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Encyclopedia > Arity

In logic, mathematics, and computer science, the arity (synonyms include type, adicity, and rank) of a function or operation is the number of arguments or operands that the function takes. The arity of a relation is the number of domains in the corresponding Cartesian product. The term springs from such words as unary, binary, ternary, etc. Logic (from Classical Greek Î»ÏŒÎ³Î¿Ï‚ logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... In logic and mathematics, an operation Ï‰ is a function of the form Ï‰ : X1 Ã— â€¦ Ã— Xk â†’ Y. The sets Xj are the called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k is called the arity of the operation. ... In mathematics, an operand is one of the inputs (arguments) of an operator. ... In mathematics, the concept of a relation is a generalization of 2-place relations, such as the relation of equality, denoted by the sign = in a statement like 5 + 7 = 12, or the relation of order, denoted by the sign < in a statement like 5 < 12. Relations that involve two... In mathematics, the Cartesian product is a direct product of sets. ...

The term "arity" is primarily used with reference to operations. If f is the function f : Sn → S, where S is some set, then f is an operation and n is its arity. Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... In logic and mathematics, an operation Ï‰ is a function of the form Ï‰ : X1 Ã— â€¦ Ã— Xk â†’ Y. The sets Xj are the called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k is called the arity of the operation. ...

Arities greater than 2 are seldom encountered in mathematics, except in specialized areas, and arities greater than 3 are seldom encountered in theoretical computer science (although in practical computer programming, it is common to define functions with more than 3 arguments). For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Programming redirects here. ...

In linguistics, arity is sometimes called valency, not to be confused with valency in mathematics. For the journal, see Linguistics (journal). ... In linguistics, valency or valence refers to the capacity of a verb to take a specific number and type of arguments (noun phrase positions). ... In the mathematical field of graph theory the degree or valency of a vertex v is the number of edges incident to v (with loops being counted twice). ...

Examples

• A nullary function takes no arguments.
• A unary function takes one argument.
• A binary function takes two arguments.
• A ternary function takes three arguments.
• An n-ary function takes n arguments.

In mathematics, a unary operation is an operation with only one operand. ... In mathematics, a binary operation is a calculation involving two input quantities, in other words, an operation whose arity is two. ... In mathematics, a ternary operation is any operation of arity three, that is, that takes three arguments. ...

Nullary

Sometimes it is useful to consider a constant as an operation of arity 0, and hence call it nullary. In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ...

Also, in non-functional programming, a function without arguments can be meaningful (and not necessarily constant) due to side effects. Often, such functions have in fact some hidden input which might be global variables, including the whole state of the system (time, free memory, ...) The latter are important examples which usually also exist in "purely" functional programming languages. Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. ... In computer science, a function is said to produce a side effect if it modifies some state other than its return value. ... In computer programming, a global variable is a variable that is accessible in every scope. ... A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. ...

Unary

Examples of unary operators in mathematics and in programming include the unary minus and plus, the increment and decrement operators in C-style languages (not in logical languages), and the factorial, reciprocal, floor, ceiling, fractional part, sign, absolute value, complex conjugate, and norm functions in mathematics. The twos complement, address reference and the logical NOT operators are examples of unary operators in math and programming. In mathematics, a unary operation is an operation with only one operand. ... C is a general-purpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ... For factorial rings in mathematics, see unique factorisation domain. ... Look up reciprocal in Wiktionary, the free dictionary. ... The floor and fractional part functions In mathematics, the floor function of a real number x, denoted or floor(x), is the largest integer less than or equal to x (formally, ). For example, floor(2. ... In mathematics, the floor function is the function defined as follows: for a real number x, floor(x) is the largest integer less than or equal to x. ... In mathematics, the floor function is the function defined as follows: for a real number x, floor(x) is the largest integer less than or equal to x. ... For other uses, see Sign (disambiguation). ... In mathematics, the absolute value (or modulus) of a real number is its numerical value without regard to its sign. ... In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ... In linear algebra, functional analysis and related areas of mathematics, a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector. ... Twos complement is a method of signifying negative numbers in binary. ... This article is about a general notion of reference in computing. ... Negation, in its most basic sense, changes the truth value of a statement to its opposite. ...

Binary

Most operators encountered in programming are of the binary form. For both programming and mathematics these can be the multiplication operator, the addition operator, the division operator. Logical predicates such as OR, XOR, AND, IMP are typically used as binary operators with two distinct operands. In mathematics, a binary operation is a calculation involving two input quantities, in other words, an operation whose arity is two. ... In operator theory, a multiplication operator is a linear operator T defined on some vector space of functions and whose value at a function &#966; is given by multiplication by a fixed function f. ...

Ternary

From C, C++, C#, Java, Perl and variants comes the ternary operator ?:, which is a so-called conditional operator, taking three parameters. Forth also contains a ternary operator, */, which multiplies the first two (one-cell) numbers, dividing by the third, with the intermediate result being a double cell number. This is used when the intermediate result would overflow a single cell. C is a general-purpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ... C++ (pronounced see plus plus, IPA: ) is a general-purpose programming language with high-level and low-level capabilities. ... The title given to this article is incorrect due to technical limitations. ... â€œJava languageâ€ redirects here. ... Wikibooks has a book on the topic of Perl Programming Perl is a dynamic programming language created by Larry Wall and first released in 1987. ... In mathematics, a ternary operation is any operation of arity three, that is, that takes three arguments. ... ?: is a ternary operator that is part of the syntax for a basic conditional expression in several programming languages including C, Objective-C, C++, C#, D, Java, JavaScript, Linoleum, Perl, PHP, Tcl, and Ruby. ... Forth is a programming language and programming environment, initially developed by Charles H. Moore at the US National Radio Astronomy Observatory in the early 1970s. ...

n-ary

From a mathematical point of view, a function of n arguments can always be considered as a function of one single argument which is an element of some product space. However, it may be convenient for notation to consider n-ary functions, as for example multilinear maps (which are not linear maps on the product space, if n≠1). In topology, the cartesian product of topological spaces is turned into a topological space in the following way. ... In linear algebra, a multilinear map is a mathematical function of several vector variables that is linear in each variable. ...

The same is true for programming languages, where functions taking several arguments could always be defined as functions taking a single argument of some complex type or "structure". A struct is the C programming languages notion of a record, a datatype that aggregates a fixed set of labelled objects, possibly of different types, into a single object. ...

Other names

• Nullary means 0-ary.
• Unary means 1-ary.
• Binary means 2-ary.
• Ternary means 3-ary.
• Quaternary means 4-ary.
• Quinary means 5-ary.
• Sestary means 6-ary.
• Polyadic or multary (or multiary) means any number of operands (or parameters).
• n-ary means n operands (or parameters), but is often used as a synonym of "polyadic".

An alternative nomenclature is derived in a similar fashion from the corresponding Greek roots; for example, medadic, monadic, dyadic, triadic, polyadic, and so on. Thence derive the alternative terms adicity and adinity for the Latin-derived arity. In mathematics, a unary operation is an operation with only one operand. ... In mathematics, a binary operation is a calculation involving two input quantities, in other words, an operation whose arity is two. ... In mathematics, a ternary operation is any operation of arity three, that is, that takes three arguments. ...

These words are often used to describe anything related to that number (e.g., undenary chess is a chess variant with an 11×11 board, or the Millenary Petition of 1603). The Millenary Petition was a list of requests given to James I by Puritans in 1603 when he was on his way to claim the English throne. ...

Logic of relatives, short for logic of relative terms, is a term used to cover the study of relations in their logical, philosophical, or semiotic aspects, as distinguished from, though closely coordinated with, their more properly formal, mathematical, or objective aspects. ... In mathematics, a binary relation (or a dyadic relation) is an arbitrary association of elements of one set with elements of another (perhaps the same) set. ... In logic, mathematics, and semiotics, a triadic relation or a ternary relation is an important special case of a polyadic or finitary relation, one in which the number of places in the relation is three. ... The theory of relations treats the subject matter of relations in its combinatorial aspect, as distinguished from, though related to, its more properly logical study on one side and its more generally mathematical study on another. ... In mathematical logic, a signature describes the non-logical symbols of a formal language. ... In computer science, a variadic operator or function is one that can take a varying number of arguments; that is, its arity is not fixed. ... In linguistics, valency or valence refers to the capacity of a verb to take a specific number and type of arguments (noun phrase positions). ... Results from FactBites:

 IFF-FOL Language Grammar (1397 words) The arity of a tuple of terms is the union of the term arities. The arity of a conjunction is the union of the arities of the conjunct expressions. The arity of a negation is the arity of the expression being negated.
More results at FactBites »

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