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- Thread starter Carla1985
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- Mar 5, 2012

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Hey Carla!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

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.$$

- Jan 17, 2013

- 1,667

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

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- Mar 5, 2012

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Consider the definition of the limit of a function, using $(\varepsilon, \delta)$-definitions.Continuous at just one point ! , then how does the limit exist ?

Combine it with the definition of a continuous function in a point.