Definition:Floor Function/Definition 2

Definition
Let $x \in \R$ be a real number.

The floor function of $x$, denoted $\left\lfloor{x}\right\rfloor$, is defined as the greatest element of the set of integers:
 * $\left\{ {m \in \Z: m \le x}\right\}$

where $\le$ is the usual ordering on the real numbers.

Also see

 * Set of Integers Bounded Above by Real Number has Greatest Element
 * Greatest Element is Unique
 * Equivalence of Definitions of Floor Function