Quotient (universal algebra)In mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation. Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is additionally compatible with all the operations of the algebra, in the formal sense described below. Its equivalence classes partition the elements of the given algebraic structure. The quotient algebra has these classes as its elements, and the compatibility conditions are used to give the classes an algebraic structure.
Finitary relationIn mathematics, a finitary relation over sets X1, ..., Xn is a subset of the Cartesian product X1 × ⋯ × Xn; that is, it is a set of n-tuples (x1, ..., xn) consisting of elements xi in Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true. The non-negative integer n giving the number of "places" in the relation is called the arity, adicity or degree of the relation.
Covering relationIn mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is commonly used to graphically express the partial order by means of the Hasse diagram. Let be a set with a partial order . As usual, let be the relation on such that if and only if and . Let and be elements of . Then covers , written , if and there is no element such that .
Visual J SharpVisual J# (pronounced "jay-sharp") is a discontinued implementation of the J# programming language that was a transitional language for programmers of Java and Visual J++ languages, so they could use their existing knowledge and applications with the .NET Framework. It was introduced in 2002 and discontinued in 2007, with support for the final release of the product continuing until October 2017. J# worked with Java bytecode as well as source so it could be used to transition applications that used third-party libraries even if their original source code was unavailable.
Public propertyPublic property is property that is dedicated to public use. The term may be used either to describe the use to which the property is put, or to describe the character of its ownership (owned collectively by the population of a state). This is in contrast to private property, owned by an individual person or artificial entities that represent the financial interests of persons, such as corporations. State ownership, also called public ownership, government ownership or state property, are property interests that are vested in the state, rather than an individual or communities.
Visual Basic for ApplicationsVisual Basic for Applications (VBA) is an implementation of Microsoft's event-driven programming language Visual Basic 6.0 built into most desktop Microsoft Office applications. Although based on pre-.NET Visual Basic, which is no longer supported or updated by Microsoft, the VBA implementation in Office continues to be updated to support new Office features. VBA is used for professional and end-user development due to its perceived ease-of-use, Office's vast installed userbase, and extensive legacy in business.
