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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.)
re(4): Oops... Oops myself... | Comment 18 of 33 |
(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

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