Operation (mathematics)In mathematics, an operation is a function that takes as input a fixed number of elements of a set and returns an element of the same set. For example, addition on real numbers is an operation that accepts two real numbers and returns a real number. In general, the input values may be called "operands" or "arguments". The number of operands is the arity of the operation. The arity is usually one of 0,1,2,…{\displaystyle 0,1,2,\ldots }.
Closure operatorIn mathematics, a closure operator on a setS is a functioncl:P(S)→P(S){\displaystyle \operatorname {cl} :{\mathcal {P}}(S) ightarrow {\mathcal {P}}(S)} from the power set of S to itself that satisfies the following conditions for all sets X,Y⊆S{\displaystyle X,Y\subseteq S}Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called closure systems or "Moore families".
Abstract algebraIn mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field.
Functional programmingProgramming paradigm based on applying and composing functionsIn computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperativestatements which update the running state of the program.
Projection (linear algebra)Idempotent linear transformation from a vector space to itselfThe transformation P is the orthogonal projection onto the linem.In linear algebra and functional analysis, a projection is a linear transformationP{\displaystyle P} from a vector space to itself (an endomorphism) such that P∘P=P{\displaystyle P\circ P=P}.Referential transparencyIn analytic philosophy and computer science, referential transparency and referential opacity are properties of linguistic constructions, and by extension of languages. A linguistic construction is called referentially transparent when for any expression built from it, replacing a subexpression with another one that denotes the same value does not change the value of the expression. Otherwise, it is called referentially opaque.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
Benjamin PeirceBenjamin Peirce (; April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philosophy of mathematics. Early lifeBenjamin Peirce was born in Salem, Massachusetts, the son of first cousins Benjamin Peirce (1778–1831), later librarian of Harvard, and Lydia Ropes Nichols Peirce (1781–1868).
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.
HTTPApplication layer protocolHTTP (Hypertext Transfer Protocol) is an application layer protocol in the Internet protocol suite for distributed, collaborative, hypermedia information systems. HTTP is the foundation of data communication for the World Wide Web, where hypertext documents include hyperlinks to other resources that the user can easily access, for example by a mouse click or by tapping the screen in a web browser.
American EnglishAmerican English, sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. English is the most widely spoken language in the U.S., as well as the common language used in government, education, and commerce in all 50 states, the District of Columbia, and in all U.S. territories except Puerto Rico. Since the late 20th century, American English has become the most influential form of English worldwide.
British EnglishBritish English is the set of varieties of the English language native to the United Kingdom, especially Great Britain. More narrowly, it can refer specifically to the English language in England, or, more broadly, to the collective dialects of English throughout the United Kingdom taken as a single umbrella variety, for instance additionally incorporating Scottish English, Welsh English, and Northern Irish English.
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