Answer to Question #19141 in Real Analysis for Matthew Lind

Question

What are the points of continuity and the points of discontinuity of the following function? Justify your answer.
f(x) = x if x is rational.
f(x) = x^3 if x is irrational.

Answer 1

This function has no points of continuity, because for each neighborhood of any point x0 there exist both rational and irrational points.