# Help Me! Functions, limits and continuity

Hey guys,

Today I came across a question about the function $$f(x)$$, which takes the value $$x$$ when $$x \in Q$$ and the value $$1-x$$ when $$x \notin Q$$. Is this function continuous at any point?

I thought that $$f(x)$$ would be continuous at $$x=0.5$$ since the left and right hand limits seem to approach $$0.5$$ near $$x=0.5$$.

Am I correct? If so, why? If not, why?

Thanks!

Note by Raj Magesh
3 years, 3 months ago

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## Comments

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Do you know what is the delta epsilon definition of a limit?

Staff - 3 years, 3 months ago

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Thanks a lot! I went through the wiki and worked out the answer to my question. The epsilon-delta definition is broader than the one I learnt in school...

- 3 years, 3 months ago

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hi

- 2 years, 10 months ago

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Hey.

- 2 years, 9 months ago

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How are you

- 2 years, 9 months ago

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Great, you?

- 2 years, 9 months ago

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These are called drichlet functions and these are continuos when both equations are equal

- 3 years, 3 months ago

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