Re: super difficult question!!

From: Robert B. Israel (israel_at_math.ubc.ca)
Date: 11/29/04 

Date: 28 Nov 2004 18:13:28 -0800

maverickcool@hotmail.com (maverick) wrote in message news:<e34aa842.0411281200.7c79f3f7@posting.google.com>...

> I'm looking for a continuous function f:R->R with discontinuity on
> irrational domain and continuous on Q.
> if u know the answer
> PLEASE send me....

If it's a continuous function it has no discontinuities!

Perhaps what you're looking for is a function f:R -> R which is continuous
at every rational and discontinuous at every irrational. Such a thing
doesn't exist, because of a theorem: the set of points where a function is
continuous forms a G_delta.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada