Definition:Floor Function/Definition 1

Definition
Let $x$ be a real number.

The floor function of $x$ is defined as the supremum of the set of integers no greater than $x$:
 * $\left \lfloor {x} \right \rfloor := \sup \left({\left\{{m \in \Z: m \le x}\right\}}\right)$

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

Also see

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