perplexus.info :: Calculus : Weird function challenge

Weird function challenge (Posted on 2006-08-15)

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: Function	Steve Herman	2015-12-21 20:21:01
re: Function	Steve Herman	2015-12-21 20:21:01
Function	Math Man	2015-12-21 19:52:59
Nice work all, especially Ken	Steve Herman	2006-08-27 17:57:19
Yet another solution	vswitchs	2006-08-25 18:06:37
re(2): Nice solution!!! Now, you Want to try this	JLo	2006-08-25 11:31:07
re: Nice solution!!! Now, you Want to try this	Ken Haley	2006-08-25 01:02:30
re: Nice solution!!! Now, you Want to try this	Steve Herman	2006-08-24 23:00:08
Nice solution!!! Now, you Want to try this	JLo	2006-08-24 18:00:36
re(2): Possible solution?	Ken Haley	2006-08-23 23:17:55
re: Possible solution?	Steve Herman	2006-08-22 10:22:27
Possible solution?	Ken Haley	2006-08-22 00:44:13
re(4): Oops... Maybe another hint?	Ken Haley	2006-08-22 00:22:12
re(3): Oops... Maybe another hint?	Steve Herman	2006-08-21 12:50:07
re(5): Oops... Oops myself...	Ken Haley	2006-08-20 23:54:30
re(4): Oops... Oops myself...	JLo	2006-08-20 14:18:06
re(3): Oops... Maybe another hint?	Ken Haley	2006-08-20 11:53:26
re(2): Oops... Maybe another hint?	JLo	2006-08-20 10:42:45
re(2): Oops...	Ken Haley	2006-08-20 09:15:10
re: Oops...	Steve Herman	2006-08-20 08:44:19
Oops...	Ken Haley	2006-08-20 00:39:50
re: Needless to say this is very confusing	Steve Herman	2006-08-19 18:34:11
Needless to say this is very confusing	Charlie	2006-08-19 16:44:09
re(3): Bigger hint (and proposed problem redefinition)	Steve Herman	2006-08-19 12:35:47
re(2): Bigger hint (and proposed problem redefinition)	Ken Haley	2006-08-19 10:04:18
re: Bigger hint (and proposed problem redefinition)	Steve Herman	2006-08-19 08:24:30
Bigger hint	JLo	2006-08-18 18:36:17
re(3): Uncle! (1st condition satisfied)	Bractals	2006-08-18 11:25:20
re(2): Uncle! (1st condition satisfied)	Steve Herman	2006-08-18 10:32:52
re: Uncle! Don't give up yet!	JLo	2006-08-16 17:34:05
re: Uncle!	Bractals	2006-08-16 11:42:33
Uncle!	Steve Herman	2006-08-16 09:10:37
Awe and quibbles	Steve Herman	2006-08-15 10:02:07

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