Find a function f:R->R (R the set of real numbers), such that
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.
(In reply to Oops...
by Ken Haley)
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