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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, where {a, b} = {b, a}. In contrast, an ordered pair ( a , b ) has a as its first element and b as its second element, which means ( a , b ) ≠ ( b , a ).
Theorem: If A and B are sets, then there is a set A×B which consists of 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 the axiom of extensionality. The singleton, the set {a, b}, and then also the ordered pair
The first definition of the ordered pair was the definition (,) = {{{},}, {{}}} proposed by Norbert Wiener in 1914 in the context of the type theory of Principia Mathematica. Wiener observed that this allowed the elimination of types of n -ary relations for n > 1 from the system of that work.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] 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 {,} of vertices, whose elements are called edges (sometimes links or lines).
An "unordered pair" is just a set with two elements. Otherwise simply called a "pair". The adjective "unordered" is sometime added to emphasize that it is not an ordered pair. Perhaps a definition of the term "unordered pair" should be added to the "ordered pair" article, which unordered pair could then link to.
Unordered pair, or pair set, in mathematics and set theory; Ordered pair, or 2-tuple, in mathematics and set theory; Pairing, in mathematics, an R-bilinear map of modules, where R is the underlying ring; Pair type, in programming languages and type theory, a product type with two component types; Topological pair, an inclusion of topological spaces
The points of the Cremona–Richmond configuration may be identified with the = unordered pairs of elements of a six-element set; these pairs are called duads.Similarly, the lines of the configuration may be identified with the 15 ways of partitioning the same six elements into three pairs; these partitions are called synthemes.
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...