Real Number minus Floor

Theorem
Let $x \in \R$ be any real number.

Then:
 * $x - \left \lfloor {x} \right \rfloor \in \left[{0 \,.\,.\, 1}\right)$

where $\left \lfloor {x} \right \rfloor$ is the floor of $x$.

That is:
 * $0 \le x - \left \lfloor {x} \right \rfloor < 1$

Also denoted as
The expression $x - \left \lfloor {x} \right \rfloor$ is sometimes denoted $\left\{{x}\right\}$ and called the fractional part of $x$.

Also see

 * Definition:Fractional Part
 * Definition:Modulo 1: $x \bmod 1 = x - \left \lfloor {x} \right \rfloor$