Universal setIn set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory include a universal set. Many set theories do not allow for the existence of a universal set. There are several different arguments for its non-existence, based on different choices of axioms for set theory. In Zermelo–Fraenkel set theory, the axiom of regularity and axiom of pairing prevent any set from containing itself.
Fuzzy setIn mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of L-relations when L is the unit interval [0, 1].
Set-builder notationIn set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension. Set (mathematics)#Roster notation A set can be described directly by enumerating all of its elements between curly brackets, as in the following two examples: is the set containing the four numbers 3, 7, 15, and 31, and nothing else.
Language changeLanguage change is variation over time in a language's features. It is studied in several subfields of linguistics: historical linguistics, sociolinguistics, and evolutionary linguistics. Traditional theories of historical linguistics identify three main types of change: systematic change in the pronunciation of phonemes, or sound change; borrowing, in which features of a language or dialect are altered as a result of influence from another language or dialect; and analogical change, in which the shape or grammatical behavior of a word is altered to more closely resemble that of another word.
NewspaperA newspaper is a periodical publication containing written information about current events and is often typed in black ink with a white or gray background. Newspapers can cover a wide variety of fields such as politics, business, sports, art, and science. They often include materials such as opinion columns, weather forecasts, reviews of local services, obituaries, birth notices, crosswords, editorial cartoons, comic strips, and advice columns.
Origin of languageThe origin of language (spoken and signed, as well as language-related technological systems such as writing), its relationship with human evolution, and its consequences have been subjects of study for centuries. Scholars wishing to study the origins of language must draw inferences from evidence such as the fossil record, archaeological evidence, contemporary language diversity, studies of language acquisition, and comparisons between human language and systems of communication existing among animals (particularly other primates).
Language interpretationInterpreting is a translational activity in which one produces a first and final target-language output on the basis of a one-time exposure to an expression in a source language. The most common two modes of interpreting are simultaneous interpreting, which is done at the time of the exposure to the source language, and consecutive interpreting, which is done at breaks to this exposure. Interpreting is an ancient human activity which predates the invention of writing.
Text corpusIn linguistics and natural language processing, a corpus (: corpora) or text corpus is a dataset, consisting of natively digital and older, digitalized, language resources, either annotated or unannotated. Annotated, they have been used in corpus linguistics for statistical hypothesis testing, checking occurrences or validating linguistic rules within a specific language territory. In search technology, a corpus is the collection of documents which is being searched.
SemanticsSemantics () is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and computer science. In English, the study of meaning in language has been known by many names that involve the Ancient Greek word σῆμα (sema, "sign, mark, token"). In 1690, a Greek rendering of the term semiotics, the interpretation of signs and symbols, finds an early allusion in John Locke's An Essay Concerning Human Understanding: The third Branch may be called σημειωτική [simeiotikí, "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough termed also λογικὴ, Logick.
Book scanningBook scanning or book digitization (also: magazine scanning or magazine digitization) is the process of converting physical books and magazines into digital media such as , electronic text, or electronic books (e-books) by using an . Large scale book scanning projects have made many books available online. Digital books can be easily distributed, reproduced, and read on-screen. Common file formats are DjVu, Portable Document Format (PDF), and (TIFF).
