Ecco che cosa si trova in WikiPedia (versione inglese) sul concetto di operazione.  Vengono considerate "operazioni" particolari "funzioni",  ma, come si vede leggendo il testo, la definzione di operazione non è affatto standardizzata.

An operation ω is a function of the form ω: V→Y, where V ⊂ X1×…×Xk.

The sets Xk are called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k (the number of arguments) is called the type or arity of the operation. Thus a unary operation has arity one, and a binary operation has arity two. An operation of arity zero, called a nullary operation, is simply an element of the codomain Y. An operation of arity k is called a k-ary operation. Thus a k-ary operation is a (k+1)-ary relation that is functional on its first k domains.

The above describes what is usually called a finitary operation, referring to the finite number of arguments (the value k). There are obvious extensions where the arity is taken to be an infinite ordinal or cardinal, or even an arbitrary set indexing the arguments.

Often, use of the term operation implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain), although this is by no means universal, as in the example of multiplying a vector by a scalar.

In WolframAlpha viene considerato un concetto più restrittivo:

Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number α, a function F from A^α into A is an α-ary operation on A. If α = n is a finite ordinal, then the n-ary operation F is a finitary operation on A.