# Definition:Length of Continued Fraction

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