Consider two sets A and B. Any non-empty subset R of the cartesian product A × B is called a relation from A to B. A special type of relation associates each element of set A with the one and only element of B. This is indeed a refinement of the concept of relation. Such a refinement is known as a function. We may define a function in the following way:

A function from a set A to a set B is a relation (or rule) which associates each element of A with a unique element of B.

Symbolically, we write

f : A → B

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