Definition:Ceiling Function/Definition 1

Definition
Let $x$ be a real number.

The ceiling function of $x$ is defined as the infimum of the set of integers no smaller than $x$:
 * $\ceiling x := \inf \set {m \in \Z: x \le m}$

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

Also see
Theorems used in this definition:
 * Continuum Property
 * Infimum is Unique
 * Equivalence of Definitions of Ceiling Function