Let f(x)f(x)f(x) be defined as 000 if x∈Qx \in \mathbb{Q}x∈Q and 111 if x∉Qx \notin \mathbb{Q}x∈/Q. Which is true?
fff is continuous everywhere.
fff is continuous only at x=0x=0x=0.
fff is discontinuous everywhere.
fff is monotone.