# 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
6 years ago

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## Comments

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

Staff - 6 years 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...

- 5 years, 12 months ago

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hi

- 5 years, 6 months ago

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Hey.

- 5 years, 6 months ago

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How are you

- 5 years, 6 months ago

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Great, you?

- 5 years, 6 months ago

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

- 6 years ago

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