# Operation

## Operation

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 = 2x + 5y. 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 : $$\textrm{T} = \lbrace \left( \left( x,y\right) , z\right) \in \left( \mathbb{N} \times \mathbb{N} \right) \times \mathbb{N}\space \vert\ z=2x+5y\rbrace$$.