Definition:Floor Function/Definition 3

Definition
Let $x$ be a real number.

The floor function of $x$ is 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

 * Real Number lies between Unique Pair of Consecutive Integers
 * Equivalence of Definitions of Floor Function