Define a partial function $$f : \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}_{\geq 0}$$ as follows: $$f(x) = \frac{1}{x-\lfloor x \rfloor}$$
If I understand correctly, the numbers occuring in the continued fraction expansion of an irrational number $x \in \mathbb{R}_{\geq 0}$ can be expressed succinctly as
$$(\lfloor x \rfloor,\lfloor fx \rfloor,\lfloor ffx \rfloor, \lfloor fffx \rfloor,\ldots)$$
It would therefore be convenient if there were an accepted name or notation for this function.
Question. Is there?