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
Uncle! by Steve Herman)
My problem is
Since every epsilon neighborhood of an irrational number contains a rational number, how can the function be continuous at the irrational numbers.

Posted by Bractals
on 20060816 11:42:33 