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  2. Ordered pair - Wikipedia

    en.wikipedia.org/wiki/Ordered_pair

    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 ...

  3. Set splitting problem - Wikipedia

    en.wikipedia.org/wiki/Set_splitting_problem

    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).

  4. Permutation - Wikipedia

    en.wikipedia.org/wiki/Permutation

    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.

  5. Ordered field - Wikipedia

    en.wikipedia.org/wiki/Ordered_field

    In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Basic examples of ordered fields are the rational numbers and the real numbers, both with their standard orderings. Every subfield of an ordered field

  6. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    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.

  7. 25-pair color code - Wikipedia

    en.wikipedia.org/wiki/25-pair_color_code

    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.

  8. Ordered set operators - Wikipedia

    en.wikipedia.org/wiki/Ordered_set_operators

    In mathematical notation, ordered set operators indicate whether an object precedes or succeeds another. These relationship operators are denoted by the unicode symbols U+227A-F, along with symbols located unicode blocks U+228x through U+22Ex.

  9. Amicable numbers - Wikipedia

    en.wikipedia.org/wiki/Amicable_numbers

    Although all amicable pairs up to 10,000 are even pairs, the proportion of odd amicable pairs increases steadily towards higher numbers, and presumably there are more of them than of the even amicable pairs (A360054 in OEIS). Gaussian integer amicable pairs exist, [14] [15] e.g. s(8008+3960i) = 4232-8280i and s(4232-8280i) = 8008+3960i. [16]

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