# Floor

This is the integer round-down of a value, $LaTeX: x$:

$LaTeX: \mbox{Floor}(x) = \max \{z: z \in \mathbb{Z}, \; z \le x\}.$

Examples: $LaTeX: \mbox{Floor}(5)=5$, $LaTeX: \mbox{Floor}(4.999)=4$, $LaTeX: \mbox{Floor}(-1.2) = -2$. Also, see ceiling.

# Ceiling

The integer round-up of a value, $LaTeX: x$:

$LaTeX: \mbox{Ceiling}(x) = \min \{ z : z \in \mathbb{Z}, \; z \ge x \}.

$

Examples: $LaTeX: \mbox{Ceiling}(5)=5$, $LaTeX: \mbox{Ceiling}(5.001)=6$, $LaTeX: \mbox{Ceiling}(-1.2) = -1$. Also, see floor.