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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.
The term ordered list can refer to: an ordered list (HTML) a mathematical sequence This page was last edited on 29 ...
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
The lexicographical order defines an order on an n-ary Cartesian product of ordered sets, which is a total order when all these sets are themselves totally ordered. An element of a Cartesian product E 1 × ⋯ × E n {\displaystyle E_{1}\times \cdots \times E_{n}} is a sequence whose i {\displaystyle i} th element belongs to E i {\displaystyle ...
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 ...
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 ...
Make an ordered list. The default is a numbered list, but you can change it to a list with roman numbers or letters of the English, Greek, Armenian or Georgian alphabets, instead of the decimal enumerator. Template parameters [Edit template data] This template prefers block formatting of parameters. Parameter Description Type Status First item to list 1 no description Unknown required Second ...
In Political science and Decision theory, order relations are typically used in the context of an agent's choice, for example the preferences of a voter over several political candidates. x ≺ y means that the voter prefers candidate y over candidate x. x ~ y means the voter is indifferent between candidates x and y.