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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: Uncle! | Comment 3 of 33 |
(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 2006-08-16 11:42:33
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