An example of nowhere continuous function on $\mathbb{R}$

Question

Is there any example of a function which is discontinuous on $\mathbb{R}$

Surely you are joking... – Michael Galuza Aug 04 '15 at 09:01 — Michael Galuza, Aug 04 '15 at 09:01
Do you mean nowhere continuous? – A.Γ. Aug 04 '15 at 09:04 — A.Γ., Aug 04 '15 at 09:04
Yes I mean nowhere continuous function on $\mathbb{R}$ – Ali Aug 04 '15 at 09:14 — Ali, Aug 04 '15 at 09:14

score 8 · Accepted Answer · answered Aug 04 '15 at 09:03

8

If you mean a function that is nowhere continuous on $\mathbb{R}$, you may consider the indicator function of $\mathbb{Q}$.

answered Aug 04 '15 at 09:03

Augustin

Thank you very much. That is a good example. I am looking for more answers. – Ali Aug 04 '15 at 09:05
I didn't know it had a name, but yes it seems to be the Dirichlet function. – Augustin Aug 04 '15 at 09:07

1 Answers1