\begin{definition}[Definition:Continued Fraction/Simple/Infinite]
Let $\R$ be the field of real numbers.
A '''simple infinite continued fraction''' is a infinite continued fraction in $\R$ whose partial quotients are integers that are strictly positive, except perhaps the first.
That is, it is a sequence $a : \N_{\geq 0} \to \Z$ with $a_n > 0$ for $n >0$.
\end{definition}