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Lexicographic 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 Sequence#Increasing_and_decreasing, increasing sequences, to which the lexicographical order is applied. A generalization defines an order on an ''n''-ary 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. Definition The words in a lexicon (the set of words u ... [...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 sequence (mathematics), sequences of numbers or other ordered mathematical objects. When applied to strings or sequence (mathematics), 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 letter (alphabet), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Totally Ordered
In mathematics, a total order 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 totality). Requirements 1. to 3. just make up the definition of a partial order. Reflexivity (1.) already follows from strong connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders. 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, toset and loset are also used. The term ''chain'' is sometimes defined as a synonym of ''totally ordered set'', but generally refers to ... [...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 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 represented: t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signed Integer
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer. Value and representation The ''value'' of an item with an integral type is the mathematical integer that it corresponds to. Integral types may be ''unsigned'' (capable of representing only non-negative integers) or ''signed'' (capable of representing negative integers as well). An integer value is typically specified in the source code of a program as a sequence of digits optionally prefixed with + or −. Some programming languages allow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer
A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as Computer program, ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the Computer hardware, hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of Programmable logic controller, industrial and Consumer electronics, consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal Notation
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A decimal numeral (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Digit
A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originates from the Latin ''digiti'' meaning fingers. For any numeral system with an integer base, the number of different digits required is the absolute value of the base. For example, decimal (base 10) requires ten digits (0 to 9), and binary (base 2) requires only two digits (0 and 1). Bases greater than 10 require more than 10 digits, for instance hexadecimal (base 16) requires 16 digits (usually 0 to 9 and A to F). Overview In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, and summing the results. Di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindu–Arabic Numeral System
The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional notation, positional Decimal, base-ten numeral system for representing integers; its extension to non-integers is the decimal, decimal numeral system, which is presently the most common numeral system. The system was invented between the 1st and 4th centuries by Indian mathematics, Indian mathematicians. By the 9th century, the system was adopted by Arabic mathematics, Arabic mathematicians who extended it to include fraction (mathematics), fractions. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (''On the Calculation with Hindu Numerals'', ) and Arab mathematician Al-Kindi (''On the Use of the Hindu Numerals'', ). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century ''Liber Abaci''; until the evolution of the printing pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Notation
Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the values may be modified when combined). In modern positional systems, such as the decimal, decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian Numerals, Babylonian numeral system, base 60, was the first positional sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
