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Arities
Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In logic and philosophy, it is also called adicity and degree. In linguistics, it is usually named valency. Examples The term "arity" is rarely employed in everyday usage. For example, rather than saying "the arity of the addition operation is 2" or "addition is an operation of arity 2" one usually says "addition is a binary operation". In general, the naming of functions or operators with a given arity follows a convention similar to the one used for ''n''-based numeral systems such as binary and hexadecimal. One combines a Latin prefix with the -ary ending; for example: * A nullary function takes no arguments. ** Example: f()=2 * A unary function takes one argument. ** Example: f(x)=2x * A binary function takes two arguments. ** Example: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguistics is concerned with both the cognitive and social aspects of language. It is considered a scientific field as well as an academic discipline; it has been classified as a social science, natural science, cognitive science,Thagard, PaulCognitive Science, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.). or part of the humanities. Traditional areas of linguistic analysis correspond to phenomena found in human linguistic systems, such as syntax (rules governing the structure of sentences); semantics (meaning); morphology (structure of words); phonetics (speech sounds and equivalent gestures in sign languages); phonology (the abstract sound system of a particular language); and pragmatics (how social con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above example, '+' is the symbol for the operation called addition. The operand '3' is one of the inputs (quantities) followed by the addition operator, and the operand '6' is the other input necessary for the operation. The result of the operation is 9. (The number '9' is also called the sum of the augend 3 and the addend 6.) An operand, then, is also referred to as "one of the inputs (quantities) for an operation". Notation Expressions as operands Operands may be complex, and may consist of expressions also made up of operators with operands. :(3 + 5) \times 2 In the above expression '(3 + 5)' is the first operand for the multiplication operator and '2' the second. The operand '(3 + 5)' is an expression in itself, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Side Effect (computer Science)
In computer science, an operation, function or expression is said to have a side effect if it modifies some state variable value(s) outside its local environment, which is to say if it has any observable effect other than its primary effect of returning a value to the invoker of the operation. Example side effects include modifying a non-local variable, modifying a static local variable, modifying a mutable argument passed by reference, performing I/O or calling other functions with side-effects. In the presence of side effects, a program's behaviour may depend on history; that is, the order of evaluation matters. Understanding and debugging a function with side effects requires knowledge about the context and its possible histories. Side effects play an important role in the design and analysis of programming languages. The degree to which side effects are used depends on the programming paradigm. For example, imperative programming is commonly used to produce side effects, to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Variable
In computer programming, a global variable is a variable with global scope, meaning that it is visible (hence accessible) throughout the program, unless shadowed. The set of all global variables is known as the ''global environment'' or ''global state.'' In compiled languages, global variables are generally static variables, whose extent (lifetime) is the entire runtime of the program, though in interpreted languages (including command-line interpreters), global variables are generally dynamically allocated when declared, since they are not known ahead of time. In some languages, all variables are global, or global by default, while in most modern languages variables have limited scope, generally lexical scope, though global variables are often available by declaring a variable at the top level of the program. In other languages, however, global variables do not exist; these are generally modular programming languages that enforce a module structure, or class-based object-oriente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Operator
In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function , where is a set. The function is a unary operation on . Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial ), functional notation (e.g. or ), and superscripts (e.g. transpose ). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument. Examples Unary negative and positive As unary operations have only one operand they are evaluated before other operations containing them. Here is an example using negation: :3 − −2 Here, the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2 (or '−2' could be taken to mean the integer −2). Therefore, the expression is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument Of A Function
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example, the binary function f(x,y) = x^2 + y^2 has two arguments, x and y, in an ordered pair (x, y). The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the ''arity'' of the function. A function that takes a single argument as input, such as f(x) = x^2, is called a unary function. A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values. The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle. A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain parameters. The independent variables are mentioned in the list of arguments that the function takes, whereas the par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Successor Function
In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by ''S'', so ''S''(''n'') = ''n'' +1. For example, ''S''(1) = 2 and ''S''(2) = 3. The successor function is one of the basic components used to build a primitive recursive function. Successor operations are also known as zeration in the context of a zeroth hyperoperation: H0(''a'', ''b'') = 1 + ''b''. In this context, the extension of zeration is addition, which is defined as repeated succession. Overview The successor function is part of the formal language used to state the Peano axioms, which formalise the structure of the natural numbers. In this formalisation, the successor function is a primitive operation on the natural numbers, in terms of which the standard natural numbers and addition is defined. For example, 1 is defined to be ''S''(0), and addition on natural numbers is defined recursively by: : This can be used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant (mathematics)
In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value); as a noun, it has two different meanings: * A fixed and well-defined number or other non-changing mathematical object. The terms '' mathematical constant'' or '' physical constant'' are sometimes used to distinguish this meaning. * A function whose value remains unchanged (i.e., a constant function). Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question. For example, a general quadratic function is commonly written as: :a x^2 + b x + c\, , where , and are constants (or parameters), and a variable—a placeholder for the argument of the function being studied. A more explicit way to denote this function is :x\mapsto a x^2 + b x + c \, , which makes the function-argument status of (and by extension the constancy of , and ) clear. In this example , and are co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
