Define a Function as a Correspondence Between Two Sets

Solution

A function is a rule or correspondence between two sets that assigns each element of one set to exactly one element of another set.

If $A$ and $B$ are two non-empty sets, then a function $f$ from $A$ to $B$ is a correspondence which associates every element of set $A$ with one and only one element of set $B$.

Symbolically, we write:

$$ f : A \to B $$

where:

• $A$ is called the domain of the function.
• $B$ is called the codomain of the function.
• The element associated with $x \in A$ is called the image of $x$.