The period of the function f(x)=1, when x is a rational 0, when x is irrational  is

For every rational number T, we havef(T+x)=1, when x is a rational 0, when x is irrational =f(x) but there is no least positive value of T for which f (T + x) = f (x) because there are infinite number of rational numbers between any two rational numbers. Therefore, f (x) is a periodic function having no fundamental period.