Collection: Thomae's Collection

Carl Johannes Thomae introduced a famous function in his 1875 textbook. It is an example of an integrable function which is continuous at every irrational number but discontinuous at every rational number. The function is defined to be 0 when x is irrational and 1/q when x is rational - where q is the denominator of x when expressed as a fraction in lowest terms. The function has an odd appearance when graphed, almost looking like stars hanging over the ancient city of Babylon. Or, if viewed upside down, it looks like raindrops. The design in this collection features Carl Thomae, standing within the city of Babylon, with an umbrella held up against a raging storm of rain in the pattern of his famous function.  

A graph of Thomae's function.