\begin{definition}[Definition:Rational-Valued Function]
Let $f: S \to T$ be a function.
Let $S_1 \subseteq S$ such that $f \left({S_1}\right) \subseteq \Q$.
Then $f$ is said to be '''rational-valued on $S_1$'''.
That is, $f$ is defined as rational-valued on $S_1$ iff the image of $S_1$ under $f$ lies entirely within the set of rational numbers $\Q$.
A '''rational-valued function''' is a function $f: S \to \Q$ whose codomain is the set of rational numbers $\Q$.
That is, $f$ is '''rational-valued''' {{iff}} it is rational-valued over its entire domain.
Category:Definitions/Rational Numbers
\end{definition}