Definition:Floor Function/Definition 1

Definition
Let $x$ be a real number.

The floor function of $x$ is the supremum:
 * $\left \lfloor {x} \right \rfloor = \sup \left({\left\{{m \in \Z: m \le x}\right\}}\right)$

Also see

 * Continuum Property
 * Supremum is Unique
 * Equivalence of Definitions of Floor Function