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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}, 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.
Download QR code; Print/export Download as PDF; ... Ordered geometry; Ordered pair; Ordered topological vector space; Ordinal sum; P. Pantachy; Partial cyclic order;
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.
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.
2. A Kuratowski ordered pair is a definition of an ordered pair using only set theoretical concepts, specifically, the ordered pair (a, b) is defined as the set {{a}, {a, b}}. 3. "Kuratowski-Zorn lemma" is an alternative name for Zorn's lemma Kurepa 1. Đuro Kurepa 2. The Kurepa hypothesis states that Kurepa trees exist 3.
Then a critical pair is an ordered pair (x, y) of elements of S with the following three properties: x and y are incomparable in P, for every z in S, if z < x then z < y, and; for every z in S, if y < z then x < z. If (x, y) is a critical pair, then the binary relation obtained from P by adding the single relationship x ≤ y is also a partial
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