# 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 $x$:

$\ceiling x := \inf \set {m \in \Z: m \ge x}$

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

## Also see

Theorems used in this definition:

## 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