Definition 5.26 (Function)

Let $A$ and $B$ be nonempty 5.1 Sets. A $\text{function }f\text{ from }A\text{ to }B$ is an assignment of exactly one element of $B$ to each element of $A$

We write $f(A)=b$ if $b$ is the unique element of $B$ assigned by the function $f$ to the element $a$ of $A$

If $f$ is a function from $A$ to $B$, we write $f:A\to B$

$\text{Functions are sometimes called }\text{‘}\text{mappings}\text{’}\text{ or }\text{‘}\text{transformations}\text{’}$