# Definition:Floor Function/Definition 2

## Definition

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

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

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

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

## Technical Note

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

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

\floor x