Definition:Length of Continued Fraction

Definition
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 $\left[0 \,.\,.\, n\right]$.

Also see

 * Definition:Length of Sequence