Definition:Value of Continued Fraction

Informally, the value of a finite continued fraction is the number which results from calculating out the fractions.

Note that formally the continued fraction and its value are considered to be distinct; a continued fraction is its sequence of partial quotients.

However, this is a nicety of interpretation and may usually be ignored &mdash; $x = \left[{a_1, a_2, a_3, \ldots, a_n}\right]$ is often used to mean that $x$ is the value of the given continued fraction.

Definition
Let $F$ be a field, such as the field of real numbers $\R$.

Also denoted as
The value of a continued fraction $C$ can also be denoted $\operatorname{Val}(C)$.

Also see

 * Definition:Value of Generalized Continued Fraction
 * Simple Infinite Continued Fraction Converges to Irrational Number