# operation

**operation** **1.** A function from *S ^{m}* (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.

# 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.

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