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

Nice solution!!! Now, you Want to try this by JLo)

JLo:

1) What was your solution?

2) I don't understand this new question. Are you saying that in
your solution p^(-2) is the size of the each jump discontinuity?

Steve