Definition:Ceiling Function

Let $$x \in \mathbb{R}$$. Then $$\left \lceil {x} \right \rceil$$ is defined as:

$$\left \lceil {} \right \rceil: \mathbb{R} \to \mathbb{Z}: \left \lceil {x} \right \rceil = \inf \left({\left\{{m \in \mathbb{Z}: m \ge x}\right\}}\right)$$

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