Definition:Ceiling Function

Let $$x \in \R$$.

Then $$\left \lceil {x} \right \rceil$$ is defined as:
 * $$\left \lceil {\cdot} \right \rceil: \R \to \Z: \left \lceil {x} \right \rceil = \inf \left({\left\{{m \in \Z: m \ge x}\right\}}\right)$$

That is, $$\left \lceil {x} \right \rceil$$ is the smallest integer greater than or equal to $$x$$.