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Ordered pair. Analytic geometry associates to each point in the Euclidean plane an ordered pair. The red ellipse is associated with the set of all pairs (x, y) such that x24 + y2 = 1. 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 ...
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.
A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer . For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as ...
In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or. the act or process of changing the linear order of an ordered set. [ 1 ] An example of the first meaning is the six permutations (orderings) of the set {1, 2, 3}: written as tuples, they are (1, 2, 3), (1 ...
The set C = {0, 1} ∞ of all infinite binary sequences is sometimes called the Cantor space. An infinite binary sequence can represent a formal language (a set of strings) by setting the n th bit of the sequence to 1 if and only if the n th string (in shortlex order) is in the language.
List (abstract data type) In computer science, a list or sequence is collection of items that are finite in number and in a particular order. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence. A list may contain the same value more than once, and each occurrence is considered a distinct ...
Set (abstract data type) In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership ...
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...