1. The problem statement, all variables and given/known data Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational numbers. Show that f is discontinuous at every x in R. 2. Relevant equations Definition of continuity. 3. The attempt at a solution I want to find a sequence (x_n) that converges to x_0 but that x_n is rational for even n, and irrational for odd n. This will show that (f(x_n)) cannot converge, since it will alternate between 0 and 1, and thus f is discontinuous. My problem is that I can't think of a sequence that does this! Thanks for any help.