Fro any real number x, we denote [x], the greatest integer less than or equal to x.

Example: [2.45] = 2, [-2.1] = -3, [1.75] = 1, [0.32] = 0, etc.

The function f defined by f(x) = [x] for all x ∈ R, is called the greatest integere function.

So, the domain of the greatest integer function is the set R of all real numbers

and the range is the set of all integers as it attains only integer values.

The graph of the greatest integer function is shown in the given figure: