\begin{definition}[Definition:Continued Fraction/Simple/Finite]
Let $\R$ be the field of real numbers.
Let $n\geq 0$ be a natural number.
A '''simple finite continued fraction of length $n$''' is a finite continued fraction in $\R$ of length $n$ whose partial quotients are integers that are strictly positive, except perhaps the first.
That is, it is a finite sequence $a : \left[0 \,.\,.\, n\right] \to \Z$ with $a_n > 0$ for $n >0$.
\end{definition}