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Discontinuous and continuous functions

Carla1985

Member
Feb 14, 2013
93
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
Mar 5, 2012
8,884
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
Jan 17, 2013
1,667
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

Member
Feb 14, 2013
93
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 :)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,884