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## operation

operation
1. A function from Sm (see Cartesian product) into S itself, where S is some set specific to the function. Such a function is usually referred to as an m-ary or m-adic operation over S, m being some natural number, sometimes referred to as the arity of the operation. The most common operations are the dyadic (or binary) operations that map S × S into S and the monadic (or unary) operations that map S into S. The case where the arity is zero gives the so-called nullary operations, which correspond simply to elements of S. There is also a more general kind of operation that involves more than one set. For example, in a finite-state automaton the next state depends on the current input symbol and the current state, and is thus given by a dyadic operation from I × Q into Q, where I is the set of input symbols and Q the set of states. See also logic operation, arithmetic operation, operations on sets.

2. Another name for instruction (in a computer), as designated by an operation code.

3. In a programming language. Whatever is carried out by an operator (def. 2), or, more generally, anything that can take place within a program: a declaration, an assignment, a selection, a loop, the call of a function, and so on.

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## operation

op·er·a·tion / ˌäpəˈrāshən/ • n. 1. the fact or condition of functioning or being active: the construction and operation of power stations some of these ideas could be put into operation. ∎  an active process; a discharge of a function: the operations of the mind. ∎  a business organization; a company: he reopened his operation under a different name. ∎  an activity in which such an organization is involved: the company is selling most of its commercial banking operations. 2. an act of surgery performed on a patient. 3. a piece of organized and concerted activity involving a number of people, esp. members of the armed forces or the police: a rescue operation military operations. ∎  (Operation) preceding a code name for such an activity: Operation Desert Storm. 4. Math. a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.