\begin{definition}[Definition:Complete Quotient]
Let $x$ be an irrational number.
The '''sequence of complete quotients''' is defined recursively by:
:$\alpha_0 = x$
:$\alpha_{n + 1} = \dfrac 1 {\fractpart {\alpha_n} }$
where $\fractpart {\, \cdot \,}$ denotes fractional part.
{{definition wanted|for a general continued fraction}}
\end{definition}