Is there a bijection between real numbers and continued fractions?

Question

It is known that there is a bijection between rational numbers and finite continued fractions, so every rational number is uniquelly identified by a finite continued fractions and vice versa. It is also known that for any irrational number, we can find an infinite continued fractions, but I don't have information is it a unique. If so, than we can conclude that there is a bijection between real numbers and continued fractions.

Answer 1

Only if the numerator of each such nested fraction is $1$. But if you're inquiring about generalized continued fractions, then the answer is obviously no.