Real Number minus Floor

Theorem
$$\forall x \in \mathbb{R}: x - \left \lfloor {x} \right \rfloor \in \left[{0 \,. \, . \, 1}\right)$$

Notation
In older sources, the expression $$x - \left \lfloor {x} \right \rfloor$$ is sometimes denoted $$\left\{{x}\right\}$$ and called the fractional part of $$x$$.