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Maplet Arrow
A maplet or maplet arrow (symbol: ↦, commonly pronounced "maps to") is a symbol consisting of a vertical line with a rightward-facing arrow. It is used in mathematics and in computer science to denote functions (the expression x ↦ y is also called a maplet). One example of use of the maplet is in Z notation, a formal specification language used in software development. In the Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, wh ... character set, the maplet is at the point U+21A6. See also * Arrow notation – e.g., x\mapsto x+1, also known as ''map'' References {{navbox punctuation Mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z Notation
The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general. History In 1974, Jean-Raymond Abrial published "Data Semantics". He used a notation that would later be taught in the University of Grenoble until the end of the 1980s. While at EDF ( Électricité de France), working with Bertrand Meyer, Abrial also worked on developing Z. The Z notation is used in the 1980 book ''Méthodes de programmation''. Z was originally proposed by Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer. It was developed further at the Programming Research Group at Oxford University, where Abrial worked in the early 1980s, having arrived at Oxford in September 1979. Abrial has said that Z is so named "Because it is the ultimate language!" although the name " Zermelo" is also associated with the Z notation through its use of Zermelo–F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Specification
In computer science, formal specifications are mathematically based techniques whose purpose are to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning tools. These specifications are ''formal'' in the sense that they have a syntax, their semantics fall within one domain, and they are able to be used to infer useful information. Motivation In each passing decade, computer systems have become increasingly more powerful and, as a result, they have become more impactful to society. Because of this, better techniques are needed to assist in the design and implementation of reliable software. Established engineering disciplines use mathematical analysis as the foundation of creating and validating product design. Formal specifications are one such way to achieve this in software engineering reliability as once predicted. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specification Language
A specification language is a formal language in computer science used during systems analysis, requirements analysis, and systems design to describe a system at a much higher level than a programming language, which is used to produce the executable code for a system. Joseph Goguen "One, None, A Hundred Thousand Specification Languages" Invited Paper, IFIP Congress 1986 pp 995-1004 Overview Specification languages are generally not directly executed. They are meant to describe the ''what'', not the ''how''. Indeed, it is considered as an error if a requirement specification is cluttered with unnecessary implementation detail. A common fundamental assumption of many specification approaches is that programs are modelled as algebraic or model-theoretic structures that include a collection of sets of data values together with functions over those sets. This level of abstraction coincides with the view that the correctness of the input/output behaviour of a program takes preced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic scripts, as well as symbols, emoji (including in colors), and non-visual control and formatting codes. Unicode's success at unifying character sets has led to its widespread and predominant use in the internationalization and localization of computer software. The standard has been implemented in many recent technologies, including modern operating systems, XML, and most modern programming languages. The Unicode character repertoire is synchronized with ISO/IEC 10646, each being code-for-code identical with the other. ''The Unicode Standard'', however, includes more than just the base code. Along ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
