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

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- June 7th 2013, 02:52 AMswarnacontinuity
Is there a function f : R->R having the irrational numbers as the set of its discontinuities?

- June 7th 2013, 04:42 AMemakarovRe: continuity
This Wikipedia page talks about this.

- June 7th 2013, 05:20 AMswarnaRe: 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 "

- June 7th 2013, 05:22 AMemakarovRe: continuity
- June 7th 2013, 05:34 AMswarnaRe: continuity
thank you

- June 9th 2013, 11:45 PMjacobpittRe: continuity
I think you search on google.