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 re(3): Oops... Maybe another hint?
by Ken Haley)
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