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In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. 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 ...
Precisely, a binary relation over sets and is a set of ordered pairs (,) where is in and is in . [2] It encodes the common concept of relation: an element x {\displaystyle x} is related to an element y {\displaystyle y} , if and only if the pair ( x , y ) {\displaystyle (x,y)} belongs to the set of ordered pairs that defines the binary relation.
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. [1] In terms of set-builder notation, that is [2][3] A table can be created by taking the Cartesian product of a set of rows and a set of columns.
An arrow from x to y indicates that the relation holds between x and y. The relation is represented by the set { (a,a),(a,b),(a,d),(b,a),(b,d),(c,b),(d,c),(d,d) } of ordered pairs. In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [ 1 ] As an example, " is less than " is a ...
Illustration of ae plane, showing the absolute values (unsigned dotted line lengths) of the coordinates of the points (2, 3), (0, 0), (−3, 1), and (−1.5, −2.5). The first of these signed ordered pairs is the abscissa of the corresponding point, and the second value is its ordinate.
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).
In mathematics, and more specifically in order theory, several different types of ordered set have been studied. They include: Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise. Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound.
Tuple. In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton ...
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