In mathematics, Thomae's function is a function defined on positive real values such that:

• if n is irrational, f(n) = 0
• if m/n is rational where m and n are natural numbers and m and n have no common factors other than 1, f(m/n) = 1/n

This function is introduced by K. J. Thomae in the 18th century. It can be proved that the function is continuous only at irrational values in its domain.