Here is a function with strange continuity properties: f (x) = 1 q if x is the rational
Chapter 2, Problem 35(choose chapter or problem)
Here is a function with strange continuity properties: f (x) = 1 q if x is the rational number p/q in lowest terms 0 if x is an irrational number (a) Show that f is discontinuous at c if c is rational. Hint: There exist irrational numbers arbitrarily close to c. (b) Show that f is continuous at c if c is irrational. Hint: Let I be the interval {x : |x c| < 1}. Show that for any Q > 0, I contains at most finitely many fractions p/q with q
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer