The floor function, denoted as $$\lfloor x \rfloor$$, represents the largest integer that is not greater than a given value $x$. This function is also referred to as the integral part or integer part of $x$. It can be formally defined using a set equation that identifies the maximum integer $m$ such that $m$ is less than or equal to $x$. Understanding the floor function is essential in various mathematical applications, particularly in discrete mathematics and computer science. The floor function plays a crucial role in rounding down real numbers to their nearest integers.