In mathematics, an unordered pair or pair set is a set of the form {a, b}, i.e. a set having two elements a and b with no particular relation between them...

unless a = b. In contrast, the unordered pair, denoted {a, b}, always equals the unordered pair {b, a}. Ordered pairs are also called 2-tuples, or sequences...

of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory. It was introduced...

multigraph) is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs { v 1 , v 2 }...

there are 21 unordered pairs of points, each of which may be mapped by a symmetry onto any other unordered pair. For any unordered pair there are 8 symmetries...

something, a pair Unordered pair, or pair set, in mathematics and set theory Ordered pair, or 2-tuple, in mathematics and set theory Pairing, in mathematics...

together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for a directed graph. These pairs are known as edges...

Most of these implement the general model of an associative array: an unordered list of unique attributes with associated values. As a result, they are...

loops. A multigraph G is an ordered pair G := (V, E) with V a set of vertices or nodes, E a multiset of unordered pairs of vertices, called edges or lines...

empty or contains an unordered pair from S, Each symbol occurs exactly once in each row and column of the array, and Every unordered pair of symbols occurs...

stratified comprehension; in ZFC, the existence of the unordered pair is given by the Axiom of Pairing, the existence of the empty set follows by Separation...

ISBN 978-0-321-39053-0. Dijkstra, Edsger W. (1997). "WLOG, or the misery of the unordered pair (EWD1223)". In Broy, Manfred; Schieder, Birgit (eds.). Mathematical...

a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In...

A } {\displaystyle \{A\}} exists. Given any two sets, their unordered and ordered pairs exist. Given any set of sets, its union exists. TG includes the...

{and}}\;x\neq y\}} , a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with two distinct vertices)...

triangular numbers arise naturally as numbers of unordered pairs of unordered pairs of objects, including pairs where both objects are the same: An example...

contains an unordered pair from the set of symbols Each symbol occurs exactly once in each row and column of the array Every unordered pair of symbols...

ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges, links or lines. The aforementioned...

{\displaystyle f} maps all unordered pairs of elements drawn from that subset to zero, or it maps all such unordered pairs to one. An equivalent formulation...

the hyperbolic plane can be parameterized by unordered pairs of distinct points on a circle, the pairs of points at infinity of each line. This space...

say that A is also the ordered pair (0,1). Both statements cannot be correct; the ordered pair (0,1) and the unordered pair {1,2} are fully distinct concepts...

usually written ∀ unordered pair A set of two elements where the order of the elements does not matter, distinguishing it from an ordered pair where the sequence...

the unordered pair of isodynamic points of a transformation of A B C {\displaystyle ABC} is equal to the same transformation applied to the pair { S ...

a similarity, turns one Brocard point into the other. However, the unordered pair formed by both points is invariant under similarities. The midpoint...

types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into...

all ordered pairs (a, b) of elements a of A and b of B. Proof: The singleton set with member a, written {a}, is the same as the unordered pair {a, a}, by...

can be grouped into unordered pairs ( x , y ) {\displaystyle (x,y)} according to the rule that the product of the members of each pair is congruent to a...

of distinct unordered points is also a manifold, while the configuration space of not necessarily distinct[clarification needed] unordered points is instead...

z\leftrightarrow (s=x\,\lor \,s=y)])].} Pairing licenses the unordered pair in terms of which the ordered pair, ⟨ x , y ⟩ {\displaystyle \langle x,y\rangle...

graph correspond to the 231 unordered pairs of elements. Two vertices are adjacent whenever they come from two disjoint pairs whose union belongs to one...