\begin{definition}[Definition:Length of Continued Fraction]
Let $k$ be a field.
Let $C$ be a continued fraction in $k$, either finite or infinite.
The '''length''' of $C$ is an extended natural number equal to:
*$\infty$ if $C$ is an infinite continued fraction.
*$n$ if $C$ is a finite continued fraction with domain the integer interval $\left[0 \,.\,.\, n\right]$.
\end{definition}