Definition:Value of Continued Fraction/Infinite

Definition

Let $\struct {F, \norm {\,\cdot\,} }$ be a valued field.

Let $C = \sequence {a_n}_{n \mathop \ge 0}$ be a infinite continued fraction in $F$.

Let $C$ converge to $x \in F$:

Then $x$ is the value of $C$.

Also known as

The value of an infinite continued fraction is also known as its limit.

Also see

• Irrational Number is Limit of Unique Simple Infinite Continued Fraction