Surjective functionIn mathematics, a surjective function (also known as surjection, or onto function ˈɒn.tuː) is a function f such that every element y can be mapped from some element x such that f(x) = y. In other words, every element of the function's codomain is the of one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y.
Bijection, injection and surjectionIn mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain. Given a function : The function is injective, or one-to-one, if each element of the codomain is mapped to by at most one element of the domain, or equivalently, if distinct elements of the domain map to distinct elements in the codomain.
DefinitionA definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
Lexical definitionThe lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience.
ImageAn image is a visual representation of something. An image can be a two-dimensional (2D) representation, such as a drawing, painting, or photograph, or a three-dimensional (3D) object, such as a carving or sculpture. An image may be displayed through other media, including projection on a surface, activation of electronic signals, or digital displays. Two-dimensional images can be still or animated. Still images can usually be reproduced through mechanical means, such as photography, printmaking or photocopying.
Circular definitionA circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic. Circular definitions are related to Circular reasoning in that they both involve a self-referential approach. Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself.
Application softwareAn application program (software application, or application, or app for short) is a computer program designed to carry out a specific task other than one relating to the operation of the computer itself, typically to be used by end-users. Word processors, media players, and accounting software are examples. The collective noun "application software" refers to all applications collectively. The other principal classifications of software are system software, relating to the operation of the computer, and utility software ("utilities").
Web applicationA web application (or web app) is application software that is accessed using a web browser. Web applications are delivered on the World Wide Web to users with an active network connection. In earlier computing models like client-server, the processing load for the application was shared between code on the server and code installed on each client locally. In other words, an application had its own pre-compiled client program which served as its user interface and had to be separately installed on each user's personal computer.
Rich Internet ApplicationA Rich Internet Application (also known as a rich web application, RIA or installable Internet application) is a web application that has many of the characteristics of desktop application software. The concept is closely related to a single-page application, and may allow the user interactive features such as drag and drop, background menu, WYSIWYG editing, etc. The concept was first introduced in 2002 by Macromedia to describe Macromedia Flash MX product (which later became Adobe Flash).
Domain nameIn the Internet, a domain name is a string that identifies a realm of administrative autonomy, authority or control. Domain names are often used to identify services provided through the Internet, such as websites, email services and more. As of 2017, 330.6 million domain names had been registered. Domain names are used in various networking contexts and for application-specific naming and addressing purposes. In general, a domain name identifies a network domain or an Internet Protocol (IP) resource, such as a personal computer used to access the Internet, or a server computer.
CodomainIn mathematics, the codomain or set of destination of a function is the set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y. The term range is sometimes ambiguously used to refer to either the codomain or of a function. A codomain is part of a function f if f is defined as a triple (X, Y, G) where X is called the domain of f, Y its codomain, and G its graph. The set of all elements of the form f(x), where x ranges over the elements of the domain X, is called the of f.
Image editingImage editing encompasses the processes of altering s, whether they are digital photographs, traditional photo-chemical photographs, or illustrations. Traditional analog image editing is known as photo retouching, using tools such as an airbrush to modify photographs or editing illustrations with any traditional art medium. Graphic software programs, which can be broadly grouped into vector graphics editors, raster graphics editors, and 3D modelers, are the primary tools with which a user may manipulate, enhance, and transform images.
Top-level domainA top-level domain (TLD) is one of the domains at the highest level in the hierarchical Domain Name System of the Internet after the root domain. The top-level domain names are installed in the root zone of the name space. For all domains in lower levels, it is the last part of the domain name, that is, the last non empty label of a fully qualified domain name. For example, in the domain name www.example.com, the top-level domain is .com. Domain name registrarA domain name registrar is a company that manages the reservation of Internet domain names. A domain name registrar must be accredited by a generic top-level domain (gTLD) registry or a country code top-level domain (ccTLD) registry. A registrar operates in accordance with the guidelines of the designated domain name registries. Until 1999, Network Solutions Inc. (NSI) operated the registries for the com, net, and org top-level domains (TLDs). In addition to the function of domain name registry operator, it was also the sole registrar for these domains.
Range of a functionIn mathematics, the range of a function may refer to either of two closely related concepts: The codomain of the function The of the function Given two sets X and Y, a binary relation f between X and Y is a (total) function (from X to Y) if for every x in X there is exactly one y in Y such that f relates x to y. The sets X and Y are called domain and codomain of f, respectively. The image of f is then the subset of Y consisting of only those elements y of Y such that there is at least one x in X with f(x) = y.
Example.comThe domain names example.com, example.net and example.org are second-level domain names in the Domain Name System of the Internet. They are reserved by the Internet Assigned Numbers Authority (IANA) at the direction of the Internet Engineering Task Force (IETF) as special-use domain names for documentation purposes. The domain names are used widely in books, tutorials, sample network configurations, and generally as examples for the use of domain names.
Domain of a functionIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". More precisely, given a function , the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that X and Y are both subsets of , the function f can be graphed in the Cartesian coordinate system.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. 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).
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
HomomorphismIn algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός () meaning "same" and μορφή () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).
