Definition:Fractional Part

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

Let $$\left \lfloor {x}\right \rfloor$$ be the floor function of $$x$$.

Then the quantity $$x - \left \lfloor {x}\right \rfloor$$ is called the fractional part of $$x$$, and is frequently denoted:
 * $$\left\{{x}\right\} \ \stackrel {\mathbf {def}} {=\!=} \ x - \left \lfloor {x}\right \rfloor$$.

Beware, of course, not to get $$\left\{{x}\right\}$$ confused with the singleton set containing $$x$$.