MHB Discontinuous and continuous functions

[Carla1985]

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

 

[I like Serena]

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

 

[alyafey22]

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]

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 :)

 

[I like Serena]

Continuous at just one point ! , then how does the limit exist ?

Consider the definition of the limit of a function, using $(\varepsilon, \delta)$-definitions.
Combine it with the definition of a continuous function in a point.