Definition:Gauss Map

Definition
Let $\closedint 0 1$ denote the closed interval from $0$ to $1$.

Let:
 * $Y := \closedint 0 1 \setminus \Q$

that is, the irrationals between $0$ and $1$.

The Gauss map $T : Y \to Y$ is defined by:
 * $\map T x := \fractpart {\dfrac 1 x}$

where $\fractpart \cdot$ denotes the fractional part.

Also known as
It is also called continued fractional map.