Definition:Ceiling Function/Definition 2

Definition
Let $x \in \R$ be a real number.

The ceiling function of $x$, denoted $\left\lceil x\right\rceil$, is defined as the smallest element of the set of integers:
 * $\left\{{m \in \Z: m \ge x}\right\}$

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

Also see

 * Set of Integers Bounded Below by Real Number has Smallest Element
 * Smallest Element is Unique
 * Equivalence of Definitions of Ceiling Function