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

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

$$[x]=\begin{cases} \lfloor x \rfloor \text{ if } x \ge 0 \\ \lceil x \rceil \text{ if } x<0, \end{cases}$$

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