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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. Ordered pairs of scalars are sometimes called 2-dimensional ...
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 ).
The wire pairs are referenced directly by their color combination, or by the pair number. For example, pair 9 is also called the red-brown pair. In technical tabulations, the colors are often suitably abbreviated. Violet is the standard name in the telecommunications and electronics industry, but it is sometimes referred to as purple.
Set splitting shown on a hypergraph.The vertices make up the set S, and the edges make up the family of subsets F.The vertices are colored such that every edge has at least one vertex of each color (in this case, red and green).
The lexicographical order of two totally ordered sets is thus a linear extension of their product order. One can define similarly the lexicographic order on the Cartesian product of an infinite family of ordered sets, if the family is indexed by the natural numbers, or more generally by a well-ordered set. This generalized lexicographical order ...
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.
Sometimes an inversion is defined as the pair of values (σ(i), σ(j)); this makes no difference for the number of inversions, and the reverse pair (σ(j), σ(i)) is an inversion in the above sense for the inverse permutation σ −1.
Let (m, n) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair (m, n) is said to be regular (sequence A215491 in the OEIS); otherwise, it is called irregular or exotic.
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