The floor of a real number \(x\text{,}\) denoted \(\lfloor x \rfloor\text{,}\) is the greatest integer less than or equal to \(x\text{.}\) The floor is also denoted \([x]\text{,}\) mostly in older texts. Related functions include:
\(\lceil x \rceil = \min \{ n \in \bbZ : n \geq x \}\text{,}\) the ceiling of \(x\)
\(\{x\} = x - \lfloor x \rfloor\text{,}\) the fractional part of \(x\)
