# Thread: continuity

1. ## continuity

Is there a function f : R->R having the irrational numbers as the set of its discontinuities?

2. ## Re: continuity

This Wikipedia page talks about this.

3. ## Re: continuity

thomae's function is discontinuous at rational points also. I want to know " Is there a function f : R->R having the irrational numbers as the set of its discontinuities only "

4. ## Re: continuity

Originally Posted by swarna
I want to know " Is there a function f : R->R having the irrational numbers as the set of its discontinuities only "
I specifically linked to the section of the page that discusses this question.

thank you

6. ## Re: continuity

I think you search on google.