\begin{definition}[Definition:Convergent of Continued Fraction]
Let $F$ be a field, such as the field of real numbers.
Let $n \in \N \cup \set \infty$ be an extended natural number.
Let $C = \sqbrk {a_0, a_1, a_2, \ldots}$ be a continued fraction in $F$ of length $n$.
Let $k \le n$ be a natural number.
\end{definition}