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Weird function challenge (Posted on 2006-08-15) Difficulty: 4 of 5
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.

See The Solution Submitted by JLo    
Rating: 4.3000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Nice solution!!! Now, you Want to try this | Comment 25 of 33 |
(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

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