Let $S$ be the set of all points at which the function $f(x)=\left\{\begin{array}{ll}1, & x ext {

Question

Let $S$ be the set of all points at which the function $f(x)=\left\{\begin{array}{ll}1, & x 	ext { is rational } \ -1, & x 	ext { is irrational }\end{array}ight.$ is continuous. Then $S$ is equal to

Professor PC Thomas Classes · Answer

The function is Dirichlet's function, which is nowhere continuous. Set $S = \emptyset$.