# Definition:Ceiling Function/Definition 2

## Definition

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

The ceiling function of $x$, denoted $\ceiling x$, is defined as the smallest element of the set of integers:

$\set {m \in \Z: m \ge x}$

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

## Technical Note

The $\LaTeX$ code for $\ceiling {x}$ is \ceiling {x} .

When the argument is a single character, it is usual to omit the braces:

\ceiling x