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Lexicographical Order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements. Another variant, widely used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences, to which the lexicographical order is applied. A generalization defines an order on a Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered. Motivation and definition The words in a lexicon (the set of words used in some language) have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphabetical Order
Alphabetical order is a system whereby character strings are placed in order based on the position of the characters in the conventional ordering of an alphabet. It is one of the methods of collation. In mathematics, a lexicographical order is the generalization of the alphabetical order to other data types, such as sequences of numbers or other ordered mathematical objects. When applied to strings or sequences that may contain digits, numbers or more elaborate types of elements, in addition to alphabetical characters, the alphabetical order is generally called a lexicographical order. To determine which of two strings of characters comes first when arranging in alphabetical order, their first letters are compared. If they differ, then the string whose first letter comes earlier in the alphabet comes before the other string. If the first letters are the same, then the second letters are compared, and so on. If a position is reached where one string has no more letters to compare ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Totally Ordered
In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X: # a \leq a ( reflexive). # If a \leq b and b \leq c then a \leq c ( transitive). # If a \leq b and b \leq a then a = b ( antisymmetric). # a \leq b or b \leq a (strongly connected, formerly called total). Total orders are sometimes also called simple, connex, or full orders. A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, and loset are also used. The term ''chain'' is sometimes defined as a synonym of ''totally ordered set'', but refers generally to some sort of totally ordered subsets of a given partially ordered set. An extension of a given partial order to a total order is called a linear extension of that partial order. Strict and non-strict total orders A on a set X is a strict partial ord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO 8601
ISO 8601 is an international standard covering the worldwide exchange and communication of date and time-related data. It is maintained by the Geneva-based International Organization for Standardization (ISO) and was first published in 1988, with updates in 1991, 2000, 2004, and 2019, and an amendment in 2022. The standard provides a well-defined, unambiguous method of representing calendar dates and times in worldwide communications, especially to avoid misinterpreting numeric dates and times when such data is transferred between countries with different conventions for writing numeric dates and times. ISO 8601 applies to these representations and formats: ''dates,'' in the Gregorian calendar (including the proleptic Gregorian calendar); ''times,'' based on the 24-hour timekeeping system, with optional UTC offset; ''time intervals''; and combinations thereof.ISO 8601:2004 section 1 Scope The standard does not assign specific meaning to any element of the dates/times r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
