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(2): Possible solution?
by Ken Haley)
This is a truly wonderful solution that I hadn't anticipated. Congratulations!!! Maybe you want to try something more difficult now:
Can you construct a function with the required properties which has exactly the jump discontinuities p^(-2) where p is a prime number?
Edited on August 24, 2006, 6:06 pm
Posted by JLo
on 2006-08-24 18:00:36