The Notorious Jumping Function of Continuum County

Submitted by Deb from Rochester, NY, 2/26/2000. Original answer and this article by Allen Stenger.

Give an example of monotonic function on [0,1] which is discontinuous at all rationals.

Hint 1

Sneak up on it a few discontinuities at a time.

Need another hint? Click here.

Click here for the rest of the solution.