Definition:Floor Function/Definition 1

Definition
The floor function is denoted and defined as:


 * $\forall x \in \R: \left \lfloor {x} \right \rfloor = \sup \left({\left\{{m \in \Z: m \le x}\right\}}\right)$

That is, $\left \lfloor {x} \right \rfloor$ is the greatest integer less than or equal to $x$.

Also see

 * Continuum Property, which is used in this definition
 * Equivalence of Definitions of Floor Function
 * Set of Integers Bounded Above by Real Number has Greatest Element