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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(3): Uncle! (1st condition satisfied) | Comment 6 of 33 |
(In reply to re(2): Uncle! (1st condition satisfied) by Steve Herman)

Steve:

Your example for the first part looks good. Applying something like it to satisfy the second part appears to be more difficult.

Addition: F(0) needs to be defined, say F(0) = 1.

Edited on August 18, 2006, 1:21 pm
  Posted by Bractals on 2006-08-18 11:25:20

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