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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: ( You must be logged in to post comments.)
  Subject Author Date
re: FunctionSteve Herman2015-12-21 20:21:01
re: FunctionSteve Herman2015-12-21 20:21:01
SolutionFunctionMath Man2015-12-21 19:52:59
Nice work all, especially KenSteve Herman2006-08-27 17:57:19
Yet another solutionvswitchs2006-08-25 18:06:37
re(2): Nice solution!!! Now, you Want to try thisJLo2006-08-25 11:31:07
re: Nice solution!!! Now, you Want to try thisKen Haley2006-08-25 01:02:30
re: Nice solution!!! Now, you Want to try thisSteve Herman2006-08-24 23:00:08
Nice solution!!! Now, you Want to try thisJLo2006-08-24 18:00:36
re(2): Possible solution?Ken Haley2006-08-23 23:17:55
re: Possible solution?Steve Herman2006-08-22 10:22:27
Some ThoughtsPossible solution?Ken Haley2006-08-22 00:44:13
re(4): Oops... Maybe another hint?Ken Haley2006-08-22 00:22:12
re(3): Oops... Maybe another hint?Steve Herman2006-08-21 12:50:07
re(5): Oops... Oops myself...Ken Haley2006-08-20 23:54:30
re(4): Oops... Oops myself...JLo2006-08-20 14:18:06
re(3): Oops... Maybe another hint?Ken Haley2006-08-20 11:53:26
Hints/Tipsre(2): Oops... Maybe another hint?JLo2006-08-20 10:42:45
re(2): Oops...Ken Haley2006-08-20 09:15:10
re: Oops...Steve Herman2006-08-20 08:44:19
Oops...Ken Haley2006-08-20 00:39:50
re: Needless to say this is very confusingSteve Herman2006-08-19 18:34:11
QuestionNeedless to say this is very confusingCharlie2006-08-19 16:44:09
re(3): Bigger hint (and proposed problem redefinition)Steve Herman2006-08-19 12:35:47
re(2): Bigger hint (and proposed problem redefinition)Ken Haley2006-08-19 10:04:18
re: Bigger hint (and proposed problem redefinition)Steve Herman2006-08-19 08:24:30
Hints/TipsBigger hintJLo2006-08-18 18:36:17
re(3): Uncle! (1st condition satisfied)Bractals2006-08-18 11:25:20
re(2): Uncle! (1st condition satisfied)Steve Herman2006-08-18 10:32:52
Hints/Tipsre: Uncle! Don't give up yet!JLo2006-08-16 17:34:05
re: Uncle!Bractals2006-08-16 11:42:33
Uncle!Steve Herman2006-08-16 09:10:37
Awe and quibblesSteve Herman2006-08-15 10:02:07
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