This function is not continuous at any point in the reals, its limit does not exist for any point in the reals, and it cannot be integrated using Riemann's method. It is piece-wise-defined, assigning the value one to any rational number and the value zero to any irrational number. This function can be integrated using the Lebesgue method, demonstrating that that method is 
This function is not continuous at any point in the reals, its limit does not exist for any point in the reals, and it cannot be integrated using Riemann's method. It is piece-wise-defined, assigning the value one to any rational number and the value zero to any irrational number. This function can be integrated using the Lebesgue method, demonstrating that that method is more general than the Riemann integral. For ten points, name this function, named after a 19th century German mathematician.
This function is not continuous at any point in the reals, its limit does not exist for any point in the reals, and it cannot be integrated using Riemann's method.
{Dirichlet} function