Continuity is not what it seems. In 1875, the German mathematician Carl Johannes Thomae defined a function *P*(*x*) with the following extraordinary property:

*P*(*x*) is discontinuous if *x* is rational

*P*(*x*) is continuous if *x* is irrational.

A graph of this function on the interval (0,1) is shown below. Continue reading ‘The Popcorn Function’