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! In my last hint, when I mentioned "monotonic", I didn't mean "strictly monotonic". Shows that Steve had a point when he "quibbled" about my not-so-rigorous notation.

Posted by JLo on 2006-08-20 14:18:06