Show that the function defined by is discontinuous at all integral points. Here denotes the greatest integer less than or equal to

Solution: Here, for any real number, ,

The fractional part or decimal part of is denoted by .

For example let us consider,

The function defined by is called the fractional part function.

The domain of the fractional part function is the set of all real numbers, and is the range of the set.

As a result, given function is discontinuous function.