The least integer function is discontinuous because its results are only integers, that is, there are no values other than integers. Its input (domain) is continuous but its range is limited to integers making a graph of the function look like an infinitely long flight of stairs as the function leaps from integer to integer. For one output value there are an infinite number of different inputs. For example, 0.1, 0.1234, sqrt(0.5), 0.5, 1/5, 4/5, etc., have a least integer value of 1, which is the ceiling for all values of x where 0<x<1.