Definition:Value of Continued Fraction/Infinite

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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