Simple Infinite Continued Fraction is Uniquely Determined by Limit/Proof 1

Theorem

Let $\sequence {a_n}_{n \mathop \ge 0}$ and $\sequence {b_n}_{n \mathop \ge 0}$ be simple infinite continued fractions in $\R$.

Let $\sequence {a_n}_{n \mathop \ge 0}$ and $\sequence {b_n}_{n \mathop \ge 0}$ have the same limit.

Then they are equal.

Proof

Follows immediately from Continued Fraction Expansion of Limit of Simple Infinite Continued Fraction equals Expansion Itself.

$\blacksquare$