Process defined by an explicit rule that, based on given elements of sets that are perfectly defined, can be used to obtain new elements.

A numerical operation may be defined by a set of ordered pairs of the form ((*a*, *b*), *c*) where *a* and *b* are the operands that belong to a set of numbers called the *set of departure* and *c* is the result of the operation belonging to a set of numbers called the *set of destination*, or set of images or set of results.

Addition and multiplication of whole numbers are operations.

The term “operation” is sometimes used in a broader sense to refer to the internal composition law in a set.

### Examples

- Consider the operation T defined on the set of whole numbers W and written as ¤, such that, for all the numbers
*x*and*y*of W,*x*¤*y*is associated with the whole number*z*such that*z*= 2*x*+ 5*y*. Therefore 1 ¤ 2 = 12, 2 ¤ 3 = 19, and so on. - The operation T may be represented in roster form as follows : T = {((1, 2), 12), ((2, 3), 19), …}.
- The operation T may be represented in set-builder notation as follows : \(\textrm{T} = \lbrace \left( \left( x,y\right) , z\right) \in \left( \mathbb{N} \times \mathbb{N} \right) \times \mathbb{N}\space \vert\ z=2x+5y\rbrace\).