Computer programmingComputer programming is the process of performing particular computations (or more generally, accomplishing specific computing results), usually by designing and building executable computer programs. Programming involves tasks such as analysis, generating algorithms, profiling algorithms' accuracy and resource consumption, and the implementation of algorithms (usually in a particular programming language, commonly referred to as coding).
Family of setsIn set theory and related branches of mathematics, a collection of subsets of a given set is called a family of subsets of , or a family of sets over More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. A family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of .
Disjoint setsIn mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint. This definition of disjoint sets can be extended to families of sets and to indexed families of sets.
Functional programmingIn 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 imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.
Declarative programmingIn computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow. Many languages that apply this style attempt to minimize or eliminate side effects by describing what the program must accomplish in terms of the problem domain, rather than describing how to accomplish it as a sequence of the programming language primitives (the how being left up to the language's implementation).
Programming languageA programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming language is usually split into the two components of syntax (form) and semantics (meaning), which are usually defined by a formal language. Some languages are defined by a specification document (for example, the C programming language is specified by an ISO Standard) while other languages (such as Perl) have a dominant implementation that is treated as a reference.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
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].
Category of setsIn the mathematical field of , the category of sets, denoted as Set, is the whose are sets. The arrows or morphisms between sets A and B are the total functions from A to B, and the composition of morphisms is the composition of functions. Many other categories (such as the , with group homomorphisms as arrows) add structure to the objects of the category of sets and/or restrict the arrows to functions of a particular kind.
Rough setIn computer science, a rough set, first described by Polish computer scientist Zdzisław I. Pawlak, is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the lower and the upper approximation of the original set. In the standard version of rough set theory (Pawlak 1991), the lower- and upper-approximation sets are crisp sets, but in other variations, the approximating sets may be fuzzy sets. The following section contains an overview of the basic framework of rough set theory, as originally proposed by Zdzisław I.
Procedural programmingProcedural programming is a programming paradigm, derived from imperative programming, based on the concept of the procedure call. Procedures (a type of routine or subroutine) simply contain a series of computational steps to be carried out. Any given procedure might be called at any point during a program's execution, including by other procedures or itself. The first major procedural programming languages appeared circa 1957–1964, including Fortran, ALGOL, COBOL, PL/I and BASIC. Pascal and C were published circa 1970–1972.
Logic programmingLogic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic programming language families include Prolog, answer set programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses: H :- B1, ..., Bn. and are read declaratively as logical implications: H if B1 and ... and Bn. H is called the head of the rule and B1, .
Union (set theory)In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of zero () sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols. The union of two sets A and B is the set of elements which are in A, in B, or in both A and B.
PasswordA password, sometimes called a passcode (for example in Apple devices), is secret data, typically a string of characters, usually used to confirm a user's identity. Traditionally, passwords were expected to be memorized, but the large number of password-protected services that a typical individual accesses can make memorization of unique passwords for each service impractical. Using the terminology of the NIST Digital Identity Guidelines, the secret is held by a party called the claimant while the party verifying the identity of the claimant is called the verifier.
Algebra of setsIn mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
String (computer science)In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. String may also denote more general arrays or other sequence (or list) data types and structures.
SubtractionSubtraction (which is signified by the minus sign ) is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3.
Password strengthPassword strength is a measure of the effectiveness of a password against guessing or brute-force attacks. In its usual form, it estimates how many trials an attacker who does not have direct access to the password would need, on average, to guess it correctly. The strength of a password is a function of length, complexity, and unpredictability. Using strong passwords lowers the overall risk of a security breach, but strong passwords do not replace the need for other effective security controls.
Field of setsIn mathematics, a field of sets is a mathematical structure consisting of a pair consisting of a set and a family of subsets of called an algebra over that contains the empty set as an element, and is closed under the operations of taking complements in finite unions, and finite intersections. Fields of sets should not be confused with fields in ring theory nor with fields in physics. Similarly the term "algebra over " is used in the sense of a Boolean algebra and should not be confused with algebras over fields or rings in ring theory.
Constraint programmingConstraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found.
