Definition:Floor Function/Definition 3

Definition
For all $x \in \R$, the floor function $\left\lfloor{x}\right\rfloor$ is defined as:


 * $z = \left\lfloor{x}\right\rfloor \iff z \in \Z \land x \in \left\{ {y \in \R: z \le y < z + 1}\right\}$

That is, the floor function of $x$ is defined as the unique integer $\left\lfloor{x}\right\rfloor$ such that:
 * $\left\lfloor{x}\right\rfloor \le x < \left\lfloor{x}\right\rfloor + 1$

Also see

 * Equivalence of Definitions of Floor Function