two centuries after his death on the fifty-cent piece, the $100 bill, warships, and the names of many towns, counties, educational institutions, and corporations, as well as numerous cultural references and with a portrait in the Oval Office.

He initially owned and dealt in slaves but, by the late 1750s, he began arguing against slavery, became an abolitionist, and promoted education and the integration of blacks in American Society.

He was promoted to deputy postmaster-general for the British colonies on August 10, 1753,[10] having been Philadelphia postmaster for many years, and this enabled him to set up the first national communications network.

Franklin became a successful newspaper editor and printer in Philadelphia, the leading city in the colonies, publishing the Pennsylvania Gazette at the age of 23.[7] He became wealthy publishing this and Poor Richard's Almanack, which he authored under the pseudonym "Richard Saunders".[

Franklin earned the title of "The First American" for his early and indefatigable campaigning for colonial unity,

A polymath, he was a leading writer, printer, political philosopher, politician, Freemason, postmaster, scientist, inventor, humorist, civic activist, statesman, and diplomat.

He pioneered and was the first president of Academy and College of Philadelphia which opened in 1751 and later became the University of Pennsylvania.

" While Franklin did not live completely by his virtues, and by his own admission he fell short of them many times, he believed the attempt made him a better man contributing greatly to his success and happiness,

Franklin was careful to stand on an insulator, keeping dry under a roof to avoid the danger of electric shock.

Without freedom of thought there can be no such thing as wisdom and no such thing as public liberty without freedom of speech."

Franklin was foundational in defining the American ethos as a marriage of the practical values of thrift, hard work, education, community spirit, self-governing institutions, and opposition to authoritarianism both political and religious, with the scientific and tolerant values of the Enlightenment.

As a scientist, he was a major figure in the American Enlightenment and the history of physics for his discoveries and theories regarding electricity. As an inventor, he is known for the lightning rod, bifocals, and the Franklin stove, among other inventions.

As the Revolution approached political strife slowly tore his network apart.[38]

Franklin was an avid chess player. He was playing chess by around 1733, making him the first chess player known by name in the American colonies.

Franklin had mixed success in his plan to establish an inter-colonial network of newspapers that would produce a profit for him and disseminate virtue.

At age 17, Franklin ran away to Philadelphia, Pennsylvania, seeking a new start in a new city.

"No society can go from the primeval directly to an industrial state without losing the leavening that time and an agricultural period allow."

culminating

There he also received instruction in piano and counterpoint from professor Gustav Jacobsthal, and associated closely with Ernest Munch, the brother of his former teacher, organist of St William church, who was also a passionate admirer of J. S. Bach's music.

contemporaneous

He studied organ in Mulhouse from 1885 to 1893 with Eugène Munch, organist at the Protestant cathedral, who inspired Schweitzer with his enthusiasm for the music of German composer Richard Wagner.[10] In 1893, he played for the French organist Charles-Marie Widor (at Saint-Sulpice, Paris), for whom Johann Sebastian Bach's organ music contained a mystic sense of the eternal.

As a music scholar and organist, he studied the music of German composer Johann Sebastian Bach and influenced the Organ Reform Movement (Orgelbewegung).

Schweitzer's first language was the Alsatian dialect of German.

Schweitzer, the pastor's son, grew up in this exceptional environment of religious tolerance, and developed the belief that true Christianity should always work towards a unity of faith and purpose.

In addition to injuries, he was often treating severe sandflea and crawcraw sores, framboesia (yaws), tropical eating sores, heart disease, tropical dysentery, tropical malaria, sleeping sickness, leprosy, fevers, strangulated hernias, necrosis, abdominal tumours and chronic constipation and nicotine poisoning, while also attempting to deal with deliberate poisonings, fetishism and fear of cannibalism among the Mbahouin.

There was great demand for a German edition, but, instead of translating it, he decided to rewrite it.[

14 January 1875 – 4 September 1965

He was a theologian, organist, writer, humanitarian, philosopher, and physician.

His life was portrayed in the 1952 movie Il est minuit, Docteur Schweitzer, starring Pierre Fresnay as Albert Schweitzer and Jeanne Moreau as his nurse Marie

"fishers of men"

Through concerts and other fund-raising, he was ready to equip a small hospital.[51] In early 1913, he and his wife set off to establish a hospital (Albert Schweitzer Hospital) near an existing mission post. The site was nearly 200 miles (14 days by raft[52]) upstream from the mouth of the Ogooué at Port Gentil (Cape Lopez) (and so accessible to external communications), but downstream of most tributaries, so that internal communications within Gabon converged towards Lambaréné.

Amid a hail of protests from his friends, family and colleagues, he resigned his post and re-entered the university as a student in a three-year course towards the degree of Doctorate in Medicine, a subject in which he had little knowledge or previous aptitude. He planned to spread the Gospel by the example of his Christian labour of healing, rather than through the verbal process of preaching, and believed that this service should be acceptable within any branch of Christian teaching.

Schweitzer rapidly gained prominence as a musical scholar and organist, dedicated also to the rescue, restoration and study of historic pipe organs.

He spent his childhood in Gunsbach, also in Alsace, where his father, the local Lutheran-Evangelical pastor of the EPCAAL, taught him how to play music.[7] The tiny village would become home to the Association Internationale Albert Schweitzer (AIAS).

He was a theologian, organist, writer, humanitarian, philosopher, and physician.

a questionnaire

many theological and musical conversations

he decided to rewrite it

devotional contemplation in which the musical design corresponded to literary ideas, conceived visually.

explaining figures and motifs in Bach's Chorale Preludes as painter-like tonal and rhythmic imagery illustrating themes from the words of the hymns on which they were based

The effects of advertising on body image have been studied by researchers, ranging from psychologists to marketing professionals.

a feedback vertex set of a graph is a set of vertices whose removal leaves a graph without cycles

With Annie Leibovitz, Sontag maintained a relationship stretching from the later 1980s until her final years.

She wrote and directed four films and also wrote several plays, the most successful of which were Alice in Bed and Lady from the Sea.

At age 67, Sontag published her final novel In America (2000). The last two novels were set in the past, which Sontag said gave her greater freedom to write in the polyphonic voice:

Her essays and speeches drew controversy,[3] and she has been described as "one of the most influential critics of her generation."

Allegations of plagiarism

Ellen Lee accused Sontag of plagiarism when Lee discovered at least twelve passages in In America (1999) that were similar to, or copied from, passages in four other books about Helena Modjeska without attribution.[54][55] Sontag said about using the passages, "All of us who deal with real characters in history transcribe and adopt original sources in the original domain. I've used these sources and I've completely transformed them. There's a larger argument to be made that all of literature is a series of references and allusions."[56]

Sontag drew criticism for writing in 1967 in Partisan Review:

Sontag lived with 'H,' the writer and model Harriet Sohmers Zwerling whom she first met at U. C. Berkeley from 1958 to 1959.

The method especially appeals to people handicapped by a ruthless work ethic—Germans, Japanese and Americans. Using a camera appeases the anxiety which the work driven feel about not working when they are on vacation and supposed to be having fun. They have something to do that is like a friendly imitation of work: they can take pictures. (p. 10)

It was through her essays that Sontag gained early fame and notoriety. Sontag wrote frequently about the intersection of high and low art and expanded the dichotomy concept of form and art in every medium. She elevated camp to the status of recognition with her widely read 1964 essay "Notes on 'Camp,'" which accepted art as including common, absurd and burlesque themes.

critic Camille Paglia describes her initial admiration and subsequent disillusionment.[60] She mentions several criticisms of Sontag, including Harold Bloom's comment of "Mere Sontagisme!" on Paglia's doctoral dissertation, and states that Sontag "had become synonymous with a shallow kind of hip posturing."

Tom Wolfe dismissed

not

Steve Wasserman of The LA Times called her

Legacy Following Sontag's death, Steve Wasserman of The LA Times called her "one of America’s most influential intellectuals, internationally renowned for the passionate engagement and breadth of her critical intelligence and her ardent activism in the cause of human rights."[46] Eric Homberger of The Guardian called Sontag "the 'Dark Lady' of American cultural life for over four decades."[47] He observed that "despite a brimming and tartly phrased political sensibility, she was fundamentally an aesthete [who] offered a reorientation of American cultural horizons."[47] Writing about Against Interpretation (1966), Brandon Robshaw of The Independent later observed that "Sontag was remarkably prescient; her project of analysing popular culture as well as high culture, the Doors as well as Dostoevsky, is now common practice throughout the educated world."[48] In Critique and Postcritique (2017), Rita Felski and Elizabeth S. Anker argue that the title essay from the aforementioned collection played an important role in the field of postcritique, a movement within literary criticism and cultural studies that attempts to find new forms of reading and interpretation that go beyond the methods of critique, critical theory, and ideological criticism.[49] Reviewing Sontag's On Photography (1977) in 1998, Michael Starenko wrote that the work "has become so deeply absorbed into this discourse that Sontag's claims about photography, as well as her mode of argument, have become part of the rhetorical 'tool kit' that photography theorists and critics carry around in their heads."[50]

Sontag was quoted by Editor-in-Chief Brendan Lemon of Out magazine as saying "I grew up in a time when the modus operandi was the 'open secret.' I'm used to that, and quite OK with it. Intellectually, I know why I haven't spoken more about my sexuality, but I do wonder if I haven't repressed something there to my detriment. Maybe I could have given comfort to some people if I had dealt with the subject of my private sexuality more, but it's never been my prime mission to give comfort, unless somebody's in drastic need. I'd rather give pleasure, or shake things up."[45]

The Temple of Jerusalem was then transformed into a temple for Caligula, and it was called the Temple of Illustrious Gaius the New Jupiter

Ivar was born weak, "boneless"

High arousal vs. low arousal

Pleasure vs. displeasure

belief is a state