\begin{definition}[Definition:Rational Function]
Let $F$ be a field.
Let $P: F \to F$ and $Q: F \to F$ be polynomial functions on $F$.
Let $S$ be the set $F$ from which all the roots of $Q$ have been removed.
That is:
:$S = F \setminus \set {x \in F: \map Q x = 0}$
Then the equation $y = \dfrac {\map P x} {\map Q x}$ defines a mapping from $S$ to $F$.
Such a mapping is called a '''rational function'''.
The concept is usually encountered where the polynomial functions $P$ and $Q$ are either real or complex:
\end{definition}