integer part

The integer part of a real number is the part of the number that appears before the decimal . For example, the integer part of $\pi$ is $3$, and the integer part of $-\sqrt{2}$ is $-1$.

To be more precise, for $x\in ℝ$, the integer part of $x$, denoted as $[x]$, is given by

where $\lfloor x\rfloor$ and $\lceil x\rceil$ denote the floor and ceiling of $x$, respectively.