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A partially ordered set (poset for short) is an ordered pair = (,) consisting of a set (called the ground set of ) and a partial order on . When the meaning is clear from context and there is no ambiguity about the partial order, the set X {\displaystyle X} itself is sometimes called a poset.
Ordered pair. Analytic geometry associates to each point in the Euclidean plane an ordered pair. The red ellipse is associated with the set of all pairs ( x, y) such that x2 4 + y2 = 1. In mathematics, an ordered pair ( a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair ( a, b ...
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [ 3] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...
Set (abstract data type) In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership ...
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, [ 1] allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist which contain ...
A set equipped with a total order is a totally ordered set; [5] the terms simply ordered set, [2] linearly ordered set, [3] [5] and loset [6] [7] are also used. The term chain is sometimes defined as a synonym of totally ordered set , [ 5 ] but refers generally to some sort of totally ordered subsets of a given partially ordered set.
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. [ 1] It supports 'lookup', 'remove', and 'insert ...
Topological sorting. In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may ...