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  2. Orthogonal array - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_Array

    The example at left is that of an orthogonal array with symbol set {1,2} and strength 2. Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once.

  3. 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}, 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 vectors.

  4. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    Given a set X, a relation R over X is a set of ordered pairs of elements from X, formally: R ⊆ { (x,y) | x, y ∈ X}. [2] [10] The statement (x,y) ∈ R reads "x is R-related to y" and is written in infix notation as xRy. [7] [8] The order of the elements is important; if x ≠ y then yRx can be true or false independently of xRy.

  5. Topological pair - Wikipedia

    en.wikipedia.org/wiki/Topological_pair

    A pair of spaces is an ordered pair (X, A) where X is a topological space and A a subspace. The use of pairs of spaces is sometimes more convenient and technically superior to taking a quotient space of X by A.

  6. Glossary of set theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_set_theory

    The set of all ordered pairs obtained from two sets, where each pair consists of one element from each set. cardinal 1. A cardinal number is an ordinal with more elements than any smaller ordinal cardinality The number of elements of a set categorical 1. A theory is called categorical if all models are isomorphic. This definition is no longer ...

  7. Multiset - Wikipedia

    en.wikipedia.org/wiki/Multiset

    A multiset may be formally defined as an ordered pair (A, m) where A is the underlying set of the multiset, formed from its distinct elements, and : + is a function from A to the set of positive integers, giving the multiplicity – that is, the number of occurrences – of the element a in the multiset as the number m(a).

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