Define a Function as a Set of Ordered Pairs

Solution

A function is a special type of relation represented as a set of ordered pairs.

A function from a set $A$ to a set $B$ is a set of ordered pairs $ (x, y) $ such that:

• Each element of set $A$ has exactly one image in set $B$.
• No element of $A$ is associated with more than one element of $B$.

Thus, a function can be written as:

$$ f = \{(x,y) : x \in A,\ y \in B\} $$

where every element of the domain has a unique corresponding element in the codomain.