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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: Nice solution!!! Now, you Want to try this | Comment 26 of 33 |
(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


  Posted by Steve Herman on 2006-08-24 23:00:08

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