Definition:Floor Function/Definition 1

Definition

Let $x$ be a real number.

The floor function of $x$ is defined as the supremum of the set of integers no greater than $x$:

$\floor x := \sup \set {m \in \Z: m \le x}$

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

Also see

• Continuum Property
• Supremum is Unique
• Equivalence of Definitions of Floor Function