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An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1. In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing. More generally, an unordered n-tuple is a set of the form {a 1, a 2,... a n}. [5] [6] [7]
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
2 Unordered pairs and binary sets are different and distinct concepts
UML class diagram of a Graph (abstract data type) The basic operations provided by a graph data structure G usually include: [1]. adjacent(G, x, y): tests whether there is an edge from the vertex x to the vertex y;
In the mathematical theory of hypergraphs, a hedgehog is a 3-uniform hypergraph defined from an integer parameter .It has + vertices, of which can be labeled by the integers from to and the remaining () of which can be labeled by unordered pairs of these integers.
The ordered pair (a, b) is different from the ordered pair (b, a), 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 (sometimes, lists in a computer science context) of length 2.
The MediaWiki software, which drives Wikipedia, allows the use of a subset of HTML 5 elements, or tags and their attributes, for presentation formatting. [1] However, most HTML functionality can be replicated using equivalent wiki markup or templates.
In this setting, an edge is an unordered pair of vertices, and a two-edge graph is an unordered pair of edges. The number of possible edges is a triangular number, and the number of pairs of edges (allowing both edges to connect the same two vertices) is a doubly triangular number. [4]