\begin{definition}[Definition:Continued Fraction/Infinite]
Let $F$ be a field, such as the field of real numbers $\R$.
Informally, an '''infinite continued fraction''' in $F$ is an expression of the form:
:$a_0 + \cfrac 1 {a_1 + \cfrac 1 {a_2 + \cfrac 1 {\ddots \cfrac {} {a_{n-1} + \cfrac 1 {a_n + \cfrac 1 {\ddots}}} }}}$
where $a_0, a_1, a_2, \ldots, a_n, \ldots \in F$.
Formally, an '''infinite continued fraction''' in $F$ is a sequence, called '''sequence of partial quotients''', whose domain is $\N_{\geq 0}$.
An infinite continued fraction should not be confused with its '''value''', when it exists.
\end{definition}