Discontinuous and continuous functions

Carla1985

Active member
I need to find a function that is continuous at 0 but discontinuous at every other point. IV been stuck on this for hours now thankyou

Klaas van Aarsen

MHB Seeker
Staff member
Re: discontinuous and continuous functions

I need to find a function that is continuous at 0 but discontinuous at every other point. IV been stuck on this for hours now thankyou
Hey Carla!

How about:
f(x) = \left\{\begin{aligned} x & \text{ if } x \in \mathbb Q \\ -x & \text{ if } x \in \mathbb R \backslash \mathbb Q \end{aligned}\right.

ZaidAlyafey

Well-known member
MHB Math Helper
I need to find a function that is continuous at 0 but discontinuous at every other point. IV been stuck on this for hours now thankyou
Continuous at just one point ! , then how does the limit exist ?

Carla1985

Active member
Not a clue. I don't get it at all. The exact wording of a question, just in case iv got it wrong is: "give an example of a function defined on R which is continuous at x=0 and discontinuous at every other point of R". I like Serena, thank you

Staff member