Riemann function is a special function, which was discovered and put forward by German mathematician Riemann. It is widely used in higher mathematics, and in many cases it can be used as a counterexample to verify some propositions to be proved in some functions. In some English references, Riemann function is also called Tomae function.

This function has an important application in calculus.

Riemannian function is defined on [0, 1],

R(x)= 1/q, when x = p/q (both p and q are positive integers, and p/q is the true fraction after reduction),

R(x)=0. When x = 0, 1 and (0, 1) are irrational numbers.