1. f has a discontinuity in every rational number, but is continous everywhere else, and
2. f is monotonic: x<y → f(x)<f(y)

Note: Textbooks frequently present examples of functions that meet only the first condition; requiring monotonicity makes for a slightly more challenging problem.

Oops indeed!  I agree, Ken, that the function identified so far is continuous at 2/3, and that we do not have a solution.  I don't see a fix either. 

I'm waiting for another hint from JLo.

Or a solution, if there is one.  Even if there isn't a solution, this problem has cvertainly been challenging and educational!  I'm hoping that there is a solution, and that JLo has something else up his sleeve.

Posted by Steve Herman on 2006-08-20 08:44:19